What is the evidence :q vn xl3oyje 9bx:(y8ik3tzxsiv6g7m) )hz 1that sound travels as a wave?

What is the evidence that sound is lelb;q 9y 0;q*rapa/pb8llu9 a form of energy?

Children sometimes play with a homemade “telephone” by atqqtcb i d-c(x4s(5q c,taching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cu 5,qts( qxc(qib4 dcc-p to the other.

When a sound wave passes ff w-0xkth8jz1 rom air into water, do you expect the frequency or wavelength to1 x t-wkhfjz80 change?

What evidence can you give that the speed of sound in air d+oix;qfi;y j 4 5ncjz,qz.tg(oes not depend signific4igxj;qzyfq,z j +; 5cni.t( oantly on frequency?

The voice of a person who has inhaled8gjyzt im 4*a +xx+-*xjji2y v helium sounds very high-pitched. Why?

How will the air temperature in a room affect t kjtjb 1qbx/hm 8ib28zj5-4a nhe pitch of organ pipes?

Explain how a tube might be used as a filter to reds41v o54gg lrduce the amplitude of sounds in various frequency ranges. (An examp1srd45lgv o 4gle is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move u01+c 51vvh fiw;fdcj lp the fingerboard toward the d5 jflv +;iw01cfh1vc bridge?

A noisy truck approaches you from behind a buil/e.9 k) czx3hwlvk/vx ding. Initially you hear it but cannot see ick/x9 3.elw vhzxk v/)t. 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 tibf4zh+9k3 ;dung )dc o be due to “interference in space,” whereas beats can be said to be due to “interfer)d9uhfb dn3 +kg;z4cience in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were nia4 6g ,;odlolowered, would the points D and C (whioa, 6ogd4 ;lnere destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of pac 2rpyi9 (tzbc4 km08rotecting the hearing of people who work in areas with very high noise levels have consisteyr9( ckp cz ibtma4802d 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 the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thougl9uc ximi- lsm.l5s.) ht 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 two comlmsx.ll i)-iuc.5sm 9 ponent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and fs vm:14ax/y eobserver move in the same direction, with the sas41/yvx ema:fme velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a pers7-w w6gg ar3cson at rest with respect to the source? Is the wavelength7a6-3w ggsrc w or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing+5pp4( p vjkc6.swqe u28fax: n vja9w. A monitor is blowing a whistle in front of the child on the ground. At which pvv4 j92ax8:+jwufqkanwe(5 6sc p.pposition, 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 echo of her sh0;qni2 h 3gabyout reflected by a cliff at the 0nayi23;gb h qfar end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hcj 1h0o:ljy (g9gazl)18uuaxears the echo of the sound reflected from the ocean fl( ag 89g:1hzxl) o 0ul1jjacyuoor 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 wavb0 za4gsv p11pelengths 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 tuna01 1n/9d)t zxkckw ado on a foggy day. Without warningd19k t)kw1c/0d o xnza, an engine backfire occurs 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 it makes wh/ax)ft/gb8vrnt.m x 8 en striking the water below is f8 nx b/vtrxat/8m.)g 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 concref2dql z42fqp4 te pavement. A moment later two sounds are heard from the impact p24qz d4l2fqf: 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 miley1j41g q2dacq of distance by the “5-second rule” for estimating the d11qg42daj c qyistance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensit rfnh:n;w*yc -y of a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a soun; xv6 zxr(/adwd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a soup8 lfd7h )(wk/7h bi3fmf)uvx nd level of 95 dB when fired simultaneously at a certaid/pffi)h uhl7 m8 v)b37(xwk fn place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplad9*s( .:j3shor 1 qmv1twikum ne with four equally noisy jet engines is experieqv 1 j3woh9.1m(:r*idmst uskncing a sound level bordering 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 signal-to-b46 i042ot bj *na/qgdmp *v fi2lgn9nnoise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the bj g/4gidm0fna q*lpo *i2n46bv9 2tnbackground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of ah8 c6gkzhy 2ke vpy9/gpq993 sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a spppk/hcq9gkez a2y y3 g 6vh998here 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 strik:t 0(tpwe+at m rap5x0es an eardrum 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 modest apx 43 2*cix.u-kd zgjbmplifier B is rated at 40 W. (a) Estimate the sound level in decibels you .zgxd4jipc2- 3x* kbuwould expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in o 3wwg; .0*iw z;cc(xd deqij6front of a loudspeaker on th ; edcwig;(w.x0 dzwjo3i*6cqe 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 differencegn baaqr-l:w+uj-3.x in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: Su-g3- q .br:anl+wxa jee Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by0)k*7p tus kl8 94 wuyav4nqlgvo8; gr what factor will the intensity ilwsynug*7; 0 84tg8 94 rkoaq)pklvvuncrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement j4j7b xluf:/f:)f dowamplitudes, but one has twice the frequency of the other. What is the ratio of their injwjf fu l f:x47d:o/)btensities?   

  What would be the sound level (in dB) of a sound wave i0 ai1c8lfkh mckz4+ 5qn air that corresponds to a displacement ampqh8+40cc 1fk5iklamz litude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone x *hac 6u4zgcekh0/-foar9n1 that xr1gz6hac h0n -of u*/4 9kcaehas a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that anza ;xk+0ej*iu ear can detect when the sound level is 30*xjiuzeak+ ; 0 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a x kh n+7qbfy)/huge range of sound levels. What is the rat/x)+7fknh ybq io of highest 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 violin has a fundamental frequency d* q ;,tgtox/ytc40z xof 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what;gt4o0tq xd xtzc,/y * tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and + 4 jmrv.ss;x(zx5h.ffuzz-z first three audible overtones if the pip.;m v z x.x4 zf(zsshr5+jz-ufe 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 wob po1 f9t;/rgbuld you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed i orbbpg1;f t9/t was 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 pipes s7kjt;4w(g fyopanning the range of human hearing (20 Hz to 20 kHz), what would be tf;4t jok w(g7yhe 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 its3bsx, nk7;uuj third harmonic. What will be,bx;s uun37k j its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0f*4l* 9zutw97rry/ue pm yy2m.73 m long and is tuned to play E above middle C (*ztryyme 92y9 puw74m/r*uf l330 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 toa)x tlp8:a, aui z+,;kb h9rshat emits middle C (262 Hz) when the temperata;p+,b za)iost 8aku9h:, r xlure 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 /s0fx 6- w1tdpll+ggft o(2o q20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece3hw ynk7dvede6,0svw, 3uv; i of the flute in Example 12–10 should the hole be that must be uncovered to play6u vse3 ,w hk;dyived 037n,wv 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 resonate at 264 Hz, 440 Hz, and 616 Hz, / y8f imn7*yst uv0(qcbut not at any other frequencies in b (8*myvq7/s0y uictnfetween. (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 lrx)yr zcai5 6(uo0 :pqong is open at both ends. It resonates at two succesyi) 06ra5cx p z(urqo:sive harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 z,:4f r641x( rqvjzl6dh ( lds3vxpm0zw e2gs$^{\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 e r2ntb827 lv e7a;cu;k2fmkf range for a 2.14-m-long organ pipe at 20 27k;lmee2 b2; n fvc7r8tkfua$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately fl)eg xhbv)k3 vg fed j219g8/2.5 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)dj3g)/28gk vev1flbgf x 9he 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 every 2.0 s when qo:nnaan7)t / p*zis( trying to adjust two strings, one of which is soundi()n pazia q7n:snto*/ng 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle Cbhu2yxso(2/ t6a6dp l (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 (brand X) operates)fzd*-xe(o* u 9ixssfr*iwqxn+ 2qe cwy(58 z at an unknown freqzd -o+sysciux n(wf(2qx)r*qfi w5x8*z*ee9uency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string producqn qe-bp/8i9e qya1*s es 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tqe bi /yas8pn* e-q91quning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings arc;8jrw cv6,wnkn,: r(/ md vdje 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 two strings are played together? [Hint: Recall Eq. 11–n ,jr:6;/kc,d dmjnvvrwwc( 813.]    Hz

  How many beats will be heard if two ide mm60( owasirk8d:sa3ntical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the otheksa ormwa 68m0:s3id (r at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forksydya9k+yi r55* ) fjvc 0mibl. i5x,qp, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B an bmq9+iy)5yr,.*5k0 ajvfi 5piydlxcd 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 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. ;4 ye 446q5/aes arf5d9oigclc-nqap2w axw6 A person stands 3.00 m from one speaker and 3.50a a4 yoswr4 ee lfdac49w2qcn-ai5566q xp;g/ 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 supposed to be vibratinhvay5t ,pv9 ,mg 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 frequencya v,,ymp9tvh 5 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 waf7ggs0 uf.u68m)tz t jvelengths 2.64 m and 2.76 m in air. How many beats per second will beu.f7mftg0 zut jg 6)8s heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz j 3sdrlt: zn4o7f1k i)when at rest. What frequency d s:njo 1kzl)d4ft7ir3 o you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do youw;qk(vt x3n: oe*g2 p;vl0yjs detect if a fire engine whose siren emits at 15*:yvk3nl exs(p0 ;qog vt;wj250 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sourah (1p odt.a ,n/unpz*ce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies p*.( tnoa/d,nu pzah1 exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one is *hw1 zm0/ kuwuat rest and 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 hornsukw/w1h0u* mz emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonhgchu 0. sk79hx1u+z wic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at .u7+gu1 shwhx h9 kz0c25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits au 2t ga,ld lkot/f26 a,/a0sc3cmcj 3zn ultrasonic sound wave /3/ l t3lag26aad,c ukcjc0s ,ztomf 2with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler e7r5eu c b5e(nhxperiments, 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 speed of 1e5 bh (c7enru50 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flz3u (wku2d*2*-sh tu b tk:rdaow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in hrsdu*2kzw: du- tu2(kthba3 *uman 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 ultraso6ajsaa i 7x(5. q*0vl qpbq/kanic 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 velocik-x./yb hpiy go/6rh ;vy*6 ohty is 12 m/s from the north, wha.6girpbky o6/h ;xyyh-h*/o v t frequency 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 movinyqs- v))p zbek-,o; z7m h/lgwg on 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 sound is 310 m/s (a) What i;a7qsw ,8d keps the angle the shock wave makes with the diq e;p8 kd7,sawrection 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 thin atmosphere of a planet where the spexn7;sw6thh+76 by0rfm x g*y4wy7qvied of sound is only about 35 0xq7yvf y b6x7n4;+ wi w7hmht6rys*g 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 t-btx5 bpnx ()/hqn y*zhe ocean. Determine the shock wave angle i(5n h/txn qxb*py b-)zt 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 l o +(yk* fpy/ug40syv$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead r63a mxu 0 mn:.hr+uk2zl:wuk and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, thl0 :z:mwr ru+ kuu2x3ham.nk6 e 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 sons-8kr 89cv ).hx yfletk,og o.ar device that sends 20,000-Hz 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 fc-er vgots .yh9k.l ok ,x8)8is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible reb7 hcke1z u72fnrd(-ange? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewermnuj b7wl mh2sz+0h. *uubnw (ku gw2 0-bm;a9 pipe symphony. It consists of many plastic pipes of various lengths, which are open js*u-wum9hb aww n 0bm2g;7b+hzk.unlmu ( 2 0on 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 thidh,+szkg 0: creshold of human hearing (0 dB). What will be the sound levek+,g :ci zshd0l of 1000 such mosquitoes?    dB

  What is the resultant soun 92q yux;j7rgfd level when an 82-dB sound and an 87-dB sound are heard simult9yqr 7fuj;x 2ganeously?    dB

  The sound level 12.0 m from a loudspdob.xb yga6hj,u ,: x+eaker, placed in the open, is 105 dB. What is the acousti+x: xb.bohygud,a,j6c power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000dc:b 4mf83anfe.x7gj+rt6jy vz )g: s Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts z )yf:+bjs3n :.7j vmgtf da64cex gr8at 15 kHz?    dB

  Workers around jet ax1 xl v5( +hknqmv(i:dircraft typically wear protective 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 aver5 mvkdlq :hx+(v(1xi nage human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, thx z1po4acyg/ie.17y -lt* h u,u.csj su7 ;wqpe 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 frequencds:2p8b7+ep c4gdver) b x z7cy 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 fundarewx gxs3o :2/7e hbcal,z6* ymental frequency of 440 Hz and a mass pwe2/xcz36: a 7ox ,eyg*brh lser 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 vibt7p pbq 19ce,lration above 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 distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the bl p,e9qp71ct frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that isibvwwlhf )/ )- open at one end and also 75 cm long. How much )hl i/-vwbw )ftension should be in the string 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 resonate aivbob ib- k825s 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 t1no/)kz l y2zge tqq*zoar vgy- n68;0one in the 500–1000-Hz range coming from two sources. The sound is 8)z0 yz - grozq/*ntaegvyn1k;olq62 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 source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistlesbi3.x vrp8 rbbh d/+cmclh6 l-4kwx: ,. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when./whb drh+3 l xbi,:r8pcx-6lvmbck4 the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches yov9j8b2g aakp4 u is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the tra j9v2g4pab 8kain moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to tovp+r-3kepd:17eds ihe difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as is dioprk d13 :e7ep+v-t goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding toge*c-v99 qd nx gc0x8 zfj6ns;duther, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the othefjdxqc 0dns8c ;uvngx z-9 96*r?    m

Two loudspeakers are at opposite ends of a r fqltw8v:;kiqu;;9u y ailroad 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 frek iwt;vl: f uq8u9;;yqquency 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 in the aorta is normally about 0.32 m/s whae oe0dwxu+4(etnq: * ht beat frequency wouht: qnu *+ex eodew(04ld you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying y) fyc,rpv. 9ttoward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the fr)9tvc y,fy.p requency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound puliy,c z)t8 b6ifee(mltg4ab 9kc v2./yses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long)(c2gkeez i v y/tlyafi.,c8b b9mt4 6. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alp6cew hx/-jfdw- rj xaoc3iz3+cw:e ;5 ine village to another. Sin+/ja wd3h5: ecwoecix z-c6wxj3r;f- ce 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.) Model as an open tube.

  Room acoustics for stereo listening can be w *o gw40v,twfcompromised by the presence of standing waves, which can cau,to0gwfw v*4wse 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 standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a loy4eg kolr +v84x7cb7e w22tuz; ojvu;ng, slender aluminum rod held in the h gx 4yrc+;;zvuob8et7ke24v 2oj uwl7and 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,
(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 o(sryl7 8h.ac;z fqv.y f about 1(;sl q.yvc.zfayhr 7 8000 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 observe; 2y psxfd5l*yd 6- iwxrqj*6cr on the ground hears the sonic boom 1.5 min after the plan c i5 d;*fr6wjy 2s-xxlyqdp*6e passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbobi+z8e+k)o2d1u5 1y2 cig l akzhkg)mat 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