What is the evidence th7qf0xe ofn mj+f;/ln,at sound travels as a wave?

What is the evidence that sound is a form of energ5ckr(fj t)hy1 k t;9amy?

Children sometimes play with a homemade “telepdf7 wohh-z -h4hone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other. f--ohd4wh7 hz

When a sound wave passes from air into water, do hcw+0o6;b;:f fds21 l: pvdnefgf g9n you expect the frequency or wavelength to change?9;ndcfbep ff+gshn f: o62gv ;lwd01:

What evidence can you give that8mp gl.kltx6:xjqcx1: n: 9hj the speed of sound in air does not depend significantxpn l::xcmj1t:6 hl9 kqgjx8. ly on frequency?

The voice of a person who has inhaled hel/4 ldbph5z0 kcium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitc* n1qr 8pc6ycxh of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sounds:2d/e6p evgyho sd5 q: in vario6phyqog/5 ev:sedd : 2us frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spacexz0w q/2j 1oijd closer together as you move up the fingerboard towardw0zo2q ijx/j1 the bridge?

A noisy truck approaches you from behind a building. Initially y fga-9 k1;5q4g*szrb:7ml w m6ohzrtxou hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Ewqmm;zgas 1:6 kotr9lhgr-4 b7 5zxf*xplain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “ints9 /ws8h3 nqc tffu *gmi9vww0.+bq ro./wjn6erference in space,” whereas beats can be said to be due to “interferengjsqqo0f9wwwnif b/h/nw 8+.9.r u 3c* st6vmce in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wou7z) 0u :jk+clo havsb 1i9zm.uld the points D and C (where destructive and constructive interfers1i:k a uhz7b9+0o cjul) .mvzence occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in are vxfa v(q5l94jmhed7 bgo1;.f as with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the am(ej5.xl1q 4 g bmvf9hdfv7o; abient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shokg)j+sdbcp x.w j6d7mk6 ;. zcwn in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves. mjzdkcp.6 +wg 6kdc ;x7b)js, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shi 3zzaz5n-:-zwhm du 7tft if the source and observer move in the same direction, with the same velocit wz3:7h5 ztnuzaz-m-d y? Explain.

If a wind is blowing, will this alter the frequency ov,-srdqu)wu -f the sound heard by a person at rest with respect to the source? Is vdu-r -s,uq w)the wavelength or velocity changed?

Figure 12–32 shows vah g 6e,ux7f9drrious positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequenudr7 fhe6g 9x,cy for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shf2 z 4kthp-u6m y3p-yl dvi0e4out reflected by a cliff 6-h dyy4ue3fpl-k 0 mi4tv2 zpat the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the wate /.qohgemtfcs0 +. q8drline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawaocdtfhe 8g0m.+ ./sqqter is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavmcd.x wosj+x)s j)- )eelengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting juskw; -ku/akc )ct above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boatkcu ka-;)k cw/ 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top a.du )+/xcpc yof a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the cliff? y)ccd.u p x/+a   m

  A person, with his ear to the ground, sees a huge stone strike thexz .b f80s)xrc concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far acf)zs xr8x0.bway did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile nm u c2b(m90p9arsto.of distance by the “5-second rule” for estimating the distance from a lightn uc9nmp obrm(902ats. ing strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of iplro0 *uy0-vl0 e ff0rd26tf 4pipz) a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of 4oj. r;:1mluy iyaf) fa sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB whev23p gsml )qfm:so*1i n fired simultaneously at a certvss3 *: p1loqmgm 2f)iain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplaneds0 qvy (;wz e* 3inx4g*3vj ht0rny p+nr5hn; with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut tiv40;nw 3n0zhrgxjvyd5+s;y* r3pqeh( nn* down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to3( kc65i8fs gbxn.k4h z v. jzimhr38()qljr y have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and th gj lx48.vhkm(63 r (f8b5ysc) hni3j.zrk qize background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outpukn/nem..fbq dp-il;p: ,cj,x h46cb st of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreaq;:p lhmnde b/s,jnix.p-,4 ck cb f.6ds roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area is unwe:1iaz jkm22 8iw 1(hk 9ft$5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifii qa *mqy bntr7jv;j;,.k zz+0er B is rated at yt +j k 7;.nr,qmvqz bi0jz;*a40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in frontby.9vih9vo pri22bfcv57g z+ of a loudspibh2 5c v7p9.i2zrb+ oy v9gvfeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typica,)hz:6 f)dxlzt bcorf (ml.is4b dp +)lly detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levelf4zlc6( bd)rm+sb:.d,) o tz fpxilh)s differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave iz5/n a/8gouc is tripled, (a) by what factor will the intensity increase? Increase byizn/ gac 8uo/5 a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the olh/e6i;8/y1 k qo dxlfrequency of the other. What l i6 ;/8q/xehld1 okoyis the ratio of their intensities?   

  What would be the sound level fye)vjgh:/ (; xt( nik(in dB) of a sound wave in air that corresponds to a displacement a(:ke)t /n;ivj( ghfxymplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone tha9on442 lqk ebst has a 50-dB sound9sebq o l4k2n4 level? (See Fig. 12–6.)    dB

What are the lowest and hrnpaeu;itkorgv 0r )c 8429h).wz:c highest frequencies that an ear can detect when the sound level is 30 dBoicaw g .uczhv hr) tnre0p;9r)k8:24? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levelsfe5xzh;1:ix ebe,(c+(i acm l . What is the ratio of highest to lowest intensitc ech5l(a+1xi:;iz b,e efm (xy at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violiv rs6:za3widrxt-pc-, ;gr a;89 ppzhn has a fundamental frequency of 440 Hz. The length of the vibrating portion is 3gr dazv ;6px:9hprrts,-a-;83 w pzic2 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamenta(bfy x:px/ u2 xt9wh;pl and first three audible overtones if th(9:t/ ;hpfxxb w2pux ye pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency woul- 7 /xdoekvw6d0z yiqn:u/yw,d you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed dke7d/ / x0-o:z yqnwyi6vw,utube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes (lq )p5 hgcev*spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes )glp(c 5q*veh required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as itshp )el2.lewb) third harmonic. What will be its funda.lb eepl))2hwmental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tunyqdi /eps08.w ed to play E above middle C (33 ipd0/e.qys8 w0 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length onjnw(ed47:spmy;byih9q 57 zy u; y5wf an open organ pipe that emits middle C (262 Hz) when th7desu;y5; 9 yb5n z7 yp nmwj:hy(4iwqe temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune a3mu(j0ta y9dgnw 12 gxt 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 sh g.t.c+,d rjowould the hole be that must be uncovered to play D above middle C at 294 Hz+.gc,djw o .rt?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, andg y.z8h8me/qpvh* sx( 616 Hz, but not at any other frequencies in between. (a) 8/se.vh m pxz8 ygqh(*Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both+f 1,h2 czj mvwuj(8yn ends. It resonates at two successive harmonics of+nmwjhyvfju 2( ,z 8c1 frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 eli z-9npkv) zw c:8i3$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the au1; wvl:*(dtl2l ygevm dible range for a 2.14-m-long organ pipe;1emw l yd(:vl* gt2lv at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the :px 5g/syvu2(5tphbw8ux o )2by +zg woutside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the2+/:vu8phwyzwy2so x)bbx(u t p 5g 5g relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat ever ryku8fu9q m.6j fx1q,y 2.0 s when trying to adjust two strings, one ouxy9q8fqk, 6 u1.rjf mf which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and b f8k,l hokny 8eu,tk 2ak24a:$C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while anotheh t5vox0)ij ;lr (brand X) operates at hlo) t ;v5jix0an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded withg ((,b news+mpojkl/n0m4+ra a 350-Hz tuning fork and 9 beats/s whejn4+me((ma lkgs,o/ 0+rwbp n n sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same h-1 n- ianq e.lxqozi:z+ .)rifrequency, 294 Hz. The tension in one string is then decreased by 2.0%. Wh a1 inz.qq:lni r-i )x-.z+eohat will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical23e)0-liafqc hvoe2a flutes each try to play middle C (262 Hz), but oh2qal3- ev)2coe aif0ne is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning foce2gzyth l:z5s1k2 t1rks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are z1512sk2 z :ltgcyteh sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speak vwk),3xu84rp arb*jger and 3.50 m from tr)rg3j x8,w 4u*apbv khe other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed tnqf8fdd5 w gqe q:4h u3ug93k9js/q f1o be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they aqq /hfd8fjkqg9efwu 3913:4nu5gd sqre played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 auv rpn, .k3*rowg4k(atm: 7qm and 2.76 m in air. How many beats per second will b n rgro.pq*k mk, 4tv(ua:wa37e heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 puun g48 ;35lo*m oxfiHz when at rest. What freq ;mu gou8npix4lo*5 f3uency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whoswb+7jcn/ art6 -q0klhw 7n6uee siren emin + -t ek6u/haw0qrblwc6n77jts at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if aas3qut j8+jar,c,gi9koxet. j6d( e( 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the tc k, 8tj a 6(qj.s,ix(uo+edtagj93erwo frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the sasnpgus:5 yse22tvk9 6ye/e:obm x: m)me single frequency horn. When one is at rest and the othery/em2e9 u gs)ntv6:ss:y2p 5xb:omek is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out u 9cv xgsqd -sss9)h )xz4o+*bjltrasonic sound waves at 50.0 kHz and receives them returned from an object movivbd-gsx9s+4q scx )zj)o* sh9ng directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an m+ (u kx7.r)baljef*uultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the elf 7uu)x+* bmjkr.(areflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuxku7el +d5 uo 8a/l1qlc q4cd/ba was played on a moving flat train car at a frequency of 75 Hz, and cq4udo l8dl ac k5leu7+/ 1qx/a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to mea1 2kqeqa*tk hn0hp0vd*,p)fv u8j b 4qsure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the s hatqk 2*p,kn8 hvb) 0jdf1 veuq0p4*qound source?   Hz

  The Doppler effect using ultrasonic waves of freq)rc;3 gkbw+h ouency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity igxg-td h(*2rq p:4ycrn7b/y is 12 m/s from the north, what frequency will observer2-yqdtgry:g iph c4*nx(r b7/s hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its spb-3hz :;m fumveed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What i27sx -c 6(x;ev+j9ovxvc cpei s the angle the shock wave makes wit-x+v evj2c ;ov(6s c9ice pxx7h the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the3duvk va0u3p/0aok 7 kpcv/3n thin atmosphere of a planet where the speed of sound is only a3uak30 knvkdvv7uo3 /p0 apc/bout 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 me :f7+ st dn 7oe (u)e0ptjdye(6,tuwb/s strikes the ocean. Determine the shock wave angle idtbwj fts+ pe6 7o0(d7 :u)ue t,nee(yt produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle ,)hejrlob v+su:4x (x$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the grounp1qsn: ,f,m ihd flying faster than the speed of sound. By the time you hear the sonic boom, the plane has travel,:1,qf pmsi nhed a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonavoifj3-;vk// l r7qzvs6i i4.dxq)vyr device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the fl v)-;k37osz/ /i.v4 rqy6d iviqjvxmaximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are tl g u7vt:,mge6here in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists z /,a 3ncnx)qn(y-k uzof many plastic pipes of/z 3- ,qyz(nxc nna)ku various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a peru2fs,s58 pul:sizde) ug2 g +cson makes a sound close to the threshold of human hearing (0 dB). What will be thezsgd: ges)p5 i,usf u82 2c+lu sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dBj p *m7ytrc zf-b18./ rwqelx+ sound are heardxwt mjr8cy/1r.qp*-f7 b el+z simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 1xnfe,psy/( ldv 9ks*,05 dB. What is the acoustic power output (W) of the speaker, assum,sn*d9y/ f,v(x kpseling it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 k.2-id-e2v mu/aop7shex ( s,t0inyn Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15i-n(ex,a-mu ksh etdn/27osyv.2 p i0 kHz?    dB

  Workers around jet aircraft typically wear protective devices oversf 3fz1+r l++nu 6uuf+*dvzxp their ears. Assume tfxpn 6uffursu +1 z++lv+3d*zhat the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications system9a*p7n-o/ iauo iba f:s, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tunedb +25,rx6avvsw-efo o to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm lotp9oag39 a; hvng between fixed points with a fundamental frequency of 440 Hz and a mass pa9v h;g9a3otper unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube fill1x3 cp,dy8m6jr +.xhtordq)znr n,4v ed with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, thpz 4 njy1ox.rmvd)t,r3x 8+,nh6rc d qe air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one i)me-twi1)nxq-w 1 af end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamentaqntiwwe- f1) -mix)1a l mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate a8g0s9i l1jfhas one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from tw1vue7,g ,ksm/b2kwrw o sources. The sound is loudest at points equidistant from the two sources. To determine k1,kvbrg msw,/72 uew exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train i0ubghzz)ov+/ 5s q(pqs stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving p ub) o0q( /+gzqhzvs5train?   m/s

  The frequency of a steam ; ,a t vkqdb20xe*5rsqtrain whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant xr sqq,k *etab5;0 dv2velocity)?    m/s

  At a race track, you can et:/8 anh uh 5zkt/l)l pliurw82gx-s5stimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes u/lt)2wiu5 5plt8gsnx/ r8 kh-a : zhlby on the straightaway. How fast is it going?    m/s

  Two open organ pipes, soundi9*;*akz fjf5d . usbging together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How j ;sadfb*u.zk5i9g*f long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pastezq o :v4, my62jyzg5h a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have jh4y:e5 6g2zqv m,yozidentical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow kz;hz hl4.p,kc yh9h7in the aorta is normally about 0.32 m/s what beat freque4 pzhlyh ;z7kh kh.,9cncy would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s whil vcgjy*5zaz1se+w,: te the moth is flying toward the bat at speed 5az*+v:jy1eczgt,s w 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency soun9y/zwz me4 i s:zm* 7-kcyhj-cd pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and eamc9wkz-:e7z y/*hjyc4 ms zi -ch is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send sid9q as m, gs/*xzkfs:4bky14mgnals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Mods/bfam,gkqk sd4s*:y mx1 49zel as an open tube.

  Room acoustics for stereo listenib y y6*q)) nee,vgu8wao5bj p+ng can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pr8nbw6oee5ubp)g *yja+ ,yvq )essure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender alumin/y nv6bbt/ u cm;(xxd/um rod held in the hand near the rod’s midpoint/v/b/n bx yc;6t mud(x. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing f:a j.pj;rfl)ror the human ear at a frequency of about jja;l.p)r r:f1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. Any 6ngf y/q gm;4z,i,td observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s alt,g4/f ,yngqz dmt y;i6itude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1aw )11ni-tfev 5 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h