What is the evidence that sound travels as a se.1w()fwa0g2ippvf7 cxm -vwave?

What is the evidence that sound is a form of energyh-uj7jve ni.x zn9)04n6 a lqg?

Children sometimes play with a homemade “telephone” by attaching a *uay2pah sw *:/xrd7w string to the bottoms of tsyw ar2dp u:/*ha7x* wwo 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 from air into water, do us j(dw+lw.8 cyou expect the frequency or wavelengt d8juww+(. clsh to change?

What evidence can you give that the speed of sound in air doeq+g,y uk6h lb.s not depend significantly , qg.hl+6 kuybon frequency?

The voice of a person who has inhaled helium s*: ykg)svas (aounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organv1:njsa / mg mz pghiln 1qbt72w1/*;a pipes?

Explain how a tube might be used as a filter to reduce the aj.ckvu..w m9s;d cro;mplitude of sounds in various frequency ranges. (An example is a car mufflerduv;om.w c;.kr9sj c. .)

Why are the frets on a guitar (Fi girp5z)t8,rbg. 12–30) spaced closer together as you move up tpgt)8r,z irb 5he fingerboard toward the bridge?

A noisy truck approaches you fromze*;u 8jlkeqq)w fv k3 k:-l7k behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly q7kk*uewekf;j3 :- klz)lqv8 “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 i 7fkflamf i)23ivok-kh11 z1un space,” whereas beats can be said 13fifu1oz 1l7kkhkmia2fv- )to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wo-n-kl9vy at zu+f.t9xuld the points D and C (where destructive and constructive interference occur) move farther apart or closer together9a vlny-uz+.9tkft- x ?

Traditional methods of protecting the heari)07c pc:c3sw ahyd d9- sjr:l ejm3j-o:ffr 7dng of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding0ocd dfl7:ahspcjr:wf 3-:e9)y c3 d7rm-jsj more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Eachcyn4)t5 4 bsp(hv,gtc wave can be thought of as a superposition of two bp, gh)s4(c45ny vctt sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if t/qbacv h 5d4qh+o5 mo)he source and observer move in the same direction, with the same velocity? Exp55mq)/ v4+daqboohch lain.

If a wind is blowing, will this alter the frequency of the sound dmxnb7/ev7v0 (;k vcjheard by a person at rest with respect to the s ;cxk/v7 j(nbd v7e0mvource? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child b1uf+ n6fiak 6;5b c+ll* ab6z3qxqfbin motion 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? Explain your reasln6*+f16q+3uax fcbbaf qbi kb;z5l 6oning.

  A hiker determines the length of a lake by listeningkl a(3p6mdtl-kes) v r: a6kk9 for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s a-()k vmtk9spa:a el 6 klkrd63fter shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the echb f*lejr4t/+po of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at t b*/+etlf4pjr his 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 aireitdr-- u hggh:1 *9eb at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuz;2moumn3 ldjx:q) z8na on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fishnz;mj2 qx3:ozul )8dm ,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when st/y :(zkn s9cmid4:qe jriking the water below is heard 3.5 s later. How high is the sn(ejiz mk / y:qd:9c4cliff?    m

  A person, with his ear *hqfpug . l*8 r (kj;a2zotem4to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds areq(tzal2 hge*.j*p;4 romkfu 8 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 made over m.kgz g5.c r1qone mile of distance by the “5-second rule” for estimating the distance from a lightning strike if t zcqmr.g1 .5kghe temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity 29 o(osl0o9hqkci 8jb of a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensj ndvls .-re6 ,cr5p;xity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously aud3b9(ejr e w .m2w.ntt a certain place, whatbewe2u. 9n( wrm3.djt will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance f vm7uhskg-a7( rom an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would tv(u7 am- k7gshhis person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a sz l jfiy78lcc5*k.p3a u3ah5kignal-to-noise ratio of 58 dB, whereas for a CD playerhji5k.8 py cc3 57z*3fl alauk it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powe zp )cjm(+slpcz qo(34r output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly zplccz( qmos3+j4 ()puniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area i 9ciug+-rpn76f at4 hls $5 \times10^{ -5} m^2$ (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 :r jtgl260i*h.q gpqfkwt1e) pkoc82k8(y ot W, while the more modest amplifier B is rated at 40 W. (a) Estik8p )fi *q2l. ygtgt(ohko1w0jcp8r: t26kqemate 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-*c er8 tfkzbk*+ u.lr registered 130 dB when placed 2.8 m in front of a loekrf ucl + *r8tz.*k-budspeaker 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 2.05dg hvbo.)2ql6jhma fj 5:pzw :pv) z0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by mb.2p5:jhvwag)d 65pfj v)o: z l0hq zthis amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fz(45+ * eac7( gtk1+hccvpifphvx zu,actor will the intensity increase? Increase (f*4+zcp ,x7chpiv 1 +ce 5utvkzg( ahby a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but on;(b r4 o.yrgc+ *p*awtuyk x7he has twice the frequency of the other. What is the ratrcy*twua hy;4b+o(. x*kpr7g io of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds t esk6 tg -g(u*0g ))0accjsoumo a displacement amplitude of vibrating air molecules of 0.13 mm at 3o emsjg(tcg- 0c0uu)ak s*g)600 Hz?    dB

  A 6000-Hz tone must have what sound lep5;fwxnraffht5w1; , vel to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12fr f x 5pwf1ht5a,;;wn–6.)    dB

What are the lowest and highest frequencies that an ear can detectu (l 8dp o, j72fnw1vnktmz+,z when the sound level is 30 dB? (Semv , p1w8zfn dj,7ok2nz +t(ule Fig. 12–6.)

  Your auditory system can accommodate a huge range of sou bt my9*s9isx*nd levels. What is the ratio of highest to loweys*ib99 msxt *st 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 fund m2/wl*uj7kua5 wbt2s amental 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 string be placed? *2 j5awslm27/bkwu tu   N

  An organ pipe is 112 cm long. What are the: qgbe *53f*wk woqrm8 fundamental and first three audible ove 5fmow* k3r*:ewqbqg 8rtones 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 frequency would you expect from blowing across the top of abwk j.bef ;vb2j +6n:q ju8r2dn empty ; + b8u br2.2vjw ejkfqbdn6:jsoda 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 op a26brp.8t 3w oye;xwlen-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengl2.; tao 6 xpebwwy83rths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 5vkhz +smrr 29h6.7v bf40 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length vmrzk672 9 hshrb+.fvof only 60% of its original length?   Hz

  An unfingered guitar string h,x7ipawera8o6/e r 5 is 0.73 m long and is tuned to play E above middle C (330 Hwoep/,7 a ir58eh6xr az).
(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 emits90xwjozqssa4/ qcn8fw s77s4 middle C (262 Hz) when the temperature is 27s8/ojq4 swsnz904w acfx7 qs1 $^{\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 r0/vitsp8ld 6 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 shoul kf, )b ;;9hoehgiax.e4a nw+i*fprs6d the hole be that must be uncoi)ew+x.eho kb ;r f,4n6ghpsf;* i9aavered 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 ls/f97qa e35 o;xnqxa264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a clfxna;7/e xl9 aq35 sqoosed 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.an no( rfmzix zc1,06; It resonates at two successive harmonics of frequencies 275 Hz acfxnzon6a1 i(z 0 m;r,nd 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 o ia0m;z-oc* vzyx0+s$^{\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 v 33sw 7 wm(sfcn;;qinpresent within the audible range for a 2.14-m-long organ pipe at 20s7 ;sf q;wvin3nw(c3m $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxi t 1xrpe)aj:/ubd2b l 3/j.anemately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12ae/.2)b plx1eraj nt3jd/bu: –6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears ol m tdqoh-zh c.jpvz9)0.g 2,cne beat every 2.0 s when trying to adjust two strings, one of which is sounding 440m z2lhzt9g-.cpv odj0) .cq,h Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle Cnwa*:/pn glr) (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) oper1w5jgmd g06zz+ .i dbnates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequenwigdj 1+ zb5mndg60z.cy 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sound ep wv4vu5-u0j1a)xb hed with a 350-Hz tuning fork and 9 beats/s when soun1bv4a-pu vx h)eu50 jwded 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, 2ei.*bit -kcm 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hincm -i2.b*ki ett: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play mnw.5bvlzx; x6 nv89b od)2snk iddle C (262 Hz), but one is atxw)b26nx;l knb89dz. svn 5ov 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork Bl)kxnc .yq3cy- 7pk 6u 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 px cy 6k7kup3.ncylq) -ossible 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 dylbvq, 2atur 1 ,r9j- 7rkf: ifa uym**zs+*p1.80 m apart. A person stands 3.00 m from one speaker and 3.50 m fr ya1*ua9zf fb2tsyr- i: k,p*7dq+um,lrr* vjom 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 vibratingm pu*kmcvx /fg3 5e/4rs6la *e at 132 Hz, but a piano tuner hears three beats every 2.0rm/e*3l 64f*x kau 5gps/mc ve 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 be odofc59,adw9 ats per second will be heard? (Assumecwd f9d9ao5o, T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when 5 f4yfzf/t wwu3nlx) 6at rest43xflf tz 6fuw5/ wn)y. What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engin-lm 0so v3ai4dknk58ue whose siren emits at 1550 nu5lk08mid 3 k a4os-vHz 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 20009rzq/ lgf2hrzx(6 d,c-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are thezd h/rg r 6l,29f(qxzc 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. When of3 jjm6 h52y6frhan 4fne is at rest and the other is movin35ff mhr4fn6ja yhj62g 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 receives t 0gf*,g jk3ys2w ob8jghem returned from an object moving directly ky8 2ofbjws30 gj*g,g 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 fliesky1z i:09o tgs, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bagoitz90:ys k1 t hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experime;j2dp-y pux.7mj. hdbnts, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba plphdpub-d2.;jx7 y. m jayed 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 measure1uoz na*y,.7t z r8lu( xmzwpd*zb,b3 blood-flow speeds. Suppose the da8 rboz3*m .,t pnbd,u(l z1wz*y7z xuevice 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 source?   Hz

  The Doppler effect usi5)ztta( g0nuf o8mog :ng 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. Whetlk;t atg m991 j6:dton the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at resj19tk6tt o9 :; atgdmlt,
(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 moaphqi0g *(8e fving 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.b 8px0vw(k )ye3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s mop) xy(wvb0e8ktion?    $^{\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 planeeo-m,.n0fj z(t1ehrc y 9:wwwk e 4z9wt where the speed of sound is only about 35 9ew4we:zr1f(jh o tycwz wn.9-,kem0 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 a7rw.9 djlrv9 vnglel799vj.dwrr v 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 )g8fq( ye9 fbf$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the grbz.p/k (l am*sound flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled aa/(l p*s.zk mb 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 puls8qcg5h l rmq;8es downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, whatmlrhg88c;5 q q is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in theawm;lou 6 k amk1olm 3s8i3rre+75f5n human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer 7ec-ab. l9u p 0 -/aibk v1rsibo9vu,rpipe symphony. It consists of many plastic pb.lvao cu b/ieis,9r0-r1 -bu9 ak7p vipes 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 f.:e xo65r2ngdpvi 3pdii6z0rxy :3 pfrom a person makes a sound close to the threshold of hu: izxr 6y .6 ddo2er:pgi 3xp3nfpvi05man hearing (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 are hea 6xbcjbm06ty*v*ud(brd simultaneously?m j xu0y(tdvbb**b6 6c    dB

  The sound level 12.0 m from a loudspeaker, placed r(h morx6+mk)in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally i( xhmkor6+ r)mn all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dropsuig jep4/ +zbu9evdmu57ee d- 4 .0gxd by 10 dB at4e/ vge pzj-.i09g74dumxued +eubd 5 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typica xqvn:ib7 (bn:lly 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 intercepted by an unprotected ear at a distance of 30 m from a jet airplane qxvn:7( bbi n:engine?    W

  In audio and communications systems,riq-y aktc qt 35dx(t6;qmn)0 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 violi -q b,2zhoq-5jl oj8nb72xntu n is tuned to 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 is 32 cm long betweec7lx/)6*y sqv oxrzuk,kv 2 ahd(8x j8n fixed points with a fundamental frequency of 440 H)/*xkhyj xu c,o2dv v6qxz7r(lk s8a8 z 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*r p 5tr65t9xpw dm4uc vertical open tube filled with water (Fig. 12–35). The water level is alpp5mwxcr 46*59u ttd rlowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open avm4/12n s/u9 z zauwjqt one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in itswz241 vnqzaj u/s9/u m fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop (s(0p7m27b;t 4qmmw*cn3swkfjeo ,f d $\frac{1}{2}\lambda$) 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 comingqk; d .nfe4tpmf3fc5d:g h 2q8 from two sources. The sound is loudest at points eq qm5d kn 8:p ;t2q4fedff.g3hcuidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor9fl;xha42hoq/q )puggv pc+ly qj .81 on the stationary train hears a 3.0-Hz beat ;2qfg apg+oyh9.qxp)clj/v1l8 4u qhfrequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hzxkf 41t5iqvni/1nv 9eo:fha+ . After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (a9t:fo/ 1a1n5vivn4+ ixhfkq e ssume constant velocity)?    m/s

  At a race track, you can estimate the speed of*2 hr8-n ng5i:3dii ygmii l8w cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How faili 8w*ni5 rni:23mggy hd- i8st is it going?    m/s

  Two open organ pipes,n 0;wk8xz.qtx7bx4n ysh 4mm(s. h5 jx sounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the othbqtx54jk s 4(80 xm.hy7wx ;snznxm.her?    m

Two loudspeakers are at opposite end87.sz)3mybu +vnga nn s of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers hanyz7.b g) an38u+svn mve 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, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blomiue4wi) ; rmg0em .m/x dt(h3od flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.im rgem 0/dhemxw)u (mi4;.t350-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying towardtv): z1:edc/jem 2ewn8mv* qf the bat at spe*jm 1 qzwe)f dn8vm c:vet/2:eed 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 reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches3hwl l 4( 66q jg71z7hsl aeud*knxne(xha,1n 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 returns before the nex enx lw6qk*nah(d,7h6(x ghn a ez14ls l1j37ut chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) wasjay/8x2(ass t6 , wvul 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 av j( tlyssw u/x2aa68,lpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listenin v)l x*)jfzmi:g can be compromised by the presence 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. Calculate the fundamental frequencies foril)v z )jfmx*: the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slenmlpuuao .. .7laupel + 8cvm *,,9gzkyder aluminum rod held in the hand near the rod’s midpoint. The rod is strogpcoe8l amv*m,k.9z,a.u 7+uul l .pyked 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 eaip 2*lz q,3xai71pzker at a frequency of about 1000 Hz i2xezl,kizpqi 1 3 7p*as $I_0$ = $1 \times10^{12 } W / m^2$ 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 atn c tsg2y*i9vr w7nz 8*8i)1;epmvmio Mach 2.0. An observer on the ground hears the sonic boom 1.5 min w*nrm n)oi 8vm2tg*z7;is vi9cey 18 pafter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboa)yxc-tq9ehvmtwz4, s2t s) ,o9i( p pat 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