What is the evidence that sound travb k5z6-(qpqc6p8 yrp6 ir+bpnels as a wave?

What is the evidence that sound/t02t j uxcr9m is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to lm9v-t r,vwc9 the botmcw t99vr,l -vtoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes fbe7luf x ncw4;(xscd;j5(w 3m 7g 5flxrom air into water, do you expect the frequency or wavelength t e5mx5g;(7s7(clxf4;wnful3 x cbjwd o change?

What evidence can you uzg0 z56i;i:w:qeunv 1k5rpe(lg z x, give that the speed of sound in air does not depend significantly on frequen:g6ezxipzi5ku,( vw z50l1 :e;qgr uncy?

The voice of a person who has inhaled helikoej.h36ub82o/e.ej1 oy*m 2 6bfq qyol zyn 0um sounds very high-pitched. Why?

How will the air temperature in a room affect gm6l s c)0mg/kthe pitch of organ pipes?

Explain how a tube miain/gf-j ya2 gr )*cz:ght be used as a filter to reduce the amplitude of sounds in variousacg*ig:2yrjz -n f /a) frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together ab pbi33ty vad0pg 7+h1s you move up the a 30y1pd pg37+hbtvib fingerboard toward the bridge?

A noisy truck approaches you from behind a buxti7sab6duout 6y- ,+ilding. 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-fr6od6ybxauitu t,+s 7-equency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be du yp bnrt;9 6r(i*7kj79n to yg-j21xbfyx6nwse to “interference in space,” whereas beats can be said to be duebw obkx*6-r9pn rnnty 17ytx;js92 6gij y(7f to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pqah2 3j1btb)/s9q2l*akw)u lnto/n l oints D and C (where destructive and constructive interference occur) move farther apart or closer)u)1 t2 j/wba l/2l9 qnqa*kbh no3tls together?

Traditional methods of protecting the heapydy djensh4)ad pr ;0/0+h.mring 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 t0enyd 4 jhda h;m/d)rpsp0 .+yhe 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 thougndaw3g o8c9. ght of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In38 n. 9agdwocg 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 s,i uxqp5xbot7g( lttia hv2f c*d3bj (1 y+57qource and observer move in the same direction, with (ibjd*5a7lchbg( yo2 t 1xuptt+7,q5 if3vqxthe same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard bsv.4knjjfmo(xhlo4 vv(;a(7:i pjj) y a person at rest with respect to the source? Is the wavelength or velocity chan.sjf)(ji7vomv av4 xol (nhj: 4; pjk(ged?

Figure 12–32 shows various positions of a child in mp7,goy x/w 4juotion 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 whistle? E u/xwypoj7, 4gxplain your reasoning.

  A hiker determines the length of a lake by listening for fvl5n34k9 e+ez5hdwc the echo of her shout reflected by a cliff at the fen hzl34+f5 w5dc9e kvar 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 3wel2i a6u-fi howp*u8 kw1 (mbelow 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 iiw(361 le a8po* fhkimwuu- w2s 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavel5s r-l6 jxzz5pengths 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 abovi oyh+ 2,,ljbve a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses y jb2oil, +,vhbefore 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 stripp l +bgh* . /:v9(ujndcscqr4king the water/u9brgcp.sqp4 (l +d: njh*vc below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a hugerr0xl-+z+d-4f b kmqv stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occ40-qdx mb r-rz f+lkv+ur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error03 v/) 2nlomqiklyx9n made over one mile of distance by the “5-second rule” for estimm)lqyn2lv3io0 n9/ k xating 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 sounucf280r6 5w dhhjd5+o41,g kq 0mcrvjyhcd d9d 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 lev b*ae7wnm9b m5 ce1j,lel of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a souv ,pb w)wb,f.yi l4:*usw4pfpnd level of 95 dB when fired simultaneously at a certain place, what willyb)u :w.4 f 4bfs,pipvww,*lp be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplanemykk2okpeu7 6u,6 59-x bvqir with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this q - kkbopem vi,267ykx u6u59rperson 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, whereas62ov08o / g;k jjzt)wjtn7tpa for a CD player it is 95 dB. What is the ratio of intensitiek0jw /ot o6aj jv;z7gnpt )t28s of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power m q3z:j 5lh)6 cdww3vgt0 oa8noutput of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere wz6mjnoag3:3) chw0tv l5qd8centered 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 e qc2vbd g 0ut(1bf3dh.ardrum 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 amplifier B is+las /:1cxubn rated at 40 W. (a) Estimate :bxnsc/+al1 u 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 when placedq akazqi0t8i o5 mls.697n9oh 2.8 m in front of a loudspeaker on theaoi.5mkan90 h il6789t zo qsq 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 dBe: g *fc)d9h/bs9 xssmb 5,obv. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: scs:s5go)/b exfvb db9 *h,m9 See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wis altb6ls*82:lpgg/6gznq *rll the intensity increase? Increase by a fact lg6sr6l8*z2atbng g*:slp/q or of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one f,vtikr7d,aog22y p 0has twice the frequency of the other. What is the ratio of their intensities?2 p,o0ykr i2,7a dtfvg   

  What would be the sound lev br **wiqr8zpbp 2-:enel (in dB) of a sound wave in air that corresponds to a displacement amplitude of n-*8prwpq : *zbibr 2evibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to e2s .tnb4gg7k qngtuhp5 *n.; seem as loud as a 100-Hz tone that has a 50-dB sound levelg;beg7 pksq uthn4.5tn 2 *.ng? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the11dnlhuc gx i2 9i,p,ikm+mz 4 sound level zgkicii,1nml u 1p,2+d49mxh is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge pz0mp,xqst1i c76 tsu nai;1;range of sound levels. What is the rai07zx,s1 6 psnuat ip mq1;tc;tio 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 fundamentc4)e08 uxbxlw al frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Underlb4 cw)xu08x e what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundam ; ghl h*islbuyk;e;)1ental and first three audible osi ) *lhg;ybe;lu;1hkvertones 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 freq hxsod j88 x9nw(gyyi/ *xy:6nuency would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if w*i6xng( yxj: 8dysy o/8hnx9you 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-tube pipes spann62l ty hpkzfd)a2 ue.:7ag5 zring the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required?f elz5a)pt ak: 7uy6g2dzhr 2. $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequen3 1 4k kwr/b*8wytpx6zwemv 5icy of 540 Hz as its third harmonic. What will be 4*yb w81r ke6mzv/x tw3ki5pw its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar stm,0cnp53n;ch-xy 6t*pwb.fbxar 4fbyj1v, dring is 0.73 m long and is tuned to play E above middle C (334fmw,cnn y v 1*p.br, 3hy6- abfp0dbx;5j tcx0 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 middle C (262l:b +( ic-ovor Hz) when the temperature is 21o-rivl (:bo+c $^{\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 4 bhsz9qcf h:d35mrf(at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 *8a k pto3( h/yleh4dvshould the hole be that must beylo8pt *eh34( kva d/h 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 at 264 Hz, 440 Hz, and 616 Hz, but noysy md1vn:+o8 t at any other frequencies in between. y + nv1smd:oy8(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 resoveyw ix15d;tnl-t 0am3w6rr5nates at two successive harmonics of0x-li5 vrwdayew 1 tr36m5;nt 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 bl: qf* 7u+wpl$^{\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 x ex1+ u9bpb4 a;,yvlsa 2.14-m-long organ pipepsba9e4yul,b +xv1x; at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 c m n35q c7du;1pie rx j4-vgb.dtlqm+4p9kc)km long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range7 qvq-mj1 g44im.) e;ux cnd+t59pbklc rp3k d) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tryimio) n8)uh:dmgd9cs : ng to adjust two strings, one of whics9h m)oud:d8mnc :gi)h is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if d n+kslg+9c-o middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) og-lg a mg9xrts)lpms6w33)ac8,i 5d kperates at an unknown frequency. If neither whistle can , agi6)gp8s3kxs)5mgd-mc3l 9tlr wa be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning0 ka bxkk5r+ oe. 5f*sogd1gy9 fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frogy01e+f 5r.9s5xgobk*ka d kequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same f30sc7sf4ksvbvvk hv/ 6i sfl*/ej.dw*5rf x.requency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be td5* e/hks.sc43* 6brv/sv kwxffvj s0vl .7ifhe 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 tryoh :vm +zv2 .y20)qlofn;vjeh to play middle C (262 Hz), but ony f22e h+0;hv)mv.ojloq z :vne is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C.qw :q o3n:nft(+l/cl9r1:r8po5aqc xvll (ug 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 and C are sounded together, the beat frequency is 4 Hz. What are the po c+ 3l(5 qnt1clofn(xrluav q8qr:9:: gpwo/lssible 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 3ae:yw*0f8ay* up rj9f.00 m from one speaker and 3.50 m from the o8y**fa9a wj0yrfue: p ther.
(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, but a pian ,/xae-p ph:fwo tuner hears three beats every 2.0 s when they are played together. (a) Ifhpe/ f:xw,-p a 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 wavelenglfaw.* ytss72*o+ct 8o5 vcrnths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assa5ywn*8osfcvr 2 .+*co7 ttslume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engin- u(ff+y2os yze’s siren is 1550 Hz when at rest. What frequency do you detect if you muzffyo2- + y(sove 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 detec 9k( is wvv8y;on8s7tkt if a fire engine whose siren emits at 1550 Hz moves at a speed of 8vi7sv8wynkskto (9; 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz q*)qb86 umeg)*lx bdq source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are tgb m)b ld8)*q*qeq u6xhey 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 freqzn ;0dfua(c;xr eyo 97uency 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 5.5 Hz0;cfr (y7xndoua9 e;z. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultras2: :-mze/qepj,,klkufzy c ,oonic sound waves at 50.0 kHz and receives them returned from an objyfk,okuql/zcjp,m:,z -e:2 e ect moving directly away from it at 25 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 igitc+ uc/5)b nbq2 un6t flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency dn6u2uc)nt/+ib cb5q g oes the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was plj0lkcy/- 5fytayed on a moving flat train cay5 cyl0 jtfk/-r 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 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure br r14j7sx zi)ubiwp, t/(/ri+ oo ff3tlood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be ztwuxo(i/r3+ )fjrfsp1r i/4 t i,ob71540 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 ultrasonkptnd6 kp i+c )fg694kic 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 vmd /w,kvz-w9 helocity is 12 m/s from the north, what frequency will observers hear who, k /-9wzvhdwm 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 objecthsl48tt (v4lkcp a kd12w-x -t 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 Mach 2.3 where the speed of souw4kau yt, s0vo -gt-nsow6b 3.nd is 310 m/s (a) What is the angle the shock wave makes with the direction of the airpo st,- ywnsw u0k-v46goa3bt. lane’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 thi m8u6-g jih)otn atmosphere of a planet where the speed of sound is only abot mgij uh)-o86ut 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 ocea nvc42l4 h )zrut1fj9ac57zeun. Determine the shock wave angle it produhcjf)445 an9u2uv17zrcet z lces
(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 s 1w:x9kjwe6 q$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead andv4*.gwthzxdbn2n w2p g6 1n+r 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, the plane has traveled a horizontal distap2+ 1xnb w4wz*r2 . hnvgd6tngnce 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-Heq-kq9 zh p2xw (ve)9mz sound pulses downward from the bottom of the boat, and then det(x ek- vqhw)e9m9pz2 qects 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 octapa5 r5bn7 7w l,q x/:, wligg/yqj.psyves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display calle v p(o7h9oqk.ed a sewer pipe symphony. It consists of many plastic pipe9opve7 .q( okhs of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound clobjocac ,3e8v -;(h vxfse to the threshold of human hearing (0 dB). What will be the sound le 3covj;ef vhb8x(c, -avel of 1000 such mosquitoes?    dB

  What is the resultant sound level when ajdu4e:*dgd6474pxvwrnn3st c6a0h q n 82-dB sound and an 87-dB sound are heard sid ua47qt xh 3 n4*6dpjwn :60v4gersdcmultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Wha7tc45xo3aby ze)r*n)gtg . cpt is the acoustic power output (W) of the speaker, as.3axztbpg74 c yo* )etg )r5cnsuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 13-1sbq1xjuh8 bp4 xuvst85 zx000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in buxhs buxqp1x- z45j3tv881s watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over-c5j j*r8e 4ux0yc3imbrb2 nb their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distcc by 38ji-2ju*berxn 4m rb50ance of 30 m from a jet airplane engine?    W

  In audio and communications (ij 6m 1ew:nipsystems, 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 t/0th6 34g i9ixsuainp o a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin w:v pc28b/0o ha4 qa;vv g,oxjis 32 cm long between fixed points with a fundamental frequency of 440 Hz and a ma;ojgvcwb,v /42hoaa0p :x8q vss 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 wit2ck wmbn0pl :85 7h3 gv4jguaeh 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 fo8p 47kvua5gcge3bn:m hjw 2l0 rk when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is ob gso 9k+qsv phq;1yn)gl 70;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) with the third harmonils0sov q q+b)ph;; knoy 1gg79c in the tube?    $ \times10^{ 2}$ N

A highway overpass was obse b(pnups2 1z4arved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range cominzim5ln2f 5/psg from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is l2i/ z5m5pfns, 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 +deile jo:lte;pg va4.q, b:0 stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is theib vjp + ,:dl;:4 0teeaegl.oq speed of the moving train?   m/s

  The frequency of a steam train whisttq pth3 p319zmle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume cons39 pzt1mpqt 3htant velocity)?    m/s

  At a race track, you can estimate the speed of cars just -7:golv ke5(+qlpld, ulfkb) by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of af )+: q7bgldve-llo(5p, lku k 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, sounu)8u 0fcwo bvt+(u+c (oxwcqul,jl9:ding together, produce a beat frequency of 11 Hz. The sho+0 cvof8w 9,wtq(cju+bu)x oucul (l: rter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past at hlo+; ho+g r yrg6b8nmdkf5,:afr0) 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 the position A, in front of the car, (b) he is between the speakers, at B, andh+0lfhr ,;rbnyk)5ord8m +ao :f6t gg (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 what b v//*s c2h (e:scvlpsceat frequency would you expect is:(hpcc/ v/cves* 2s lf 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 whucj12wkalq7y7qw*w ) ko gd( wgl+5c-ile the moth is flying toward the bat at speed 5 m/s The bat emits a sounlqw kwjg-15qc 2)duk *+g yowlw7(a7cd wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequencyd-hbhln/ xr51 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 echo from one chirp x/5lr bhn1 d-hreturns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send sig bn5xgnlzf:1pxc/.xm(d t/ v1nals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overton/ gbl xzf( m5n1v:dnxx 1ct/p.e is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be comp,dci/:e5 /c u0 lwxgjh 6:hsefromised by the presence of standing waves, which can cause acoustic “dead spogejcl6u 5h/:he,w i:fds0 xc/ts” 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, ca. gcz9bd0fcw(7yrq /q6/da uglled “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit7 0b d qac. u/9yg(wqfrgzd/c6 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 frequei +u fpxon7,cw6. jan1ncy of about 1000i1unw6c, +opa7 nfxj. 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 observxekkp ;vxw5p kz /3 )l0kand.u)+(gaver on the ground hears the sonic boom 1.5 min after the plane passes dinv3k;.gx e /zak5kau(px wpv0+) dk)l rectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 3e*ixibve53 xpe 2i8a fbpn *:$^{\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