What is the evidence that sox4(9xc 4bh+m-k *mts dl9gfbc2g e5stund travels as a wave?

What is the evidence that sound is a form of eec-*plo;gr234nc 5i :k c txbknergy?

Children sometimes play with a homemade “telephone” by attaching a 7g, .mmptl rt7string to the 7rt,7tm pm.glbottoms 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.

When a sound wave passes from air into water, do you expect the freque4k7-rl uriwl f2: tlmg3ot5h,u5 lrp2ncy or wavelengw-rml u lf,rt5 po2 7l4ikgt: rhl2u35th to change?

What evidence can you give that the speed of sound in air does not depv.phht km2 h58 mzof*w*lm)3zend significantly zvpow 3h2hktm l*.f*mzm)h58on frequency?

The voice of a person w*tg 9+ozis cj 1/.hlg+uia0mr ho has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pqx-y :0sue1d ,reaz ,c8e;k,pw+zo qtitch of organ pipes?

Explain how a tube might be used as a filterqjbg8h+86 p(+r yqt+5x jacuy to reduce the amplitude of sounds in various frequency ranges. (An exampl+u gjcjb+(q8yx68qprth + ay5e is a car muffler.)

Why are the frets on a7i;jyfj3nu r4 guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toj3r4j 7 y;niufward the bridge?

A noisy truck approaches yo: 278 ggw kgo;ar0uqh* acftk(u from behind a building. Initially you hear it but cannot see it. When it emergr 8w:gqo *gkgt fk2(ua7a;0hces and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in sboh -wfj 9 6i0aeofjp:mm 09j1pace,” whereas beats can be said0jpm1if ohf-9bmw a:o6j 9je0 to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency otg) ar-8 ;ko- a6;llhxop7 eimf the speakers were lowered, would the points D and C (where destructive and constructivgik xa7;lomepo a8-l-;t6r h) e interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peo siidug6ps)ktt3gr z6 95d,j3 ple who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, ht)j tp 6,gd3zsku35isd6 i9r geadphones are worn that do not block the ambient 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 shown in Fig. 12–31. Each wave can be thoucgtt+jc1)q + aght of as a superposition of two sound waves with slightly different freqcg +t+)qtac j1uencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sourvmwtb,j auw2 t8j x880ce and observer move in the same direction, with the same vjwm8xj 2, vtb 08t8wuaelocity? Explain.

If a wind is blowing, will this alter the frequence9fhkmc 0;g;vy of the sound heard by a person at rest with respec9kmefv cg;h0; t to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swin*aa l3i ue)0i3llo8 rrg. 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 frequency for the sound of the whistle? Explain l3aioer*u 083ll)ia r your reasoning.

  A hiker determines the length of a lake by listeni30lp-9s 5nxjq orzw3 dng for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate thes5wdzj l3x pnor-30q9 length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below 3y1rc ),kq e mu 0;tanmdmftl),miy5 .a s)1ejthe waterline. He hears the echo of the sound reflected from the ocean floed0l ;a,c.jm)1q)3mimk 5y,tsn ty emr) 1uf aor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air ax )nbll)p sg4m( 4 5ltydj:7rxt 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 just above a school of tu7owmufo r- o7 ms9ql47na on a foggy day. Without warning, an engine backfire occurs on a7or7 s 47o 9wufomq-lmnother boat 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 of a clify jtx.q-cc dsjz)k893f. The splash it makes when striking the water below is heard stxdqk9jjz)c3y c-8.3.5 s later. How high is the cliff?    m

  A person, with his ear i pd71y3cpmjfq q*2o;* *hyszto the ground, sees a huge stone strike the concrete pave3q f***j7m;q2ihpy1 sc yzo pdment. 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 away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance bben/f/zit q7 s8*cx;. tnxc z1y the “5-second rule” for estimaxq *nt/;cc ze81zi n/.sb7xtf ting the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soun.vwfk1jw k0e19ewkjr 8 64yoh d 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 a sound whoc-k1r g0e5 5,czhujiutjqgrhw :0.x 7wy c13cse intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously atz6jaqe :c y3 yamm3yj9.dl4/s a certain place, what will be the sound level if only one is exploded?.y4mc q:y a9/ljz3yme sdj 36a [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance fv p7i0d1 q +mdbulrk3k;: f9lurom an airplane 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 down all iqpl10kmvfr73: ;9 lukd+ bud but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-nowippt 8q7gws-*33 xc mise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensitieqs37wg* ppi m3w-tc8xs of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in *st :g4w2oave yh4sw; q hr;/wnormal conversation.w*:qh/yrwa w 4g;e4hvs2s ;to Use Table 12–2. Assume the sound spreads 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 eardlx+nl-i.. cw5s r0folh/9+se e 3dbnirum whose area is $5 \times10^{ -5} m^2$ (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 modes1enqo5rt6bj;g h)zx* t amplifier B is rated at 40 W. (a t) 5johrxebng;z1q*6) 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 w7qcyct:*aw bicvqv6u*p. xa u/8 tb, /hen placed 2.8 m in front of a loudspeaker onx ,t*viqqcc* w/u vy87.6 tcu aa/pbb: 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 typically detecp2)gm(oj suihy7w8q9 t a difference in sound level of 2.0 dB. What is the ratio of them (q8y )h9owj2igs7p u amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a soun*i)o(a 8d8 e(ozz snvod wave is tripled, (a) by what factor will the intensiov) oz*anie 8((8 zosdty increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twic *uzup* :vage*qaq:, pe the frequency of the other. What is the ratio of their intens ug,qzv: :up*apae** qities?   

  What would be the sound 8 1xf*svellz6level (in dB) of a sound wave in air that corresponds to a displacement amplitude of visz*fx86le1 lv brating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sou4vz5 ,csexm3 9 xvvtr/nd level to seem as loud as a 100-Hz tone that has a 50-dB sound leves txvv/34zrvm9x5c e ,l? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the e -6a)( wja spb )pwg2/dppxg7sound level is 30 apd jp7wg) p6 -pesw(xg2)b/adB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of xuf;mvg3yzz ,q8ko pl,d*+oj o3j4i* sound levels. What is the ratio of highest to lowesmjydv* ,ofxzp8okiql3+ j 3,o* u4z; gt intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental freqq (m+vd9vn cwhfm (1p2uency of 440 Hz. The length of the2m vp+9mchn dv(q(wf1 vibrating portion is 32 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 fundamesezo y:1u* ji.w3,uihntal and first three audible overto3u hi1zi yes:uj*w ,.ones if the 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 would y;itntc69u ,s4d5 eqo bou expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assu os65 ;et,diu9cqb4ntmed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build vz:2ru:e a4 sxa pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range oeav::zsr2 4xu f the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its t)-x *gedqj9p7d af d2lhird harmonic. What will be its fundamental 7dj qa9eddp-l2*f)x gfrequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 4vp(uv 5e ncy;zwm3- xm long and is tuned to play E above middle C (33ey 3 cwn4x5-v;upzvm( 0 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 lengthfcht.i57d d fsqsjx0 hx 9* )arlbpwrn.y93 21 of an open organ pipe that emits middle C (262 Hz) when the temperatureflpqird9xt*3 hcy. )7.s9awrjxf 1s 5d2n b0h 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 at 20 0l+8rqbjp ,j r$^{\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 should the hole b pok3/k. jngii9ihq1/e that must be uncovered to play D above middle C at 294 Hz? 3 iohiq g/.1k /pni9kj   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, and 6 me4cuvya.w;5eg y:y 116 Hz, but not at any other frequencies in between. (a) Show why this isgwa y;eevm.5y :4y1cu 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 ends. It resonates at two f ;9d2q8fpru be+6 dnksuccessive harmonics of frequenci 9r debun2fqd; 6f+8kpes 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 *q ,unex b8ou5$^{\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 d68tl0o/ v+ tz9us efqpresent within the audible range for a 2.14-m-long organ pip0d qvu8e 9tt6loz+s f/e 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 o:g dfza273:om,rmwwg) b, qillqp -k ;pen to the outside 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 the relationship of your answer to the infogdplbmr:,72q)w omg: w- ,fk; l ia3qzrmation in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every52flno0 )b djq 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off f2q0 5djob)lnin frequency is the other string? ±    Hz

  What is the beat freq s 7*q2,4xq xfnh0fgnh5cjt+ cuency if middle C (262 Hz) and $C^＃$ (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.i3thiss i1ti 4vwkwxpq- m)jt5r 25 kHz, while another (brand X) operates at an unknown frequency. If neither whim i iw2 )-srq)k5p.x4w jhtsttv 531iistle 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 6kdhn-j) rjvkp+5znztt 5m03 sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355knt3m5jz-) 6n+jrhvpz5t 0 dk-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to th1ajh us;e -ws,mp+kj7e same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11 s+ 7e-kampwj j,uh1s;–13.]    Hz

  How many beats will be;x;aakcjs(bk- n ,t9w heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the ka-,skj;9wa tb;cxn(other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a f)rf3z6 gsd fq0requency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequenci 0sgd fr3fq6z)es 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 mh adva v.4/9w+3erj qf from one speaker and 3.50 +whj./favad 9vr3q4em from the 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 oksb2 i eqzr)ii+62xsu, 6vl2supposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequeni2 2 lix2k+vz6)b ,uq6 reissocy 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 wavelen)wt( 3te ;ysc zp-1uoogths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assuy;-1) ce3ps(wozott ume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a cer (67 tw+hingqjtain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a spe6+ntw7qhj( i ged of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do yoma.0-l5spmg f.g;zk3h,2i e db m1sr uu detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/ f-s.mm3ep; adgl, zmuhgib. ks 02r15s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you aux hn1g69c0o cc9dy;a e9jd ym 4:yvc*a2g5uet 15 m/s versus you moving toward it at 15 m/s Are the two fryc9y:99u45ao61 0cj2 dgcc *de v a;meughxynequencies 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 witijyu4 ji8 78quh the same single frequency horn. When one is at rest 7jiu8j4u8iq yand the other 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 ultras* mc*skgm;l) oonic sound waves at 50.0 kHz and receives them returned frog smm;l c)ok**m an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wyt wlx(m u-8mc-e-* q1hxyfp -all at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frex8q-cf1 u*l wp--my ymh-txe (quency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler exi7 ay wuj59nldvn7n5(,w yr+u periments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and 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 w+,95n yjv y uui5(wld7a7nnr speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasoun xv 2ajzfw,v0/d waves to measure blood-flow speeds. Suppose the device emits sound atwxzf,j vv2 /0a 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 sound source?   Hz

  The Doppler effect using ultrasrpybbs66r 24v 9wvr/aonic waves of frequency $2.25 \times10^{ 6}$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 vce +jqb 6hn9:+ 0lcwk7gyfd.rz6 pb1w elocity is 12 m/s from the north, what frequency will observers hear wh6cb6f g jqz+p yln:k7+db.hww1 rce90 o 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 landb.u 3ncr ;cq 8r5lylzp(;.ecfbe w7lul 0)5rn if its speed 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) Wet09 2 t2s,- wi 7pqkd2zcmdzphat is the angle the shock wave makes with the direction of th wd t-p92pt, 22mzk7sd e0qczie 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 the thin atmosphere of a planet wsyhbj9t ;,i 4lhere the speed of sound is only about 35 l jy, h;94btism/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 m/s strikes the ocean. Dete54 q)p-sewksd i4 cpz.rmine the shock wave angle it producekz5-d) 44piq scw.p ess
(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 e6e4lkd19 sjvd j;*sgz0wxp-$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and se 10m: oq3cnmawe a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontamc3 0m1o:qnwa l 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 sonar device that sends 20,000- /bq oc*fogdqu zc3 /pc5ld072Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh watouc3q2*dzop5l/cg cq0/fd b 7er)?    s

  Approximately how man,s+ ja52c f60q p.zvgkj utnd:y octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. Ik 6bzsav;gopk5-)d s8* .phyu t consists of many plastic pipe.zkdsvy ahp5buo8 ;-* 6g)skp s of 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 person makes a sound close to the thresholdnxu 6fj(j 5w y5wc*mv0 of human5w6 5cjvyf0 j(m nwu*x hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an wa2-fmf ) r*hjhbu*a1 87-dB sound are heard simultaneou) ar *au1 jh*2h-fbwmfsly?    dB

  The sound level 12.0 m from a loudspeaker, placu .sx6u whi+w4yi bb vcp78f2-ed in the open, is 105 dB. What is the acoustic power outpu7+f cxuuby- p .wi8s6iw4bh2vt (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The pldw06go2 :lm tower output drops by 10 dB at 15 kHz. What is the power outputm20t6:oll wgd in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protecty8ja. /ms5r uqive devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear hsjy r.m5q/a8u as 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 communicatioqff18wh2x- gm lhe5 s)ns systems, 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 tunyhxjcj9z8 2 ee jwi9d-+-v 0wned 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 long between x5:veu)sgic/ql0 ni/n 88ngbfixed points with a fundamental frequencyninbg 50g8n/:ul e8isv cq)x/ of 440 Hz and a mass per 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 vibratibf/1 hdc(n p6ton above a vertical open tube filled with water (Fig. 12–35). tp chbd1/nf6(The water level is allowed to drop slowly. As it does so, the 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 np,x o.:b2g s lx4xk,ud9vl (kis near a tube that is open at one end and also 75 cm long. How much tension should be in the string ibg(k,4 xxol9sp: un x 2kv.d,lf it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed 02vt8m hl 3o60q0m)dz :digsrt jeg z;to resonate as 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 tonth2xhu:h0i sw gd 7a).e in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine 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 oneh:t). au02 iwx7 hdgsh source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor wwr4p2vxxu4l(i.,hl pi .m)von the stationary train hears x,) wu4.xlipi4vmhw 2.(lpr va 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whisnl: wfp7tzvb 1 3pt9xxkme0u s)1*zt*tle as it approaches you is 538 Hz. After it passes you, its frequency is measu pxz fs1tt3x*0wb*7tmve 9z :nkpu)l1red as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estim vxbn(+r5sf rsk ;g1ijpy9 o0po,t v05ate 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 (frequen+v5;jv,nt p9s5 f gsbyroo(01ikp 0rxcy halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produ; k4i 45kd n z7o,ufpq*1bzxkuce a beat frequency of 11 Hz. The shor5qk, ndz kz14i47pu;* bofxku ter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car +.y; gohatix1 as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer wt+ig yo.ha1;xhen (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 in the aorta is normally as;ls,f+/brwc bout 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound; sc,rfs/ +lbw 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 mv 7 9 *vm00nyxpk)glzo/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detecxmok0vn z *p0lv9g7y) ted by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sounw(o- lmb4f+:9r u( vru;)nifqog d(cwd pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so tha4w+()orb (qwgl(:9vdim uf-fn r;o uct the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signal lf 2-tvzr*di6s 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.) Mod6rt 2-*f lvdizel as an open tube.

  Room acoustics for stereo lisyrome4w 9 o4f n+n-b9etening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing9o n9+we o4m rn4e-ybf waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, 0a3(ne7i*rkd 4wxk elv0v;05m okj qncalled “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, louervjd 4 vo03n7ki0 0 x5em(nw*lkakq;d, 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 for the human ear at a frequencmv rcnmcws z,rg pm m760+8(z3 iiq91qy of abou 6mr z1gw8i mq c3ivmrq c7z+s9nm0,(pt 1000 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 2.0bvvqm1 1g g.pr/t *vn-. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly ovnmv*/1vt.1-g gqpv rberhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedby3k5 2io4wp gqoat is 15 $^{\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