What is the evidence thd84(m;4msx, qw 8ax4jrvv xr eat sound travels as a wave?

What is the evidence that sound 7 fpcb9w-m r2fis a form of energy?

Children sometimes play with a homeng w 7qb0ac(b/:u 0lnwmade “telephone” by attaching a string to the bottoms ofb( ublwwnn:/agq0 c07 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 d:w b-bsq qb+ :r;u4sointo water, do you expect the frequency or wavelength t+bq:usrqb4 -b;w dso:o change?

What evidence can you give thatr59a:mrd e xw9 the speed of sound in air does not depend signifr5xamr:dwe99 icantly on frequency?

The voice of a person who has inhqj. 6k 8h4+;-gfnt5yxkdqxkd aled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of8s x jd36z+hgb organ pipes?

Explain how a tube might be used as a fi5dj1 tcofup-i:sb/ r,lter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muff td ip u,b-:rocs/f15jler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer xf95oxk ai*,ll ;l cy5together as you move up the fingerboard towal5lfl ,x* 9icoxy;k 5ard the bridge?

A noisy truck approaches you from behind a building. Initially you hear iryb6r h4c o5rg 1tn54xt but ca o55 hgxcrt6nr14b ry4nnot see it. When it emerges 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 du 6 zy eb6x2f/yes*.cjke to “interference in space,” whereas beats can be said to be duekfyebc 6.yxzje s6/*2 to “interference in time.” Explain.

In Fig. 12–16, if the frequenczd* adqdkx jg2.-)p2k y of the speakers were lowered, would the points D and C (where destru-pqdkz)a.kd xgj 2d2*ctive and constructive interference occur) move farther apart or closer together?

Traditional methods of protectin. n5cy lqz-m hf;,rd1v5 d1dlp6w lo.sg the hearing of people 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, headphones 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 nlf-yr51 6 ozl.s. ;qcvwlp5,dmh dd1 the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wh0a m i5x:s*fmave 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, (a) or (b), are the twoxim0h mas5:f* component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shif n *:lza-gi*ow m57yant if the source and observer move in the same direction, with the same velocity?wg a**on-5alm ziy:7n Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a yg1j 7 q45owygperson at restyy5j7 gwoq4 1g with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in m c0, u nv 0i+xlqnpla9f38ptg;otion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through Epl 9tan+ nu0fx0vp8 i;,l cg3q, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by likgedtz5vj ,+- u(0ypi *vss j4stening for the echo of her shout reflected by a cliff at the far end o,jzig-0 5pdy+jes( ut*4vkvsf 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)ixxyzrzhxt( -5h) 4a ship just below the waterline. He hears the echo of the sound reflected t)xi( ar -54xxzhh y)zfrom the ocean floor 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 e/x tp*;fgw9l 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 just at/0 o8e5izg f n;je/qabove a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–a/ 0e o gqntfe5ji8;z/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 cliff. The splash it makes when striking kj 7l4+y72wr y2 cski0yxduh. the watehcs j 77kki20yyy d xu4w+2l.rr below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pavv)k 0cgk-3 k+ixbj gpn7kw3r/47 uwm zement. A moment later two 3gw7x0gk7) 4/zvckw+u3ibnm - j kpkr 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 oq,vc+ sp9 l6r 2s5qv86lzqhi cf distance by the “5-second rule” for estimating the distance from a lightning strike if th6qsq6,c vl r95iqh2vp lcs+ 8ze temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of ah a)lj *+l ls4te,pej(nb, lw( 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 adk(shsump(* ( sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound -dn s1 fjn85yelevel of 95 dB when fired simultaneously at a certed1nny s5 -fj8ain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certaed.,mc p*n- .xwfr9a nin distance from an airplane with four equally noisy jet engines is experiencing a sound level x.cdn9n *r,p.m we-fabordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a sig j3 j.guid: 8rt2ng :an(ni3gjnal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensitiejgg3n38n ijt :gn.uai d:( 2rjs 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 pe/i(z1bjk v0kwrson speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered wvi kkzb/(0 1jon 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,g3midomg7p p61uo v 2)o7h( jw9okok 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 modegm4qun vz3s )t/uk;2h st amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connectedk;tmn2h4suqvz g/u 3) 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 pl 6g ecu2+t7opc5theo:w, i0j paced 2.8 m in front of a loudspeai0oe765 ,t pp u:cht2jogc+ewker 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 typically detect a difference in sound level of 2.0 dB. W ynq /t7a-yim5hat is the ratio of the amplitudem 5qy7- ntiay/s of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is triple7gugi58 yads6*auda )d, (a) by what factor will the intensity increase? u d*ayg6uida) 7s8 5agIncrease 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 twice the fre3 ;uxy sw78ztzquency ozsuw yz;t 8x37f the other. What is the ratio of their intensities?   

  What would be the so0yyur7fx. r(dund level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.( 07yrrfd yux.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level 9p 9n y1*v:q)qztywtyi7ph2vto seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6p )7w1p :yh9yv*yqtq2vit9 zn .)    dB

What are the lowest and highest frequencies that an ect-rkttz3 ,vo,: ;tl4iwd .kd9pggi .ar can detect when the sound level is 30 dB? (See Fig. 12–6p.l:gtt4k.c,9d3 vtkw r odg;iz it,- .)

  Your auditory system can accommodate a huge range +ph9 *bsfhln z/p0w+d of sound levels. What is the ratio of highest to lowest inte h*slbzdp +0 fp+nhw/9nsity 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 frequency of 4 f5cd0 yc:ysb;40 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must tb;:yc5 d 0fysche string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three 7jic0-,xkme- mtbij9c+bsd4 audible overtones if the p9 m 0cmkdjisb7t- +cj, 4ibxe-ipe 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 you expect from blowinxa+v+ fl gf,0ug across the top of an empty soda bottle that is 18 cm deep, if you assumed it wax0+, gffav +lus a closed tube?    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 pipfmb rtzip+2m u5)z27fes spanning the range of human hearing (20 Hz to 20 kHz), wh5zmur+ 2t 2fimfpb z)7at would be the range of 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 third harmonic. What wyanp:t +tm5tix 9,r 6akm yv89ill be its fundamental frequency if it is fingered at a length of 6ty t n9a5xpki9yv m8r,t:a+m only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E ab6/j832i ;z i(oqiw i wtxo8eesove middle C (330 Hzi/eoe i2x zs6;wj8t8(o i3qwi).
(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 of an open org.6ixa qj cac-6an pipe that emits middle C (262 Hz) when the teqa-j .i6 c6axcmperature 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 a(+ gnq gyny5g(dy/v4 9rstnv0t 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 should the ggo;mzi1.,vx hole be that must be uncovered to play D .mgz;v,goxi 1 above middle C at 294 Hz?    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 616 p xy ve5v9*mg h.qdfihk +sn9l:3:e0e Hz, but not at any other frequencies in between. (a) Show why this 0ek5 g y+p9 .v*hnime9dq e::hx3 lvsfis 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 l7o-md 1 - zfyeilq+3tv:/ hfgyong is open at both ends. It resonates at two successive harmonics of frequenc +dy /ovyg1qfhlit3 mf:7-ze- ies 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 awysqh n8)7j5azqwo 24h* 2yt$^{\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 audible,rb; zn22 q px-v-wbbd*5jaew range for a 2.14-m-long organ pi* nvd 2b2w,e;raw zqj-5bb-x ppe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm qbzya5cb-k* cfx g lc/)k/1m6e )k/ozlong. It is open to the outside and is closed at the other end by the e c )) bxo/ mk gqlc1/cbz*y/k-k6af5ezardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the 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 everyh:k (xc.rgf) f4 hw-5vjx bx1c 2.0 s when trying to adjust two strings, one of which 1gk()f wv5:4jx hh b.ccx-rfx is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middlxw xow* nh(i980 -azose 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 kHz, while another (bra62*hami gj6la nd X) operates at an 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 sh i6a2*gml6jaimultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hza8r 2r6b a/ syv9xio,q tuning fork and 9 beats/s when sounded with aa 6 9, 2o/qrysarx8ivb 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings arsk wtrd9jxm-z)(j lw.+q nk,1e tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the twlxjks nwd+rk- z,.9 tmq()w j1o strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fl6 ty yk,ot)x4dutes each try to play middle C (262 Hz), but one is at 5.0°C and the oth6dtt x k4y),yoer at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of w7 k*zidhmo:8441 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 frequencies are possible when 7h8dziw*ko:m 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 speaker and b3jz8jptn 9gsdsb/078 xo *ctix6y b1 3.50y/p8s8izb7j sd*j g1n6bxot3b9 cxt0 m 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 suppos- yzg-nyi; k+hed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are+yzk ni;h- -yg 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 m (;mfm j/pnr1y and 2.76 m in air. How many beats per ymm;p(j/rn1fsecond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’4xp3gh9 ry + x-(dkvksoho 0+bs siren is 1550 Hz when at rest. What frequency do you detect if you move with a spee3( boxk0kxhh+og4v- rys9 +dpd 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 fir3dyuxk alrb j 6nv9)1:e engine whose siren emits at 1550 Hz mox kvn9b)1dy6u3:jarl ves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequencwrcn-,br(y+w rt7 lv-y if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly thew nrv y-r -l+ct,7rwb( 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 same singz 8nikz l(,1).ye0ps)j5a3snpyv epz le frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears s)05e, epzzn .i3 pzp vyys8la n)j1k(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 ultrasonic sound waves at 50.0 kHz and receives themg0qq mor: axdpg)+.d8oj*r7 m returned from an object moving directly away from it at 25 m/s What is the receive:q )r d78qopgdmgj.amx+0or* d sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5;7l c:rmtan jrj5-np3c3w7 vc m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 5c3rjn :m jv;actp77r- cwnl3kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimentsojmv 3 q/z4ot+sr 2rs8ng+ o9z, 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 approan to4r8o9rvs+ms qj z2g+z3o/ched the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter usesbmktetr1,1 g4 ultrasound waves to measure 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 expectt41,rkbg1 tmeed 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 ultrasonic ht gaz x7xtp1 k.v6+e2waves 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 velocity is 12jg(fhv9 :hx.+ enouo -9alm:x m/s from the north, what frequehh- fl+e.v:g99uo:om(n ja xxncy will observers 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 o;*kew(xp48 kz d vxk5qn land 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 souyin7 pnwv3ab(jo +0(h nd is 310 m/s (a) What is the angle the shoi7 w3 vh+ja(nbpno(y0ck wave makes with 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 the o4trt;+tnl16np0gbpthin atmosphere of a planet where the speed of sound is onl1pt4;t6 g+ob nptn 0lry about 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 m/s strikes the ocean. Determinw -j :9y +2:kstkefg7a2typepe the shock wave angle+pypskekyf tga w- ::tj2e792 it 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 hetd+u:zwkr bq*p8//$/theta$ 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 lyut*6xg wu53above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizoyux gwut*365lntal 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-)poi kpgjl2 i3 b4*)3r5mkc knHz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth forj23gikk5)krpnci)34lp *o b m 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 there in vml32m yrajn;x3w 2e0bw f *a.the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called fp,n v wxnuky5;;iekv(abj t z/98 d *lj*(b;va sewer pipe symphony. It consists of many plastic pipes of various lenn/jz(( j5*fvy ;kn iwlp;ubt8a ,v*9v ;edxkbgths, 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 clos cn.h9am3 *:nvxp35gzic6r wle to the threshold of human hearing (0 dB)p a.5g 6:nmc*zcrliwh x3n9v 3. What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant (b()t7 wyr kqnsound level when an 82-dB sound and an 87-dB sound are heay7ktn wqb( (r)rd simultaneously?    dB

  The sound level 12.0 m from a loudspeakerp:h:fkrz;) , e8qjnqb, placed in the open, is 105 dB. What is the acouskq)jr ;:phf8zb :ne,q tic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 0mfc0dco8bzi;+kxjqgpj. jn*c0t5 g: k-) ywHz. The power output drops by 10 dB at 15 kHz. What is the power outputcd 0 ozp;wjgx0n:)+-c8gjq ki.mf j bk0ct*5y in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectiv;s2u. *i*hb.if lhz6 .teyhgse 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 has an effective h*;.lef2y*tuh. .sgsihz bi 6 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 systems, the ga enf era 7zdjv: +l;1p)eq2sy(in, $\beta$ 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 tuned tfo*: s( e zhlf18fl4pfo 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 tbb6s8iv ia5 90wx,cg0yu cd 4qxk* )pbetween fixed points with a fundamental frequ)gx iuw pt5 q0x*a cks84bdb9,iy06cvency 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 vibration above a vertical open tube va y4buu0)so 7filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in thevo)us7y4 ub 0a 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 strhd43*bk soid( ing of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) wibd*shdoki4 (3 th the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to tz.edz 282- izp kv6std,3wjhresonate 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 tone in the 5*gszy+ becg0400–1000-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 thatcbsyezg 4g0* + 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 is stationi cl*et: d:jwk3 b0we*ary. The conductor on the stationary train heaewi:c ek* d:wj*b30ltrs a 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 whistle as it approaches you is 538 Ho/u ; a+ccr)h pa,5lm+(u h3iailq4 prz. After it passes you, its frequency is measured as 48+l4q/u cpp)c +r(;il5a auhr mhi3a o,6 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to thd xjwx9u.jpmap 8:; j8e difference in pitch of the engine noise between approachinga8x pwum.;:9jj8 jpx d and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beac0rl (3tq(w ust frequency of 11 Hz. The shot3 lqw0(r (ucsrter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as d.n y5vm/uc *kit 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 obmvd*y5ncku. /server 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 in the aorta is normally aboub8s3h4o(h)vj nwk h i8t 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed)kwo8 bvshj h4h8in3( 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/ni; x q4a,4f pwxpq)t*s while the moth is flying toward the bat at speed 5 m/s The bat emits a sounpw xta*q4 4 qp;)nx,fid 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 sound mrbiophfjd )* t-u 328pulses as it approaches a moth. The pulses are approximately 70.0 ms apab*rutj d)ph-m8i2o3f rt, and each 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. 12f5 ck :c 0xli/5tsxaz+9 gaoy*05cnhq –38) was once used to send signals from one Alpine village to another. Since lower frequency sounds gikx*/5sa +xt c a:o00f cch559ylnqzare 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.) Model as an open tube.

  Room acoustics for stereo listening can be compromise)w, rjz/g-u+t0i u qzwd by the presence of standing waves, which can cause acoustic “dead spots” at the loc+ju 0r/i-wzqwtgz u,)ations 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 standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” invos5-/wl*s+ pzh5pv yhis- gup 5fkj -4rlves 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, loud, ringing sound. For a 90-cm-long rod, jrgf5spwl py-/4sh-5v* p- uk+ 5shz i
(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 frequency okl7:n( ozpb *nf about 1 kl7n no:pz(b*000 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. An observer on the ground q9ln je ut,e(9t. wj:nhears the sonic boom 1.5 min after the plane passes directly overt,t enw 9nu:j. e(l9qjhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedb/wwl: izcj1ie,v 5d h9oat 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