What is the evidence thag t,97z5aloke-u ffbag 4hn54t sound travels as a wave?

What is the evidence that sokgs+ ;q 8v 0edz2kiv)zkk j,u,und is a form of energy?

Children sometimes play with a homema f(/t zrjq4odv;cv*x*de “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into c/v* txo;qf(rv*4djz one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect2 t,l: 1eg dp8s-ucmtn the frequency or wavele, tm -ds2pl :uen81tgcngth to change?

What evidence can you give that the speed obd jsl7 lglo7xnl,6/ p f1kh/5f sound in air does not depend significantly 1l b5h o/,dg6f/s7xj nllkpl7on frequency?

The voice of a person who has inhaled helium so +iwqfxy3,j -q( bl*smunds very high-pitched. Why?

How will the air temperature-j jyfk3c a7 jjyr1*,k in a room affect the pitch of organ pipes?

Explain how a tube might be used as a fio; b)o9 ot7uftlter to reduce the amplitude of sounds in various frequency ranges. (An)9 ; otu7otofb example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced cl edw)-:pfe;k joser together as you move up the fingerboard toward the bridge? wpjkee -d :);f

A noisy truck approaches you from behind a building. Initially you hear it but c /reru3 - pu.:fhzt1upannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-freq3t-ru1.zefu: /u rh ppuency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can bx qgd:is p) g.oky8s68e said to be due to “interference in space,” whereas beats can be said to be due to “interference in time.” Explain:o8y)s.p kgxgq 6ds8i .

In Fig. 12–16, if the frequency of the speakers were lowered,7gqi 9*vzfuw,ef s 2-k would the points D and C (where destructive and constructive interference occur) mov,v7ff2-s iek uw9gzq *e farther apart or closer together?

Traditional methods of bg 0li/.z*xl3d7ovd do3v 8cn6y eq d(protecting 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 the sound levels reaching the eqc7lvzd3*eodin o(/vgdb.8 d3lyx0 6ars?

Consider the two waves shown in Fi2)l3lz pm9np3sbee 6e 3jhd+aj yep-7g. 12–31. Each wave can be thought of as a superposition3 speb 2a93y m)6lhpe elp+ jz7e-djn3 of two sound waves with slightly different frequencies, 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 x vmfeoxhd+1q,gq: 7/move in the same direction, with the samfge+ox17qmd vx/qh ,: e velocity? Explain.

If a wind is blowing, will this alter t7g9g)4vfzi(tb/ ;yyslk j q6k t5r c.she frequency of the sound heard by a person at rest with respect to the soby9.g/v)cqz4r yl 5(k6j kgssi;7tf turce? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in mot ht;)zll cj(o(ion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistl(lz lt) jo;c(he? Explain your reasoning.

  A hiker determines the length of a lake by listuh sv j1* 1bh,h3e-a ,4uxd rp-pwb6q0t kadx2ening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the t , -kr3spjb 0hda1p q12 b64x-w*h,dea vuhxuecho 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 hears the hrg:g66mrwf0 .bj( sj echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean atf(66:gbhg rrw 0.mjsj 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 wavelengthc2z.)c spb94izc f0hcs 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 frvhlix71.dx1woh) s :)hp y d5oggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time e1.x5lhpvihx)d 1d7:o w) sh rylapses 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 thmv4 /qpv ,nn setg68tz5+i25 urlw(kk e water below is heard 3.5 s later. How hps,5/vq6(4zw v2gimn+ nk l et5ukr8tigh is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete 6em4 n8 .94womftfc*ocg *cje pavement. A moment later two sounds are heard from the o omce f4f9mcw*g 6 4tce8n.j*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 ymddh/.)ztj c(;zh h us:;up.g+uqcc0g09 exone mile of distance by the “5-second rule” for ecm .d+g9y hszuxpcdgh ju zc(t)0;u;:e 0h./qstimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at thevq4lwwr / b3 79c rpmqpibny26510jkm 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 lj7jo. - u) 5i.z(pry+yzefal of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneouslynb:72 uo ss1j(gy i)rl at a certain place, what will be the sound level if only one isl (n )us:ris12o7ybj g exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance frv:10wro kevv )om an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would )vwor01e: vkv 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-noise ratio of 58 dB, where3gqce42bcb 8sl5h 5ba as for a CD player it is 95 dB. What is the ratio of intensities of the signalhlb245b a5q 3e b8cgcs and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in nort 5a91o5em, h fv6jwhrmal conversation. Use Table 12–2. Assume the sound sprehw,v6jo5t 1 e9af5 rmhads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an earbfgz)i3- :vz, jirmpu*. e bgcxi9cea.*5x 1bdrum 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, w. g1ucnt bdm54 z+w7:mhm p,kthile the more modest amplifier B is rated at 40dm:.kuzct+n5 m4pth bw mg7, 1 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB w ixg fq1 :p;mo6)w3w /bifpp.phen placed 2.8 m in front of a 6 g;q/io31bffi p wp)ppm.xw:loudspeaker 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. What i2em q,h, l/ltd,nkk xv3)pgk6 s the ratio okxkev / 3 ,hqd plkg,6mn)l,t2f the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a souy(n;jsk;3 e u0d:-8px y:i1julnuwn und wave is tripled, (a) by what factor will the intensity increase? Increase by a yul 8; jnndy:;w uux( pn:euj13ks0i- factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displace4a/m4-ipi n mqf3eig/ment amplitudes, but one has twice the frequency of the other. What is the ratio oiimfniq g/ ep4 3ma4-/f their intensities?   

  What would be the sound level (in dB) of a 96o9ky z 7jmqlsound wave in air that corresponds to a displacement amjqyz 9km9o6l7plitude 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 10d;j)b3: lzuv ty1q93hmdvk *p0-Hz tone that has a qdv:;z)ykpvm htdj b*u1339l 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detebfo 5w 9 o5ch )tyzx9n:g /g;x0*nqwjfct when the soundj w;95)oqwh*f 9xfcg/ nt g50ozbxn:y level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accomx+8+- )8,kwgx .y sbcgdcthedmodate a huge range of sound levels. What is the ratio oyd wgs)b8xtcg.+ -cx, e +h8kdf 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 hask(hhzt) iz35f a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, an(5h3fkzt ih) zd 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 firstuqdgy 8eow6/: ;otu( w three audible overtones if the pipud;g (e/:o86oqutwyw e 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 bl2 /+zcsim: zrkowing across the top of an empty soda bottle that ckm z2+ sr:/izis 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tubjm03rw5x 4fa:j ye,l9j*ezte e pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the le ej9 e jayxj4305*:e,lr wtfmzngths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency o7pku1s11l secdsm - k)f 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60%p ke)lc m1-d1s7us1 sk of its original length?   Hz

  An unfingered guitar striz y; f/2(cirxzfbqye5v *1d y5ng is 0.73 m long and is tuned to play E above middle C yrxz ecv*f(/21q5y fdy5 i;bz(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 that emits m rdy evlrs/6a*1,u0, skeqf7yiddle C (262 Hz) when the temperatuyse a7/*r,r,lsf1 vd0kuye6q 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 y k;h.rn*wrhi: 6 bq;xr,eqg*20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece u((xgl-non va .h-(l rof the flute in Example 12–10 should the hole be that m (a.-lnvnx((l hrgo-u ust be uncovered 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 resonate al6h dx0tm0bw1810s ow ro+qvct 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a cloo+dxwl 161shcv 8o0q0m btw 0rsed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates i1u37awapd(( e/ y/nwg2 utr wo0caf7at two successive harmonics of frequencies 275 Hz au7i3gdc/eryt0 w1 w/ faown((paa u2 7nd 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 6pv ilelkge)*fd)sy s3 (+uy9$^{\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 aree rgob(7s 2ag5 present within the audible range for a 2.14-m-long organ pip2ag reobs7(g5e at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm l5-hr fbqy/e;uong. It is open to the outside and is closed at the other end b5eyuh-;bqr/f y the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears oneqs;bhbb z/7kt- hu 97q beat every 2.0 s when trying to adjust two strings, one of whic tksb77/;-bhqu hbq9zh is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle-f ebrf) cz3r6r-rl)p 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 (brajwmz uz8hr+,nnx.,ie l7erh0u,v e +7nd X) operates at an unknown frequency. If neither whistle can be heard by humans wx7h wjr+nz7v8elh0 , .e,+r imu,une zhen played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tup:9 g bk.nk2aoning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequenco a.:n2g 9kpkby of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension ic;6cynbwb,o)t +0e k;xi f *knn one string is then decreased by 2.0%. What x0ctifn*bc b)yk,6+kw; ne; owill 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 midoiocax2q- n wpzs3cq/1.(7 uwdle C (262 Hz), but one is atic3pwu7 2s.xo/a(nz-o c1 wqq 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B hplf/alqqcx;/; k :qv4q)1pdg-ine;gdvdy-* as a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when dvp/ dq g;c*dv qi)ng;:; pllfqa4yq --xek/1A 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 frz7il ).tjywcrudg75k a:ul3 ,om one speaker and 3.50 m from the j7t cal7,wdzuuk g3) .r:y5il 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 vibrating at 132 Hz, bb--o8g ft :jys uevy:d5lv*5d.-yt hsut a piano tuner hears three beats ever.y-y e-fsdts55v: h-ul*y8o t:g dvbjy 2.0 s when they are 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:4i- njt(ewgx wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assu-ng ew:(tix 4jme T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sify5g3hlh ;wyi 0,gcs25r-0e )frpd b(4al f qgren is 1550 Hz when at rest. What frequenqr dff, w- 5ylhgl)20h a40 y5g3bfpcreisg;(cy do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose sir eik y;+ab6got1n 0qe2en emits at 1550 Hz moves at a sio6gke0+;qa2nbt 1e ypeed 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 c m 9dzgej.+7kp hyk;n11r;zs you at 15 m/s versus you moving cdm.1g7rke9; zjk1 z+nphy s; toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equip-0kea)e sni.vff5 l j3xdun*8ped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of ei 0nfkfs vd.-a*j5ule38xn)5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrass/ob0w)p6niko5 n7h la;b(bnn,dh7 fonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received soundnfi/bh)n5b0slbnn7dook ;hp a w76 ,( frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of zf d /4/z bt3gyk:cl7f5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does theg/lz47 z/3 df: bfckty bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimeiknwfvpp* /3nlax 7re;ru*98 nts, 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 *u9e*v8krpr;7fnxan pi /l 3w the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speedsr doa/3t.ano1c5q q 2qp ;wpj/. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries np awqq.o15ajro qp/c 3/dt2;at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrw71d4 sa3trf,;io czw td89arasonic 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 p6 22:qlomhmowind velocity is 12 m/s from the north, what frequency will observers hear who oo2mm 2:l ph6qare 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 objectuzrd4nf 4q ls:+hjg2(ho. ds3 moving 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 Mahsc3.x : epr5sch 2.3 where the speed of sound is 310 m/s (a) What is the angle the shockrc:5p. 3hessx 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 thin atmosphere of al5*ebl:eskm/ 0o3kkmua:x4 f s(7xwh planet where the speed of sound is only abo3hsx ek5fll k:mwo0x*b7 :/ks( muae 4ut 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 a .( z0s 1hgzr.0zhwer8500 m/s strikes the ocean. Determine the shock wave angleh .10 (zsrw0a.zg zher 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 zkd2i7a-o-ui.5r g q un)s 1o8nim lc;$/theta$ 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 ab6t(w1kf4my-stz:o p t*vj q *dove the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distan16*ypz4tjo- tt(f *dkqwms :vce 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-Hz sound pulses down7zv 5wyw g,zl2ward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (inz ,yv7zwl 52wg fresh water)?    s

  Approximately how many octaves are there8jku (t0afg a* ,ibvp2 in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display cx; +vl)eshe95 lhq+ wl pd07bpalled a sewer pipe symphony. It consists of many plh70 )l ew+hsb;lpl vq 5x+pde9astic pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sv irq c/3f)iq490u5gbxai -(vi8 srop ound close to the threshold of human hearing (0 dB). Whascfg-u)ir ib85v3v aorp9q0 q(iix / 4t will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB g 8-nlk/ecbbal) z4+gsound are heac ) e/gbb-4 nk8+llzgard simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placj*y f2 ommsw;/+j( ymwed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directioofs;(m j jy 2+*yw/mwmns?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The po- fdjxzsn9qy6u 6r :0mwer output drops by 10 dB at 15 kHz. Whatmfyx 90:u- jnz 6rdq6s is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devicepm,lrd1v la.sfz); i1s over their ears. Asfm l1sz av;.1d,rip)lsume 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 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 gain, 7eg. hg*t3g6 ol)xsliv ro. t2uvw 6f)$\beta$ 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 o/oedrw/5m v6 frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed p 7sp7tllz6 g 0btykn5:oints with a fundamental frequency of 440 Hz and a mapyt7t0bs 5g76nlzlk :ss 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 filled :/res.gfs9ah5gz0f 4/k 5dpv x xxhl5with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above h pgh 9ze k/dx r5a05/xlff gx5v:ss4.the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2fop:)p 6h 5iei.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) wio:p f6)h5ipi eth the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate asru3 2ghaiwo q/9;uwv4 av*;un one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from twovwjm; tc)6 .6xn2pujo sources. The sound is loudest at points equidistant from the twj; 6xo2wv6 t mc)n.jpuo 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 whistles. One train is r- ktd,t1/pl dstationary. The conductor on the statttdlp -dr/k1,ionary train hears 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 whis -1hhrou6knp-ydjf .wf ;5x+atle as it approaches you is 538 Hz. After it passes you, its frequency isfn xy h-kd1oh5.-+ arf;6uwpj measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate th,2 1oavdl1kkm e speed of cars just by listening to the difference in pitch of the engine noise be11klmkoa2,v d tween 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, tok/.5un dm 1oproduce a beat frequency of 11 Hz. The 5k./ odm1unot shorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are h pz57zsrk1d;zm.i2v 3; jgfjat opposite ends 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 frequency heard by the observer when (a) he listens from.d 3;jrzvhps;zgz5fk ij 271m 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 z-ifwsobg 7p3ejf dbd a,i(c/ 8(4-nyis normally about 0.32 m/s what beat frequency would you expect if 5.iscw3i-a 7b8p(eyf f,nd4d (ob/jgz-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 mj7 .:xmq9y lmqrgu-d 8oth at speed 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 kHz. What is the frequency of the wave detected by the bat after that wave reflej q y9gxq. rul:7m8m-dcts off the moth?    kHz

  A bat emits a series of w3bo(cr ;h18tmz 9t cihigh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echtzco 8c ir(hw31tb9m;o from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was ondf7kv7u 0 px)jce used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long7 p0xuv)kj df7, 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 c9q5y h ot7dtah,p*.nb an be compromised by the presence of standing wave7 hy*. t95qod,bat nphs, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involk 3/bd 3-bsdwowygk8 8ves 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 k8y kb8bso- 3d /d3wwga 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 of bo(y;kpo 2+ byabout 1000 Hz is ybp (yk+b;2oo $I_0$ = $1 \times10^{12 } W / m^2$ 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 a: yzuh6.mn e) ztnl(+wt Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes direz.enm:h yn( u6wz)+l tctly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat:7 k 5i nu66vscbp,:h4tqdcue 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