What is the evidence that sound to3zm6gleb/7u ravels as a wave?

What is the evidence that sound is a f zbev-ma /j 0k;hn(f6torm of energy?

Children sometimes play with a homemade “telephone” by attaching agc t:cgwfrx*.: ehj.: 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 fw:er c: :jg..ghx c*tthe 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 tblbumr3iud6:. omw4 9qp.a p: he frequency or wavelength to change?b94 q:r b63ulmwmp:.aiu dpo.

What evidence can you give that the speed of sound in air does not dependv x7a/r5 4ivgr significantly on frrr iv4a7xg v5/equency?

The voice of a person who has inhaled helium sounds very high-pitched. Why(p (fbgv;f tudn3o za.mj9(e 6jq*z-z?

How will the air temperature in a room affect the pitch /e,rjs(z qq8tx(i sx7 of organ pipes?

Explain how a tube mezf lie:f3 uiexjiiv (;24k2 )ight be used as a filter to reduce the amplitude of sounds in variousx22 zii:;i3k fie( vue fe4j)l frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spar(9u7uakloou * : wbs8ced closer together as you move up the fingerboard toward the bridgews:kbla ou87r9 ou u(*?

A noisy truck approacx ms*2nmhd-76,qrh fx hes you from behind a building. Initially you 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. Explain.x-7msm26 fn d,qhrh *x [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference inzu,s2jl188b lhesi6 j space,” whereas beats can be saiduzs,2ish l8e1l8jjb6 to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would*dfb2f cl/+w.eul9qz the points D and C (where destru we/ 9+2*zuf f.llcbdqctive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who worat6q)b+ p /r e(sqzxw4: yv:kkk 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 noisevbxt6k e) (4 kzwqrs:+:ya /qp, 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. a4:knte2n dv7i qwzfv.y) a3,Each wave can be thought of as a superposition of two sound waves with slightly different frequencies,tzwyqn v : nfavei7 3)a,d42k. 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 source and observer move in the same direction5a2m:t o k pjupj,a0:z, with the same vemj2u0aa 5k :tjpp,oz :locity? Explain.

If a wind is blowing, willz 0hccdq/l++.n92va qdx ag1l this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velon0/2+ z cqclaxq glvdah19d. +city changed?

Figure 12–32 shows various positions of a childxuvvq2(qph aav. j(:. in motion on a swing. A monitor is blowing a whistle in front of the .2 pav:( h v(.jquxqavchild on the ground. At which position, A through E, 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 listening for the pfo(i*:vxq. m8c3osi wc vp) ;echo of her shout reflected by a cliff at the far end of the lake. She hears the echocsp3v:;m iv8( .* ) oopfwciqx 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side ofi n4k8-dwpcp (c,o.e t his ship just below the waterline. 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 seawater is 1560 m/s (Table 12–1) and does not vary significant8p edi4.-cn,kowct( ply with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengtep1+n6 zg9 qm3ad:tpxhs 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 just above a school of tuna on a foggy day vx)xe4: .orppqi,lj5u -:k lldr)im 9j5o3b j. Without warning, an engine backfire oc9 iv::p5rojbo x p5l jr)x l ,dke3ul).mqi-4jcurs on another 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 cliff. The splash ibas dk5k/j68 it makes when striking the water belksa/5i8 kd b6jow 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 6h m0cox0)i** .eb xb51c(vu vdjwbafthe concrete pavement. A m5oixf )m(ub vcv d0j*.cbawx0he 6b *1oment 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 onrq(o4ip+f1fkgj u:; thd42 kre mile of distance by the “5-second rule” for estimating the distance from a lightning strike if ru42hidr(o +4 tp;j qgkf kf1:the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sounqvvo9 pc /hhx )517xksd 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 sbdaptw/u+)g; uuy( s3-efx5x 5n av:i ound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound leve0 wc w-qm .u0rfpc16uhv2pu7gl of 95 dB when fired simultaneously at a certain place, what will w pu0qh.-gv7u c6mw rf01p2ucbe the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four 5*6 q6cc6ydb nn qc6;1gem0lf dkc pt5equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experiec c6nd pg0fn6;t qke* 5qb1ldm65c6ycnce if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said tomq4s/s6 w8t3fw2t79qb zf aqpx,b2mf 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 the background noise for each device? apqm2m sbt9682 ,qw t/w sfb4qz x7f3f58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normalmd y-neh(*iy ;:pak(p conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth(kh* (ma:y-p ;pidn ey. $\approx$    $ \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 whos*ewwgq w0o*t1q0m9jrec,) k ge 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 modesrbi s,g6 x4-j+4rhlch- t*tlet amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m frh,x6lsr crt *+ 4-igl4bh-jetom 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 front of a1dp3w8za7 0 a/drldm n loudspeaker on the stage. n a70pdl31 rd/ wdma8z
(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 l :a(x9b+mepoc3svoatkt+h7iel c 7+ *evel of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: xo+o++mpa7 7 kl*eb3i 9:stv cch tea(See Section 11–9.]$\approx$   

  If the amplitude of a 4g5sretbzu: 7cjue6 v24dk1osound wave is tripled, (a) by what factor will the intensity increase? Increasbuo 16t45ere:zk 4jugd2 vc7s e by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves havecj, zf5v*(r rk equal displacement amplitudes, but one has twice the frequency of the other. What is the ratio ofrj5v,(* fckz r their intensities?   

  What would be the sound level (in dB) of a sound wave in air that gskvj 24 h ha;3rm*q+z,dh+yqcorresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz? g*mh sh +yqra+ ,kzd342;jvhq    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100yrgy kt- *dw ky7t.b)8-Hz tone that ha-8)y7dywgt ktyb.kr *s a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can de:-yp l bc9:tbzd4 sgfwv.c 2eamc-porxh)6 03tect when the sound level is 30 dB? (See Fig. 12–6c.-t-pa43v:l sb9e)2 mcxz : wy6rh0o c pgfbd.)

  Your auditory system can accommodate a huge range of sound um/lt (yq67 fjlevels. What is the ratio of /u ymt6q7f (jlhighest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violi .ckgm z,wp*5(lgyzv -n has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32c5 v(kwmgpzl .z -,gy* 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 fundamental and first thrz (7w21emihgp4kl zl;o z) c2dee audible over1(z m2khd z epilg;z247wlc )otones 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 you expect from blowing across the top of an oncpa4y, n,zz5 8ep*h empty soda bottle that is 18 cm deep, if you assumed it w,5noypp* zc8,a zhe4nas 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 opo8j q(qq x; 8 x1.xi8ozoi6fqpen-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the oi8 ;1 p(zoqqx8 .qxoix8f6qjrange 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 rmiz;04josq- 0vw ud *k /6tdmHz as its third harmonic. What will be its fundamental frequency if it is fingered at a length ok z jmi0/d6 ou4wm-s0rv;dq t*f only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above mifp-hk*.t ,;rd8ut31 xjjjk dbg;4e lkddle Ct8lg1jeuf;.j dhkd p,j; 3 btkk-4 *xr (330 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 of an open organ pipe tbc ipunk3 h0-8hat emits middle C (262 Hz) when the temperatun bp0iuhkc83 -re 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 v4mdq+t*oxs 97vm se1 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 12–1ew mz+s -/.zf1yju /oq0 should the hole be that must be unc-zs 1uj e/yfw.ozm+/q overed to play D 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 resonp e7jxykn4 2ov a7g;;nate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequenci;vpxng 4yane727 ; okjes in between. (a) 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 ends. It resonaf)om9r4)xsu t) sxy3ates at two successive harmonics of frequencies 275 Hz and 330 H muf 43so)y)ts)9xxa rz. 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 ky p4f34mvd5i392ky1 zy +uqfro)moq$^{\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 range for a 2.14-m-l jim a/p1 t3,:nmi7sn (aij-pko .adg8ong organ pipe at 2-iagndmm38pspaj .on/ai 1: jt(,i k 70 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximat -nq,7z niqz hja.6j4gwr6+hfely 2.5 cm long. It is open 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 rh-nzqj i7wa4qjz 6 r. fgh,6+nelationship 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 onqs(w(n clw -c3emp ed2wt.z-k/ f7v.ie beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other streim-.d pe(knf/wlt q z v(wc32ws7.-cing? ±    Hz

  What is the beat frequency if middle C (2 rx4ad.+l5 fifi5buyjwrqnr l/08/9i62 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 2kuw q; p7px +iya,6u93ylahbh0b 6 jx:3.5 kHz, while another (brand 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 simultaneously, estimaw y6;aplpi90q,jxy6bhbuhxu k7+3: ate the operating frequency of brand X.    kHz

  A guitar string produces 4 beac+mu ue:vz64lyog4* yts/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your v6 y elu+4muy*go :c4zreasoning.    Hz

  Two violin strings are tuned to the same0kb mjc 3ub7pr2/h,id) hc*bo frequency, 294 Hz. The tension in one string is tm2 i 0 kud brh7cc3hjob,p*)b/hen decreased by 2.0%. What 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 identical flutes each try to play.lohwfnf i 5 ;hzmm4-r6 gkn;b4a6*rz middle C (262 Hz), but one is agnfhl;w.bmiza4h n 6*rfk- om45rz6; t 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequ7 .z9v a lbx54kmbg;v)wsxa 7hency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded togethe5xbsl g k4b7.z7wxv) vh;a am9r, 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 speaker aop 5 kh6nq u 8pz4/t3+x jqa;guai8bl;nd 3.50 m from the other. ux;b3;azgq8 up/ak5ijt p4ol86 nh+q
(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 to be vibrating at 132 Hz, bj q; fr7,pepgd7+gq0uut a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrati7r g0q;ppgjd+q u,7f eng 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 and 2.76 m in air. oy;;- sn7xn o7+l q65 tuwvgvdHow many beats per second will be heard? ( t7q;v6u dv+g-75;nowyxons l Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a cero ;krn9/6cyumn7,r z.ojoi r 6tain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you u nr6;9 .oocno7ij6 /zrrym,k 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 detekk f8p vwx* 48he(+znvct if a fire engine whose siren emits at 1550 Hfnvpwkh8( 8z* e+ kx4vz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward ysct q33rg3z b*ou at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies er*zsq3 c3bg t3xactly 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 eqzg3gp; q.8mh suipped with the same single frequency horn. When one is at rest an3 gqm;8zg. pshd 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 ultrasonic sound waves at ;y/qsf*v4adff+vh9n*i2 w6 c cuvee;50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s Whaec;/v* fh wy s *nc2dvq6u;4ifafe9v+ t is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As itu9t +ean/3lml d,0 wqg flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does l+0l, nmg/3eu9adw qt the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movinddxc7zrer4l 77o,n8 ,u jw f;ug flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway stan7dc7 w;,,u48rxl 7efdurozjtion. 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 ultrasoujrk6 shja/7q( n 6et1wnd 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 ehq 17 /e6nsjwkrjta6(xpected 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 u jsuv4 l.(vw 0+zuo61m*cegcsltrasonic 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 veloci0(q vt1qi3fxlj0+ xgg ty is 12 m/s from the north, what frequency will observers hear who are located, at rest, xfv0tgj(lx 1gqq+ 0i 3
(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 itgcai*.b(pv u 2pnm0lgq- (a+ ys 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 where6d+temj3mb2 nvpa 9 d6 the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airpland da j2pmn+b69m 6tve3e’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 :;qgc o 8s9fppatmosphere of a planet where the speed of sound is onlyqp9cogfs 8p;: 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. Dep)0t08 vq+3gn4lly lp8s4v o0x koa tftermine the shock wave angle it produces tlfvsn8 l38+ 0o4yo)p 40 ag0p tvxlqk
(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 2 k0 wnxppa0(py ax0x4$/theta$ 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 aboy k,).dulx) jlve the ground flying fasterdl ,).u jly)xk than the speed of sound. By the time you hear the sonic boom, the plane has traveled 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 sonar .,yby+py,t-: cr vaed device that sends 20,000-Hz sound pulses downward from the by: d,tcy,b-r va+ep .yottom 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 water)?    s

  Approximately how many octaves 94oucb6 3 zvdpare there 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 of mfkutol.z:y6/1lnfa/z a u5i) any plastic pipes of various lengths, which are open ozu/aok)f.l :l6a1 / yu5z itfnn 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 permodg51ng*v 3h)t u hdsi),) jason makes a sound close to the threshold of human hearing (0 dB). What will ht h5o,*)3))u diagmds1 njvg be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sounwkffi4e65gj970e2 u bpo r gl,d are heard simultan5e62, 7wg0ffp rb49uijlk o geeously?    dB

  The sound level 12.0 m from akisl/ 1ok u:; p4u/jfrda l8v+ loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally ;/sf+i1p:8uj4kr kv l/aoludin all directions?    W

  A stereo amplifier is rated at 150 W ou;f2*m(x gcv.c7 hsvsytput at 1000 Hz. The power output drops by 10 dB at 15 cm(2sv.7fc gxh v s*y;kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear prhcr5 yfmt b tt3fc-5bq u(835zotective devices over their ears. Assume that the sound level of a jet airplane zrqc5(by3 f 35ct htmfub-8t5 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 communicationslanp(-mz5a* r ;2kbk k bv*ph, 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 tuned to a frequencypag7;sa mn.g , 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 fixed points with a fundaita4e7h2c, p0wcob5yjw0y, txt 4 , bb:vou/lmental frequency of 440 Hz cw,,ahvjwoup 7:0 4yb 05 c/tbtxt,o4 lyeib2 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 c;;m yy27 wrababove a vertical open tube filled with water (Fig. 12–35). 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 dym ;2 rcw;a7byistance 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 ma nv;7ijfqv* r8ss 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 strinqrvf n 87ij*;vg if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate4q2: qlo(lymk txac2ohzb 2)7d/-ay e 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 500–dn7 uq)5jsg n21000-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 one source5n2 nujs7)qg d than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor oa).:l4(zclmvael q0o n the stationary train hears a 3.0-Hz beat frequency lqz4alc(o.ml :a v 0)ewhen the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle asa/ /njoads*yk 53t dae9x y4p9 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 velocityj*dyap9 sxot59e3k4y /nd / aa)?    m/s

  At a race track, you can estimate the speed of cars just by listening tlsz/2v +*vaci: (kxu(c/ jws fo the difference in pitch ous/ avzcik/w * l: +v2s(fxc(jf 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 by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat ffn+u+7mtmamhj *ja7 , requency of 11 Hz. The shorter one is 2.40 m long. How long is tn+,u am*7 7mamh+jf tjhe other?    m

Two loudspeakers are at opposite endef/ 63*pw8,q8q(1uzgg9qct 8 azjhcaz4 lfk cs of a railroad car 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 jccz,8cgf3q pfz8*klat86q(4hg /e z 1 auq9wfrequency 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 i vst +o )y/pd*r6em9pmn the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume thatms9op+e )pv6/*rmy d t the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at p+rg a t4y0w2oafds3h2)ru zt, xkz38speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kH3k f szt+uzp32x8y2d,)4a th0gora wrz. 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 pulses as it approaches a moth. vmv5( l8wp8f0r b ljy2The 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 that the echo from one chirp returns before the next chirp is emitted? mwyv88l2 (jlp b50vrf    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine vill ,jcd qsfae(m31qt1v )age 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 alpenho(tamf , e1cdq j3)qv1srn 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 compromisedc5n4ar, ;mzpc 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 mcn;r54a pm, cz 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,” 5-q-s wlwisv4 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, lou-4qs5lw-w isv 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 frequeng,5 d3zin-tv jcy of about 1000 v3int dzg- j,5Hz 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 obs dl.p;:djx (vtd suhk7v3-q0perver on the ground hears the sonic boom 1.5 min akx7qt(0pl.s ;jv pvd :-dh3 dufter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 2+ fk zxuk s4s+-:4qhqab5nk r15 $^{\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