What is the evidence t1q:ee d/whab712jg ; krctk 7zhat sound travels as a wave?

What is the evidence that sound is a form of j3qvxz;+ous;, o:zi au15iln energy?

Children sometimes play with a homemade “telephone” by attaching a string to tnchhcn3hkslj90/ b+ s4:sd +phe bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be h0csd hkj9chblph+4 +3nns s/:eard 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 airz: d rwd is27*emje0a. into water, do you expect the frequency or wavelength to jedr2ims.*awdz e0:7 change?

What evidence can you give that the speed of sound in air does not g):ae k1s ky1g*agp)w depend significantly on):wak *pgkgg sa)ey11 frequency?

The voice of a person who has inhaled helium sour6z7p7x1 z. u1 i aej8jhj/zx0ypzs +lnds very high-pitched. Why?

How will the air temperature in a room affzlk6 o16udq4k)v i8n fect the pitch of organ pipes?

Explain how a tube might r3na.mj6qrxc+om/+ jfm5en 7be used as a filter to reduce the amplitude of sounds in variousjm.o+m 7 +xf qcr/653rmjann e frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer ;4yyzuibw/9 /71 shco/q,(lg0pz -ea n ej hvwtogether as you move up the fingerboard toward the ,-o7i4hpq j9vh uw(aee ; yz01lzb/ /cwsnyg /bridge?

A noisy truck approaches you from behind a building. Iq q/n6hw 8zuz 2)/nqp(afk.lpnitially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the h)pn(n.6qqk 8 p/w 2zu/alzf hqigh-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “br0;/ gywr q)yinterference in space,” whereas beats can be said towb)y q/ y0r;gr be due to “interference in time.” Explain.

In Fig. 12–16, if the 7 su6e31q xlrhuoqn;2 frequency of the speakers were lowered, would the points D and C (where destructive and constructive interference or2;7xnuo1 3eqq lhu6sccur) move farther apart or closer together?

Traditional methods of protecting the hearing of people 1 6 -s6 0(gxqwhill.wnh czn7rwho 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 addic1x r z 7hw-qnlsigh. 6(06lwnng more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be tseztd 3u4an0 .hought of as a superposition of two sound waves with slightly different fs0.nzd4 au3e trequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer moveqs,kfn g+1- uxev6om( in the same direction, with the same ve fq+xk6su1n-,omeg( vlocity? Explain.

If a wind is blowing, will this alter the frequency of the souner-lqkv+z.(exl- + mk p5e3t od heard by a person at restp-3o et kx+5 z-+lerkl(q.emv 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 monitc(+g7dr,zhyui+i g6o or is blowing a whistle in front of the child on the ground. At which position, A thu+7 r( og ,6zidhgyci+rough E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines theod:ako z h;4a/d4, lg(du.ue.bov kt0 ugea5+ length of a lake by listening for the echo of her shout reflected by a cliff at the far endd:. ud d,0gga+4et4uo/zeva .lkoub (; hao 5k of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the d3pk*/ce2f n qn0h8v3 ekq1qe waterline. He hears the echo of the sound reflected dn v*q 3chqk1q ekpn/e8032e ffrom the ocean floor directly below 2.5 s later. How deep is the ocean 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+ hmxu6vjhpnq6 q:7m/ in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy dayp,hd)7j y2p v* tox1oo. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses befo o1py dvop)x*, 2hto7jre 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 splal(6q (2 cndck: axv6dksh it makes when striking the water below is heard 3.cnx v acq d(k(kl66:2d5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the conck(7 6 ; ljop9izucwa0lrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apar0cpizo; l w967juak l(t. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile ofxbo*jry .3i* r distance by the “5-second rule” for estimating the di .br* oxjy*i3rstance 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 thtp+y mers2,3aw k;iq9e 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 intensityls /t.+pnhbnkfpw11qjp+2eml, -a,dm e( *tl is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneous( ).2je mgy9zuh+j8nl b).bt :tamxkvly at a certain place, what will be the sound level if only one is exp9zmja8gnlv)e tm+ :uy.h j xk2 )t(bb.loded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplaj l sqn.z/dbmelg* ()rp r2-2wxh/3gone 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 a/ dlgp( lo )3x-rhrj2g 2bw*qs.mnz/e ll but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise razl:tg6f 6opm6:,pnnkq8 d zc: tio of 58 dB, whereas for a CD d:kfp, zomnz6tl866pqcn g:: player 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 power output of sound from a person s9,)6ii wwqb dgx: ok nmg4h3h5peaking in normal conversation. Use Table 12–2. Assume the sound spreads roughi4i5g dmo)hb3k,gn6ww 9q x :hly 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 strk-y7 +20rmr-wqapqde;v kp/ qikes 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 moresv -.6a ot8znsn+ch, l modest amplifier B is rated atntn cav o,s6-hzs 8+.l 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front u- uh:74xepuxgj q-igam1g+2(wge h2of a loudspeakewugaxm74-igx - 1jphqu2(g:eh u2 +g er 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 typicabjsf:b+(8 hjwqw i11 qlly detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount?i+bqjwq1:1 hwfbs 8( j [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wavx9 w 9eo/b/ mtuhqv74ze is tripled, (a) by what factor will the intensity increase? //zv7ox eubwm9h q94t Increase by 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 the f4frvyi(k 2kc r5l.s(hrequency of the other. c v(rrlhk25 iksy(f4.What is the ratio of their intensities?   

  What would be the sound level (in dB) 7fff;ww)my s )of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules) s) f7;mffyww of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to see ;vp +dclwl*d:qet :f8m as loud as a 100-Hz tone that has a 50-dB sound level? (lq+; d*l8:fdpcv et w:See Fig. 12–6.)    dB

What are the lowest and highest frequencies t,/i7(xwndrwe-dt u ho:0 bq5va/ t-;8knqu bb hat an ear can detect when the sound levelbt7ei,/:roknbb w5t d-du 0v;xqh8unaw - (/q is 30 dB? (See Fig. 12–6.)

  Your auditory system can acd:z 0rq 10owmncommodate a huge range of sound levels. What is the ratio of hi 1m0w:rozdn0qghest 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 fundamental frequency of 440 ulxhb9hu-d/3u g-*/b tf)oql Hz. The length of the vibrating portihubt-lg3quouh d -*b/)l9/fx on is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audib *-ketwx cp :4qlmk)b6(ju1yzle overtones if the pi4wtl6epmk: uy-* k bcx )1zqj(pe 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 alcx73u/0pk ;d 4qhm)2 q lm ,jx.mwnodn empty soda bottle that is 18 cm deep, if you x qlh md)op7uwn;m. j3,md cx4/kl02q assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanbcx vhp;fwrez: fj,o;1) bn7, ning the range of human hearing (20 :e; cjpz,n,7b);f x1rf bohvw Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as it.q4kui.wkxh xa7 7h7es third harmonic. What will be its fundamental frequency if it is fi7.x k.eakh 4 hxq77iuwngered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tune0jfm3 yzus8-vioudoeb41+ -kd to play E above middle C (330 Hz). uf4+sz-mbd38yk0v1 ej uoo-i
(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 pipe2 (t++6l1 ntijianbwey5m* jv that emits middle C (262 Hz) when the temperatu2 1mj*wl 6jt5+ytaib+(n nei vre 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 .0l)ul 3 zeiwd(yt.x z$^{\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.rgm.9in m lh zdc:5b+3m gdm8d the hole be that must bhm 8dmb+m.r :3z. d9cmggn5 lie uncovered to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, buoad6 8qig na,t:2tp71d3oj m kt not at any other frequencies in between. (a) Sh:8akdnamp6qtg 3o2ojt17i d,ow 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 resonatedvqy3,lojqr38 cc)(ejjg0 x6 s at two successive harmonics of frequencies 275 Hz an)cdo3r0yj6 j3vlxcqqe g( j,8d 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 n7 wic itji*0wl13 m( ujyjx7;$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-longl *wkoi3 ojuwl.4 5fb5 organ liof4 lw*. 5jb3u kwo5pipe 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 the outside a.do*0dgm- qcr nd 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 dmq0cdgo-* r. 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 /keg; tir8 /cmwhen trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other strit;mkic/ /gr8e ng? ±    Hz

  What is the beat frequency if middle C (262 Hz) an x;,6x/dqng5qbgfd,mq . i lh7d $C^＃$ (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 (bran00 vv4hpsk e/*ftc+pm d X) operates at an unknown frequency. If neither whistle can be heard by huma+p*sm4fc/ ehk 0t v0pvns 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 produugjn- p)fm/-+3 grfweces 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. -)3g wp/nermgf-f +juWhat is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The ten*zv7 /n7xvnzg sion in one string is then decreased by 2.0%. What will be the beat frequency heardn7v*7/z z ngxv when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle C (afk s83s 3cw7w262 Hz), but one is at 5.0°C and the othe wsa3 38fsk7cwr at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frepfmj9b *tbfk g.pc/+r5lc ;ugt6 :(pxquency of 441 Hz; when A and B are sounded together, a b;j rggp tf6(* 5p/:ptl.9bmuxf+k cb ceat 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 1.804 qk 6h+jkw;lu m apart. A person stands 3.00 m from one speaker and 3.50 m from the ot+l k4qh; uj6wkher.
(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 zdy;pu-rh 9- fni8gjl p 2h11ovibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vippz28yjf;hol -1-1 rin 9 dghubrating 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 beatyt.r8ra6rp qe ,h k;oa-g 7qf1s per second will be heard? (Assume T = 20 q,gr7h-t1 r.kya;forpa e86q $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is seqm4 m8x qx:9y. yzp p)/9vmx1550 Hz when at rest. Wh8m9 qym9x4 :pxs ) z/xvmqype.at 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 frequen9qln,1 0kp fyjcy do you detect if a fire engine whose siren emits at 1550 Hz moves at a speen, 1fjp0kl9qy d of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 067kcdfj45y ctbo j, a2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Abfj7d5c yo j6kta,c 04re 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 h(rm*xa wdte7 )orn. When one is at rest and the other is moving toward w)a(dm7r x *etthe 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 receivesiyzt myaadnh6u2.:8*7a fx4f them returned from an object moving directly away from it at 25 m/s What is the received sound faz 84ui.d a :72 f*xhfmnty6ayrequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an ulth8 / kfgc8ped (/*udhyrasonic sound wave with frequency 3/d8g/ hu(c kfh8pe *yd0.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played 1n( q64 jxnm ppfio iz222io8jon a moving flat train car at a frequency of p(j6o ijp1zn2i4xm ofi82q 2n75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speen2 0:am ncfui,:ouorb9ko7r-n s1q (o ds. 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 auk1: q2nrb( oun 9 7mf:cnrs0o -,ooiat 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wapr*mv aga7 .7 ymicmas4d63; jves 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 5f8o2 s (hpk .bsog85ug70 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at r8 guph(ob2k5 fs8o. gsest,
(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 land if its speed at 240rfqbo3zyt,f4ln fn.q5 m ryt ia4(10 $^{\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 gvqxdll1; ,1+u9lnry)ae kr; speed of sound is 310 m/s (a) What is the angle the shock waveya);gd r,;ql r1x9l enk1 l+vu makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the tr7 dl)fn4r 0euhin atmosphere of a planet where the speed of sound is only about 35 m/slur e 7)n4rfd0
(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 tnd)nw-:6 eqne d dd60id)7w (h tvx+h8500 m/s strikes the ocean. Determine the shock wave angle it prodxd6nd )e (t6+t)qdn:dh-ewd0 v inh7w uces
(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 5yne 3q:u68fz9e 9on ;iski yl$/theta$ 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 ground flying xw:xnfsenncxu,, 2+r8r* 5lg faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fixn:x 5le,nux,8rgwf*2r + cn sg. 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 sou t4r, ;vsjaz)hh:,doz nd pulses downward from the bottom of the boat, and then detects echoes. If the mzdot; j,s) :vz hh4r,aaximum 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 tros n(x 5g3f7xhere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of *z ceqj9p 7(xamany plastic pipes of variou 9 7ajcxeqpz*(s lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close todsk0r/5r ,uj e the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquituk,rd/ rje5s0 oes?    dB

  What is the resultant sound level wc6.is 6lu r6s.hiwkg)6bbm 0ahen an 82-dB sound and an 87-dB sound are hearurbg6i)h l6wss6 ikb6.m .ac0d simultaneously?    dB

  The sound level 12.0-*mmffhldd hax o 3k3po ix(; +)fd3b/ m from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power -3 3( khf lmf oid)fxdoaxhp /;m+bd3*output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier ia/ifp2bko/g8a0+ y bk s rated at 150 W output at 1000 Hz. The power output drops by 10 dB i/ 8k+0a gbf2bp/akoyat 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectivet8l.nd( n ycpxp* 6e8w devices over their ears. Assume th.w68x ltpcd* 8(npyn eat the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sysb + 2f74km4+lrk:c) lbe azdbatems, 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 9p8l0)i.al:mz xmj nd frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundig2f;qtr y8 of*v;8 koamental frequency ofoyt ;f*2;8g rqik8ovf 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 vertic0 qmmndih w51.al 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 foh.5qd0mn iw1m rk when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at og6 on/9 omwsdkjn+6n( (yg3-uxe fq6l ne end and also 75 cm long. How much tension should be in thuo9we fd6 gm / noxn+3g6j(yqk(6s-nle 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 resonate as ovjr)qyq jg*j+z36 4tft;xkr2 ne 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 rangeuh32d;l1x q/rcev -p+um+f rtc :imn- coming from two sources. The sound is loudest at points equidistant from the two sources. To d;et2+u-p mc1xfir/:d3 uh+cnmlvq -r etermine 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 mf- vv +pt6gt;conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the spee+pgmt6v ; tvf-d of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hj u:mzjk.cal fu91 6;dz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume consa lk691.ufu;d jzmj:c tant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listeningc;31ost:* u/tcfje fgu5ni. n to the difference in pitch of the engine noise between approaching and receding cars. Suppn :tcs/jg .cou*f5ne fu;t i13ose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. Thekxdco)gp z1dxn,05gh(yg.h 8mq7 dvi g/9mg 7 shorter one is 2.40 m long. How long is thegdg,8m5o7d v 1(dy9pxiz7gg chkm)gh/ x.qn0 other?    m

Two loudspeakers are at opposite ends of a railroad car ad nx.3gq.z/hcv5 om5ns it moves past a stationary obs nghd5cx 5 znv.3o./mqerver at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, 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 0.33b pjw zt0:-ob2 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood 3otp-bb:0 j zwcells? 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 towarbhb1)-k7reo hd the bat at speed 5 m/s The bat emits a sound b)1- roke hh7bwave 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 approaches a u7/ yba x;es t4)mlwhv/exj p5*(psaok4m8 , smoth. 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 beov/7*a 4yp )xjkaexhwu t m,p458/m ;ls (esbsfore the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once u1ypbzk m3py.k 0 ss65tsed to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long hokp kmyyszs1p06t 3 5b.rns 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 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 presence of*gs f u8h1vhs) standing waves, which can cause acoustic “dead spo8 *shhgvf) us1ts” 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 rx7w au45m , ae;n+rm q/8qfmdlods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoiaqu+, 5f8dq rw;7x n4ammm/ lent. 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 f(jh 1fg*uh:jb8 nt8k y4sgeu/ or the human ear at a frequency of about 1000 Hknsg14e8fh8(bu *jhtjy u:g/z 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 sonic boomz2434 lnfowy;fe+u lcf9vgu1mz: ;qn 1.5 min after the plane passes direcegn lu+ 3 mzz4q;uwf;cv f2fol:n194ytly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat 5+yd;f,n; u1bp dxhbz 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