What is the evidence that sn0w bhb.(fq 1pz lqn4e df4(-oound travels as a wave?

What is the evidence that so-2;j rr*egyw nund is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to f+9k1bh x4xpo1nr xa,the bottoms of two paper cups. When the string is stretched and a child speaks into one cup,b4k 9oarxnhxx11,f+ p 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 yo)t7x 4yszhm1 .:p bqonu expect the frequency or wavelengt )qz.h psy4ot1 bnxm:7h to change?

What evidence can you give that the speed of sound in air does not depend signif7b c9 1rehr(vi otj /5/-hibnkicant kj7 9/hr51bi/eibv(-or nhc tly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. W*tjgfi7 i4 : fc3(wzqphy?

How will the air temperature in a room affect the pitch of organ pipee+ 580szl2l)mshjwp qs?

Explain how a tube might be used as a filter to raj: if1/ w-fpteduce the amplitude of sounds in various frequency ranges. (An example is a car muff/fwa p- 1iftj:ler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togethed-jl/k zfw 56lr as you move up the fiw5 lfkz6j-d l/ngerboard toward the bridge?

A noisy truck approaches you frwm9,shq,y/j xrcktl. x.-0du om behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brightewk9/s- .,x cd jm.urtqly h0,xr” — 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,*xs* jd++ luxmw:xdtgw1(yjc 5*4ppd ” whereas beats can be said to be due to “interference in timex* xpmw+ws14dcxd +yud p5j j(g*l *:t.” Explain.

In Fig. 12–16, if the frequls,- rem9sh1oency of the speakers were lowered, would the points D and C (where destructivhs1o 9r,e-sl me and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas witbg:ew8 vfk5p 5h 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 usg8e vb:p5k5 wfed which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of a0fy mxro r9xvb.,)5hf s a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two comp5 x0 rhxrv,m9.o)fyfbonent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sou4f-;al-yomsn je3; -b, hv dt2nbx jz8rce and observer move in the same direction, with the same velocity? o s3x-bfn m-tbalzj8 ;yjdv2 -4e;hn,Explain.

If a wind is blowing, will this alter the frequency of the socdwqi,gr7w e)(y8s;ic ,2 7ato plv;iund heard by a person at rest wic wt8sye,;i, dqoa(rcw;)g7v ip2i 7lth respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positi72g)7yidb po 6x)bxipons of a child in motion on a swing. A monitor is blx bo)bdi) 6y72i7xg ppowing 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? Explain your reasoning.

  A hiker determines the length of a lake by lio ni5z 81zrs2istening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s aftei o85z21zi srnr shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline.h dih3:, kye0feg q0,e 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? As,ie0:q d3hgehk y, 0fesume 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 wavelengthsbtsk 6 smph-(9 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 scj d7*t oek+jzgjy 9lb:+6c 6qlhool of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 kmjdj6t ozgq +jl: kyl+*b7 6e9c 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 cl;8mv7ophb6 y nn6o.wyiff. The splash it makes when striking the water b6mwo87vbn pyy; 6n.ohelow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strcl,2 poyv/k 6dike the concrete pavement. A momyv 6dok 2,l/pcent later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error maden (tq2g lovx9q5w 3a1k over one mile of distance by the “5-second rule” for estimating the distanceowtkq9ql x1vng52 (3a 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 the pain level obvetj14g9r q4mc1h0qo7c1k9rly 9 ot vn3:ebf 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 sounna9m 1ovk2km+d whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a soz fuu4:v2q+9 tnflb1rund level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.4uvt z2uq:nb+rffl 91 ]    dB

  A person standing a cert y1mnz+qu 7/pp;o8um zain distance from an 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 down all but one engine? [Hint: Add intensit1pyq /z+znm u8p7;mouies, not dB’s.]    dB

  A cassette player is said to have a signal-to-2omz a2so3h-49k) awn( l.std-folyp noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each devi)hw 4s 9(apfl3 z doakmtyl -2on2.o-sce? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal convers vjdfzpu2ksuhm.9wxa)wy7- y r4: q/(ation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere center )js7yp-m/way zfu h xu.w4:2dvrq9k (ed 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 eardrum whose area d l.pkp.: s.uvis $5 \times10^{ -5} m^2$ (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- v-z)k1hreetqp-lu m +3v-se is rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in-m --e -rlk3q)+ tphse1eu vzv 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 regif a+b5ojv20 flnp*f prrr5 +3gstered 130 dB when placed 2.8 m in front of a lou5 ol2ff rrng*5+3fjpv+br0a pdspeaker 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. qkld6(, ebrn*What is the ratio of the amplitudes of two sounds whosek,(*l qed rnb6 levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a s5* oaj/n bz+w m ;4vg8rf0mvpfound wave is tripled, (a) by what factor will the intensity increase? Increase bypz*wv 4m/ffm ;08njbar+v o g5 a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice thhfbox *pg s/5+e frequency of the other. What is thbs+ x5 *gpof/he ratio of their intensities?   

  What would be the sound leve 3hb8z-4bmayg l (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molegy4z3 8h bmb-acules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz j9 ob+v0hci0+4qcryd (9wik l tone that has a 50-dB sound level? (See Fig. 12–6.) 0+99wyo ic+chrv( q jiblk40 d   dB

What are the lowest and high6 ;sp53dag mbgest frequencies that an ear can detect when the sound level is 30 dBs;b mp5a63dgg ? (See Fig. 12–6.)

  Your auditory system canl4+8mqli: a )6d3b8akc6-mi q g ijsgu accommodate a huge range of sound levels. What is the ratio of gdk:u 3a 6al qi)i688msgjbi4qm +-clhighest 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 funmvtzni+ qcz/ j2u.;eb yig -)*damental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the stringt/.jg ucz zqyn2ibm*) +e;-vi be placed?    N

  An organ pipe is 112 cm long. What are the fuh2r2b +jn ks/yndamental and first three audible overtones if k2jh2 +s byrn/the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you4 u /tuo-y8vd xlti z /w;kisd3xh)-(p expect from blowing across the top of an em/ p-h48kd i;osvuu txx-/ (3)dit lwyzpty soda bottle that is 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 opez2 j :w7qnua5an-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requin :w2qz 5a7aujred? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string y*d1wkm,p2p; q0dzd3 mdp +au has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original py* qd0;p az1+d p,m32wmukdd length?   Hz

  An unfingered guitar epk.3 +3kjc +lrxe uo7string is 0.73 m long and is tuned to play E above middle C (3+3l.jkecuep 7 + xo3rk30 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 miubcfsm db;;)v3.k6 f jxj ;./yirdj4 hddle C (262 Hz) when r.sh . bf/; yjc4df3jjibu; );mxkv6d the temperature 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 i z 4p8fd ,d.e/snwlu:t,4cyc$^{\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 hole be so4zw ;p9m- jnthat m;so9 jn4 -pzmwust 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 at 264 Hz, 440 Hz,f)(rc ys (*wpk and 616 Hz, but not at any other frequencies in betwee*w r p)(kfscy(n. (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 boq1 b89yo 3xlbzth ends. It resonates at two successive harmonics of frequencies 275 Hz andy1oq 3b8l9x bz 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 dvh2y + /.ngp2d7fcww$^{\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 w)a1wqf p 0*ucaudible range for a 2.14-m-long organ p*f )p qau0w1wcipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to tz8yf4fj ,)zjthe outside and is closed at the other end zyj j84tz ),ffby 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 adjun;k ;ox0kvjuxm0-rj 8st two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? nrj0o -mk8;ku0;jvxx±    Hz

  What is the beat frequency if middle C (262 Hz);n xa3 b6kovg( 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) operate-(x nsey (t 99aqleam0-np4q vs at an unknown frequency. If neither whistle can be heard by humans when played separately, bu 09lq na-epe9a(qn m(v stx-y4t 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 ww+8m la 1 n wjx77rmdp4r6s.cc1skwl(hen sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibm 18.wa4 snld+sp6rclkj r(ww mx71c7rational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in oju) /tdr4otm 8ne string is then decreased by 2.0%. What will be tht jd)4m8to r/ue beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be h(4svgwj .yim:eard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the ots( :wygj4.mv iher at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of(21tbw7dqxtapl :x l : 441 Hz; when A and B are sounded togetq 27l:xp1tab t(: lxwdher, 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 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 stand iwo :mn;xsumo4p,y:0 s 3.00 m from one speaker and 3.50 m from the o,oiy nm 0xm p4su::;wother.
(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 atskk s2 /vk+lyqto:)33q scm9zw,9g da 132 Hz, but a piano tuner hearls)q 3co/k yq+ks d,wvg3z:ts ma299ks three beats every 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 wavelengths 2.64 m and 2.76 m in air. How many beats p dd1. f3oefvfu b xfr(low) 9zdq77/n9er second will be heard.9endf wf qo)f fvox3d9/(br 7 l17uzd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fd1,p(i(6-paxpbvdlt2 eye/ t ire engine’s siren is 1550 Hz when at rest. What frequenpyd6l(t b /x-vped2e1(a ip,t 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 ymq -i 6ls 1zwiags7u7.ou detect if a fire engine whose siren emits at 1550 Hzmlw sgi 1 i67.sqau7-z moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is mxdhvcg: jx368 oving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly 3dchjx v68xg: the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When o)e1r93rq88s)32it1, frm q e dlmqh b wrr:qdcne 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 Hz. What is the frequency the qrfsh ,rlt1e i 88bw: qm3m)2rc9dqr)3qe1 r dhorns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic s ieuh5)26nkm7 5jwrk hound waves at 50.0 kHz and receives them returned from an object moving directku5w 6rjhn mki752) ehly 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 it flies, the bat emits ak30g v/ jylz9w* i)5pkgcqv(pn ultrasonic sound wave with frequency 30.0 kHz. What frequency9ppkv lj i(0/z5vqc*g)y3 kgw does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving fla2 qq,*vhndt y9t 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 appr*tn d,qqvh y92oached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to medjckj7b20a+g b j /l1xasure 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 mxbd k jc1gj0 2+7jba/l/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 us re ma/r encr786.u9aorkm08 fsqk-m8 ing ultrasonic 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 velo ioli*f)2 2dvp vxbi)2(is8wicity is 12 m/sdiios2 )lfw2bv 8ix* p)( iv2i from the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on l. xomv-ke81r wj4 p2,:vdyars and 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 avh8x+ws*w9ml d)hl o7 t Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makel8 +wms9whol h7)v*xd s 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 a planet where the speed of sou+ 2 awfpazws7/ycojz /ej.r.3nd is only about 35 m/swpzzw3a s.+ae2/rfj7/o.c j y
(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 850 m(gj.wn1 :bew6nsh :w0 m/s strikes the ocean. Determine the shock wave anglen1: whsjegmw:bn w( .6 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 e*hci -ha *yp1$/theta$ 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 k uq.v k7vp82y na i6m:p:zcu8cm above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled cm8 v.v:zkpu8nu qp a26y: ci7a 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 20,0 g6jdforw +hp0j0+0cuj7bc( m 00-Hz sound pulses downward from the bottom of the boat, and then detects mohc u +gf0w 6djjcp0(jbr07+ echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible rangmnqqw ala;:,-chae 4+e? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphamm pdb2s pzxtb-8kt62:9 t9qony. It consists of many plastic pipes of various lengths, which are open on s9xt8a2pq:t 2kd9 mp t-mbb6zboth 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 persons20--g euilpa* (l vzd makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 (* a2id- e-vsll0upzgsuch mosquitoes?    dB

  What is the resultant sound level pxs14gdmm3it elz /h8x0 .y3awhen an 82-dB sound and an 87-dB sound are heard simultaneously?1/3a0 em3h84l tgiyxx sp.zmd    dB

  The sound level 12.0 m from a loudspeaker, placed in the open,us.- ,zqt vtt)s q+2g fw)8huc is 105 dB. What is the acoustic power output (W) of theg wf +usq8 ,tzt)2u -ht.cq)vs speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W ou bu 3v:xk8 +t85k00bibbnuw eotput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is tuuv bbe3808 ikxw 05n +bbk:othe power output in watts at 15 kHz?    dB

  Workers around jet aircraft typt*kmp bsurev5; uywgji4;85(c w b-8p ically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power interceptep5r -m4ciwket*;8ysuu jpb( vb;8 5w gd by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gaqb 6/t6c1h07 7 k t:tnfdsazlkin, $\beta$ 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 frequency 0m+rl /)he ebt t0lq;d1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a02h+tdj hwu5 u fundamental frequency of 440 Hz and a mass per unit lengt205 duhutwh+ jh 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 ap )x;4xg udxj* vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distaxd )*jxp g4u;xnce 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 nel*,a kyzvr h:u7 s02pxar a tube that is open at one end and also 75 cm long. How much l2xask :r0h,yz vu*p7 tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to rb.lst pa*m 1tk4t1bz8esonate 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 500–1qx5by yhx;qk 0 i82z,(fm6pze000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source thap6mqx 0z z ke, qy8ybxfi5h(2;n the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor o 9 fs.ihkk58v pii5ej4n the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What he.45if5ik k pvis 9j8is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you (m2619qs)g7oard8ulzht of n is 538 Hz. After it passe )fml zgdoo 97anrh 182(tqsu6s you, its 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 just by listening to mm2zvqkbn t/,l3-h +i the difference in pitch of the engine noise between approaching and receding cars. Suppose the soundlqktn+,h 2m b3z/mi-v 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, sou-f t/t ncq/v 5hpls*f*nding together, produce a beat frequency of 11 Hz. The shorter s- ctfnftl/5pqhv **/ one is 2.40 m long. How long is the other?    m

Two loudspeakers are at oppositeqtfx .-(z*czjxf;b5j 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 fb5 xcft j.zzx-f *jq(;requencies 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, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s wh lxqdh mb5;7s5at beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume;sb 7m5dxl5qh that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while,vxr1jticsx7j 2b9* j 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 afterixxjj ,ts*2j 1vc b97r that wave reflects off the moth?    kHz

  A bat emits a series of high frequency dpqw1 k (e rdsl9)szl)1/mf,csound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is abqsmdk9)pe,zl w/cr(1 s) dl1fout 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine 2h.,dc8i(x amgmf6 5s kyozn+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 frequengm c(aky x65.sz2dhf+,m ni o8cy of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presenq+m kq.hkj -fg02hy;e n26 gewce of standing waves, 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. Calculj2m2 fq ekghqgw6+ ;h- nyk.0eate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, callxy qnsjnki65uw.th3*): r r2 bed “singing rods,” involves a long, slender aluminum nt2nyh)xw: 3 rsb kj.ri*u 65qrod 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 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 hearingp lsvlcc(cig v+vr0,6ezr22 3 for the human ear at a frequency of about 100,r 0 lgpcvlsivv3r2c+e (z2c6 0 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 ax4kbpoxe6 dmgn .w+g 9tglv.; htq0 ;:t Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitu9 .x 4lhgkv.tb; 6exmn:gq; pd otw0g+de?    $ \times10^{4 }$ m

  The wake of a speedbweusj e ae-2.se 8+7dzoat 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