What is the evidence thaq,zen + c),m;ism.judt sound travels as a wave?

What is the evidence that t k.jl q0n7c0kqe;f lah; fst,od;7; msound is a form of energy?

Children sometimes play with a homemade “telephonwt. zi,2ndh y:e” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can bw i d,:.tynh2ze 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 passe ng+pg-axgudfa 2 .77cy gkk.2s from air into water, do you expect the frequency or wav . +2cgupgg.xdfak7k nya-g72elength to change?

What evidence can you give ti;dp j20dg+e ehat the speed of sound in air does not depend significantly on pd02d+ie j;egfrequency?

The voice of a person who has inhaled heliopkr (g/7mk )l9t zy-hum sounds very high-pitched. Why?

How will the air temperature in a roomvt,eh9xv2 xr2-*nambz t-e+s affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sou+et9ne609m e18it-dku vcm jqnds in various fr99 emq 0ck68u-1 iet+ntd mvejequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) space fm(now+7p4c o7x7h pjd closer together as you move up the fingerboard toc4 h777opjm fo+( npwxward the bridge?

A noisy truck approaches you from behi:nufebus 2fijg147i3m5 u p7zb qu5f 0nd a building. Initially you hear it but cannot see it. When it emer75nse4iugu1bf 72ff5m03z j: quibup ges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” wherearp5dz -3qya0y s beats can be said to be due to “in53 -qzydrp0y aterference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowerede :ix* wml9ag9eu:i p4, would the points D and C (where destructive and constructiumlwx 9g*:i e 9i:e4apve interference occur) move farther apart or closer together?

Traditional methods of pcp42 rb9ji+x.lqc0 m trotecting 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 n crpcql+40xb .29mtij oise, 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 thouv;v+( *( b+y0xtyca 1,omssenyatjm 0ght of as a superposition of two sound waves with sligm +1;+tbjysyasty0nxecm* a ,0 v(o v(htly 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 an)0l0 l,ki2tx( scftt41b7yhrpvvgd8 d observer move in the same direction, with the same h)l0dyt7 vsbc l08txf2vpg r4t( 1k,ivelocity? Explain.

If a wind is blowing, will this alter the frequency of the souvjv(.c q+j* chnd heard by a person at + c*h(v.cjjqv rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A moni); icxfoehky;n;cw , fo3m86;c0 jvuktor 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)k xfjfin wyov h uc6c; c;oe;3,mk08;e? Explain your reasoning.

  A hiker determines the length of tc1uxas4f; sgf 1au3: a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the l4xsa 3:1g;cstufaf u1ake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes themtgk29;:u moq side of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the oceaqt 9kg2mo; :umn at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 2 ccs;s:maohip3 n1 /easmh;hbo, f26 50 $^{\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 isstf s ac+urd()fuu ci *b/-0r9 drifting just above a school of tuna on a foggy day. Without warning, an engine backc+s uf irtr 9afuu0/d-c)s b(*fire 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 whe7jy wrp(z.k+2b:y w7,a vpvbln striking the water below is heard 3.5 s later. How high is the ,j2y pk+7zvy.va:lwbrw( 7 pbcliff?    m

  A person, with his ear to the ground, seej3)u: r i0 ex3a+jsyyhs a huge stone strike the concrete pavement. A moment later two sounds are heard from0:eyay+ )rji3jsh ux 3 the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second roj9h7k4yjbn31 p1 ylpule” for estimating the distance from a lightning strike if the 3 b9hp4y7j jykopn11l temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at y / jql/c ct7h.f,s,atthe 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 souypbxxz4 bx ;1;nd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneousy7 suqfv9 vd z(xzi) u9*z mf9z7m5ny8ly at a certain place,fdy999y fz5z uq 7()8v7x*zsmnuzmi v 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 a7whb8 mb*sxg-jlt)2xn airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut do8s7gwbljt*mxxh ) 2b-wn all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to h r3bf3kga5 d.have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the rr335bd. kh fgaatio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a perwxc 76hldi/k;,5kb kbson speaking in normal conversation. Use Table 12–2. Assume the sound spreads ro cb/;,kkbd 5h7wkli6x ughly 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 st9vil +vid. pa1z-vj1 bv+(z dk9d;7 elj2zdvtrikes 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 modestq07vwkkgty 81 amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would0w8ktvqy7 k1 g 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 front of a onclw4e/e;t) . qkik. loudspeaker n qcweteo;lk).k4 i ./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 i*zph iqp1x9c+s the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hinq9h z cpp+xi1*t: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will )sh9jyex9 f,k3j.ouj the intensity incr9 uxy j)so9,jh fejk3.ease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but omb0: (j qqvg+y) jfc.sne has twice the frequency of the ot.0j+:bcgmsf (qjqv) y her. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds h s0jwo5*td-rtt b ):v pk.g+wrxt6m*mwi,y;to a displacement amplitude of vibrating air molecules of 0.13 mm at ikoby)w- + 60.pstdjh**m rw5gmtt;xr: , wtv300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem q3ex /7x+lgnnp.b ;xf as loud as a 100-Hz tone that has a 50-dB sound l3nl q. ;f7bxgep xx+/nevel? (See Fig. 12–6.)    dB

What are the lowest and)gb( qel, cd 1(yqn+yoaj4 vm+ highest frequencies that an ear can detect when the sound levelcyqd, e(ya+n4lb)v(1 g q +omj is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of 6so .w6oahur1kx:d3/x egj -usound levels. What is the ratio of highest to l gd63eo6u.x- owhu: sa/jxrk1owest 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 frequnwc :z k.-jo*.dqvb k+ency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass oncjz qk.wo.-+b: dv k*f 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first y/1i5kh ccgv he;v1+ ythree audible overtones if the pipe cv1keycy hh g1 v+5/i;is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of az zabi+rv;e0(-fsr l 4n empty soda bottle that is 18 cm deep, if you a4 v+bflzi;asr -0(rezssumed 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 spanning the ranotyogi2 (+, vfge of human hearing (20 Hz to 20 kHz), what would be the range of the lengths f +o iyo(gv,2tof pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. What w+wirl +py((n rill be its fundamental frequency if it is fingered at a leyn(iw+ pl +(rrngth of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above *gn 7:jkmyzz 2middle C (330 Hz). *2zn7:kzg y mj
(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 (2+ c+jh2woa/z hfa1r-u/z 2n9jj2tua;cvsk4t62 Hz) when the temperavrt;fkj4 2t a2 ac-ujs j/+2zhnw+oh 19cu/azture 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 20 ;u6c l6c- d j9bew.gr5xknn6y $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the h3z)2 9 aqlbaoes:o2-hn/ oebwuph ;5 oole be that must be uncovered to play D above middle C at 294 He3slhb2 o;) 5p2a:b / nuq-9oeazoow 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+nlqm3(sx x ,y,: ttql 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in belxntq,3l+:tx m q(y,stween. (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 resona xcb y6ixo (8:1vs3b9 p.7y)ddtsnmb mtes at two successitdd 38m 19nxs: o bcb)s y6yb(xvmp.i7ve 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 9 gbv y4bxo* zuy6oe;mgg9+mh4+o;vh$^{\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 the2v8h)8 syxk/tvsn :af audible range for a 2.14-m-long organ pivnysvtf2ks : /a)hx88pe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5+xzfw;6 ukx4f cm long. It is open to the outside and is closed a 6wx4fzu;xk+ft the other end by 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 one beat every 2.0 s when trying to adjust two ;c8-edc:ej4 kaxw rg7 strings, one of which is sounding 440 Hz. How far off in frequency is the othjr7dag: 8cw xke c;e4-er string? ±    Hz

  What is the beat frequency if middle C (262 H*gy8 /yn 5pkgmz) 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 anotherv9jg amews,y.8(d wrh5h. m;n (brand X) operates at an unknown frequewmhj(v yw.9a;.h m rgn8, d5sency. 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 produces 4 beats/s when sounded with a 350-Hz ) t g*tu0uop*ztuning fork and 9 beats/s when souto0)g zptu** unded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in one 2,xj3key u// 4r yhb+.gdkmav string is then decreased by 2.0%. What will be the beat frequency heard when the two strings aremvjk/ er yh+3kxyuga/ d4,b.2 played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fl-vop792ysw c hm( 6bcputes each try to play middle C (262 Hz), but one is at 5.y(cvm b6-2ow 9phcp s70°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, mh21a , pmexdr)h.ap.dn n+i2B, 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 and C are sounde2+ i2emp1.h,ad) xd n.pm nhard 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. A person stands 3.00 m from one 7oubd,(fb1ig/g rzm8bads, *speaker and 3.z871ab(irgd mo ,*s fb bg,ud/50 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 vibrating at 132 Hz, p lahezq22/8 bbut a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is blqze/ h2p8a2 vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many btx)ob)s 8*qxieats per second will be hearo)b 8q*t) xxisd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequencg;q39o 4coeqzm8 iybh 4 wkb+8y of a certain fire engine’s siren is 1550 Hz when at rest. What frequewq4;8 3oey 9b g 8h4z+ciobmkqncy 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 freovtfg1h20- dcquency do you detect if a fire engine whose siren emits at 1550 Hz moves at a spe 20hdgtv-f1 coed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 20lzq9q4d y(y r900-Hz source is moving toward you at 15 m/s versus you movyd(4q 9qz yrl9ing 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 equipped with the same single frequency horn. Whp rb7kzlo7ln8j z.ng g)610 vsen one is at rest and the other is movingv.)no bg pljzlz17r08 sk7n6g toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and xbp-h)+iad xf 5 duy:9receives them returned from an object moving dyu :i bd-h)dxx+f9 p5airectly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a +8hb/gvdm)s zwall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound +sv/db)m g8hz wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler expe+1 crnt7 0aaomriments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical t1n7c+ a0motra uba 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 toeiiibv 5 qa) huy1n4ao/ +s,b. measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound so)/yn4o.ih1 a5 aiqsvbu ib,e +urce?   Hz

  The Doppler effect using ultrasonic waves of frequency nalybn602ymp,iw- (d $2.25 \times10^{ 6}$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 thek stcgk15x p1* wind velocity is 12 m/s from the north, what psgc5 kt*xk 11frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on fyx3 ((2vbdib 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 iwd0 /fmtil; / ,sj b(p8ygi ,*v.nxdvss 310 m/s (a) What is the angle the shock wave makes with the dire.bs;s ftwv,jxi dg 0p, /y/ndm( 8vli*ction 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 spe,qy+e 2k+a jduyue17k cw .2tzed of sound is only abouedjyyc+k u +tu,2ae k21.qw7zt 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave angled*h ae 3tn-e4i it produces ee* 3iahnt4d -
(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 r*z x;toqv0x/o)(b pk$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see ov j * ui*8c4y6/a7op-zryqz f-vb:iia plane exactly 1.5 km above the ground flying faster than the speed of sound. By *vif4ojv oi/6ybyz:7*auc zp- ir8 -q the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses7 lw;ocdqb/ odciq,24 downward from the bottom of the boat, and then detects echoes. If the maximum dw27oqo 4bcqc; li/, ddepth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in tu of0;mp;wsi8 he human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It c: a2hxsl68sx9;sic 2p: d/gnzyq, rtuk-phe 2onsists of many plastic p 2 h lun;xry-dq/k ,6aet2zghip:8 sxp9s:cs2ipes 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 fromk -lf(cny0df5 5faam:tn0 m.z a person makes a sound close to the threshold of human hearinft.5cl(0fym5a: f nza0k -ndmg (0 dB). What 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 sound g: e,oi31nvv oare heard simultaneou3:v o ,nv1eigosly?    dB

  The sound level 12.0 m from ab:r. xtysl g496sn6b t loudspeaker, placed in the open, is 105 dB. What is the acouss496s txb:6yt gr.n bltic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Thov bo6;/pkn 0ce power output drops by 10 dB at 15 kHz. What is the pow/b; c6ono k0pver output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their earsat ic02;u5n4)rpu y/y3ab 3trvaqp7mo. 4r ps . Assume that the ;)v4i 32r 3p5 tqppmyc.r/07au4uaby nst roasound 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 communication*y 06tfrprp jukgz55* s systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frbp,k g1ddyow-9 ,h-sjequency 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 ,cne6 hi7ug 4gv0cpr1 long between fixed points with a fundamental frequency och,gu04 r 6nepgc7 1vif 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertica-e(s. f e-aoaol open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, e(.oaf-osa e-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 frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tk2u7dju k1:a:;a kbgxube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonancex 7b 12au :kj:akk;gud (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonx3 +(sx3ikc+b hek y8r ,bm8adate 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 coming from *8kfmrw y-kh8c(9zho ua* z/ jtwo sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person mocy jk a*(m8zo/zufr*h8 h -w9kves 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 stationary. The conv un, tls;bgu 41r45ejductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of th45jv l1bu ugrn,;t se4e moving train?   m/s

  The frequency of a steam trp 9uw u2m:ig2oain whistle as it approaches you is 538 Hz. After it passes you, i:m2p2wgiou u9ts frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars jus a1gqfl4rms*2 uih 2;ft by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car dr*qmh;i2g 4 f1u lsfa2rops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, soltvisz d.l. v()cez6: unding together, produce a beat frequency of 11 Hz. The shorter onesedvvz zt.l l.i :)(6c is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a: o4ez1 qi2tun 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 whnot: uq1z4e2i en (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 u5( crccp )8bkuhx5l 7the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed alon8c bu5uc) cx(h5rkp7lg 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 wh2/,d iwhxr p/hile 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 refp 2/hxh,rd/w ilects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as/-8 c;ebzribru c*o;hit-1 mv 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 mib zmuc;/rb - v;1eot8c-r*i hoth 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) wasag9 u7t 7lz35fgi kco9 once 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 long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtonel3ig9ak5czu97 of g7 t is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the prese8nqdsgsc:gd )xe;u(4))h lx)i p vd5bnce of standing waves, which can cause acoustxc )p))d ei8;4q 5l: sghbnd (usgvxd)ic “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,” i.nm e;oub/c)m nvolves a long, slender aluminum rod held in the hand nearb)u;o.en/ cm m 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 + )kld*bu i(pbht -5 rne2le2kof about 1000 H k5enldk )2b ieplb2h*r t(-+uz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the son1gwlt-q3zbwzs * nz2-ic boom 1.5 m-z3zqtbl2w wg*-1ns zin after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboaty jx c 6 j6t.u pmfib3fce+pf.w4nh1-. 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