What is the evidence that sound travels as a wa)./blz ucpwu nm:dx n7 -gs916+rsl cm4wujv+ve?

What is the evidence that sound is a form of ,ae retg/l( ,tenergy?

Children sometimes play with a homemade “telephone” by attachi 7t wg(n sonn2xkm/pbcn+d+*8ng a string to the bottoms b2ng/ t7dwxn+8 k+ monn*s(pcof two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from aw ee *wp5ng9m, n7rbp5(a hozv2y(oe ,3dk9xlir into water, do you expect the frequency or wavelelp5gey(vh e5n997 e,nrbpo2m, dw3 oxka( * wzngth to change?

What evidence can you give 88 -7+cwyopsoenx +rithat the speed of sound in air does not depend significantly on fries cr xo 7pn+8w+y8-oequency?

The voice of a person who has in:trx+jwg v- hlg/a idw 0 f:ec;d,52jrhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipei f:u-fm-58vmug(rc -zp maru0aw:v .s?

Explain how a tube might be used as a filter to reduce thei n72hksll5mr;3f4sw amplitude of sounds in various 3l4mshsf wi; 5rk7ln2 frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mo: a9)pnavgbzar/ u:;jve up the fingerboard towa : a/b;urzvpn:9jga )ard the bridge?

A noisy truck approaches you from behi-/n twcvoa+mx, ;tg5*3+lvpep 5kzce f+n/dq nd a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffract ;ev*+p nav-p5fx3nzo//5mq gwt tcd+,ek+lc ion.]

Standing waves can be said to bjc+ a9ldebv 08e due to “interference in space,” whereas beats can be said to be due to “interference in t8+0 vacj 9dbleime.” Explain.

In Fig. 12–16, if the frequency of the speakeraz fdz(v65sh g*z1fqw9 g1 ce:-bmh r5s were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart:z 1mvzr1zg(q-wbg fe5fchd5* 9a s6h or closer together?

Traditional methods of protecting the hearing of people who 9m//;8inuy ns e /is2e-poit6ireub( work in areas with very higestor9i6 ib8iu (/e -y iu/nmepns ;2/h 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 adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown ivx1 *9rktu*tan Fig. 12–31. Each wave can be thought of as 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 com*9ktuv1rx *taponent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler s.k ; zxbca::*bp-f7dneuc4 fy hift if the source and observer move in the same direction, with the same velocity? Explaedy.k:fnb7; c-xc zbp4*af:uin.

If a wind is blowing, will this alter the frequency of the sound heard by) r81a8,e0zq8fk4ybfs ma ogf a person at rest with r ,b81sk 48yqfgf0r8)maaoe f zespect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mdsaoswv0p1++ onitor is blowing a whistle in front of the child on t0s+doap1w v s+he 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 listening for the echo ofp8vj8yv0 cn)j her shout reflected by a cliff at the far end of thev 8cyv8p0) jnj 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 hise)o9shl1 h.zm q .on2i/ ouoe7 ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and doe7os1hn/z e quome)oih9 .o 2.ls not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in ail*o9xq)k3vww iqu (u 0r 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:bi nsq)4n*o j1vjq d: school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses bsvj q1n obdnj*4iq::)efore the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. /*5 t2azaddpl The splash it makes when striking the water below is heard 3.5 s later. How high is t /za2*d 5pdalthe cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrev+ij84 r kcvu)lcgb x 0a-67pote pavement. A m r7)vc6 vkg0ioj84p xubc l+a-oment 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 made over one mile of distance by th fpi*h(:nl*8 ym p( 9ncfxny0ze “5-second rule” for estimating the distance from a lightning strike if the tem9xnp:(nymn(h8* fz* ipf 0lcyperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the paia- asd3n3xq twyw-:rnve) , :wn 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 f/movjzqeco:u7 +-* 7 ty0 qymsound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simulta ;jmie- ze*bla) hb c76,i0nx0g:r jdmneously at a certain place, what will be the sound level if only one is expj0ba jld n,rczx m0ie-7*e:6);hi mbg loded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisj)lpoln 0 dyqs2nm(,be)5- dy y jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person ex,-)dbye( 5ql nj yp0nd)2oslmperience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio owiwp 0pvk.yn:3ijn ;/f 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 eacivw:3pn0k yjp i.n;/wh device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of s6bx y7)k6 gqw*mpf2itound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreay)fbxk6p7 6imtg2w *qds roughly 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 strikes an eardrgilxn) 69 3 +e9wsovf vcipva. ;r0d.yum 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, * p mhi-ef* *4vf6d8ixrnd eg.while the more modest amplifier B is rated atm4e pdif n6vhgr-*x. 8i fd*e* 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 rs; v6zr qpya*7egistered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. qyz*p;sa r76 v
(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 m 3b ;bye05 wlf,sfy):neoc4yin sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels 0;nf5 ocwyy3 )yfb,l4 ee:bmsdiffer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a 6lr hsbpo93.l sound wave is tripled, (a) by what factor will the intensity increase?l6 lrsb.hop93 Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displachwq/j8 swt*qj o-4cx(ement amplitudes, but one has twice the frequency of the other. What is the ratio wqj oc- /j8ws(htq x4*of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that correspondxb*v0dzro..n s to a displacement amplitude of vibrating air molecules of 0.13 mm at 300*do.b v0nxz .r Hz?    dB

  A 6000-Hz tone must have what sound level 83xn;/q:xg5/jnas1kgyolo0 y c bn*b to seem as loud as a 100-Hz tone that has a 50-d/bxy:5 g1no0sa ogq83jxykc n;l/b*nB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies tha +iez0d,p;4) cue(sazv 9o-m z zzf+tht an ear can detect when the sound level is 30 dB? (See Ffu t +zcs(9o4m)ia0e-v+ ph z,zd;ezz ig. 12–6.)

  Your auditory system can accommodate h xgqsn*q.2,sa huge range of sound levels. What is the ratio of highest to *q2 s gxs.h,qnlowest 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 q5d3 z- z3b)hnibzlh1Hz. The length of the vibrating p dl3) izhhqbz-b 13n5zortion 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 aukv2avoqyr5 t4(x) f*n dible overtones if the pf*n(t5av )yr qov 24kxipe 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 expec7pmm lszto)j3bxxn*s 52+ 1id nec6v1t from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closex sis2e5)+6l1 vbzt mcxm7*do1pjnn 3d 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 o *ofej n-s*itwl5j00 open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would b o05*n 0jjlift-eo*s we 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 n edu.d2p1/ks0:( zk ulivv9c its third harmonic. What will be its fundp k(evd0.2kuin/d9vz1 ucsl:amental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73h x b9v2)ia:pj m long and is tuned to play E above middle C (330 Hj)92p iha x:vbz).
(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 organg9we -zi9 p6u*t d*j9tkgmi m; pipe that emits middle C (262 Hz) when the t-j wi;t9mke mp9gu * g6i*ztd9emperature 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 a1h:85ni qmp3m u7ywpqarwp/ 9 t 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 E/:7spdcw n06 lat topa*3y)b lxample 12–10 should the hole be that must be uncovered to play D above middle: 3a7olw/an6tp*bc)y0 tspl d 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, gpv : 1l-fcqv vw:) 0*1oyfcgtc,u5d b440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closewl:v d )f1vo*05u y,vcf:qgc-p ctgb1d 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 * r6 im 6aqn76zhyej/eends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hzjihaee76m ryz /6 6q*n. 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 pnikv8+ d-ob*h ux(o1$^{\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 fq:1rk3 :rs1,//smobt02 h c bvfx jtvuor a 2.14-m-long organ pipeqv rs :xt/bkvhsufr31t0:, mj ob/c21 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 andg /n :pa elxi6kvs*-c;qq:5gi is close: *i5-gan:v/s 6lq g cepx;ikqd 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. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2 uiw2w0vthd:xwfs5mi 20mp4d12 pt k 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other 2p120 5tw4pfvwth2imwdu02 x ksm: id string? ±    Hz

  What is the beat frequency if middle C (262 Hz) an7rg)v rm zw;gh8h-i1j d $C^＃$ (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 5pd(4zi o)cwd at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, dip5 d4)(wocz but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with vzq3 5 :haojj9a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explai hjza5q:3voj9 n your reasoning.    Hz

  Two violin strings are tuned to thezqw)*yo w.;tbzz3c o9 same frequency, 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 played9zt3c. yzowb)q;* owz together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fluted5govhz*h.v3 e 0f oh;s each try to play middle C (262 Hz), but one is at 5.03 hh hvd;.voo*gz5f0e °C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency0 bk hs:lnbx8,r(b7y k 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 0y( s bnlkx 8kh,:brb7are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m y+3(vo*m j - hpw*tttlfrom one speaker and 3.50 m from the othe+3wm pyjtot l*h*-(v tr.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a p+j ydvzu2*dgx2k tca)* tjp* 0iano tuner hears three beats every 2.*ajj vt x 2cuktdzg2p*) *+d0y0 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 d wj*2v0s2 yxnof wavelengths 2.64 m and 2.76 m in air. How many beats per second wilj20s *2xv nwdyl be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freqc2*w1yze:y p s:fk9 xmuency of a certain fire engine’s siren is 1550 Hz when at rest. What fyk2:1xwf pz :em c9*syrequency 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 vnh3 m209fty wbn3b3 lfrequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a spee3mnfbt0 w v n3hl23y9bd of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

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

  Two automobiles are equipped with the sakjkz v,l0;9kwx ,cpvje29jc6rz t g05me single frequency horn. When one is at rest anwtjje2; 96k,vkk,g9czj vlr p0xzc 0 5d 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 horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic soundmacv3 w+9h;i; b;ij4tcpxi rz sue)32 waves at 50.0 kHz and receives them returned from an o+mp9siz);34j xbi 3 wciv;reu c 2hta;bject moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the ba 3;w2ul;mtnt 5x0hvb st emits an ultrasonic sound wave with frequency 30.0 kHz. Wsu2;t wnt 5bhl vm03x;hat frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiz p(r dr v5abh*q8 :6dj/ iup9l -)adp1xiy-wnments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second i:r1ddi( )jb9vr nyup xapp/la5*- zd i q-hw86dentical 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 metero s/du-,xk2v(pm7isi uses ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue isvpoimsk7s du2-(, xi/ 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 using ultrasonic waves of frequenu tcupqq91iezky/c2 u3)8s2d cy $2.25 \times10^{ 6}$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 1u- 02p.z cvevo,vesb the wind velocity is 12 m/s from the north, what frequency will observers hear who e,p-20obv z1.ecv vs uare 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 movingv,y3dx fv3pphie*w 5tfd *(+ dgys ;7e on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where t7pl 5g hvkew9 ov ymc43hrb9h(,b4 qy2he speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the49bhyw75yg(2,p 43vq h9 mhlbver ck o 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 qq3q )zwf0 0cx d:k5prspeed of sound is on 0qk)50fp w:3xqcdrqzly about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. 8 c2fv*rcy 2ghDetermine the shock wave angle it producesyv 2f2g cr*ch8
(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 l y 6 wy)/iye-h(/hlkvhn)vpl82 qy7yht /n5q $/theta$ 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 kue (2fn4ek*ovm above the ground flying faster than the speed of sound. By the time yfu(kn 4ve*o2eou hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulsyw4nq dulx2r.(y;z1 z es 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, what is the minimum time between pulses (in fresh wl. quy(nwz4y 21;dzrx ater)?    s

  Approximately how many octaves are there inrzqjqi)0k8l 6 the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It c * kg8dw2jh2 6zhdi-etonsists of many plastic pipes of various lengths, j e 6k2h-*8 diwhdzgt2which 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 to the thresho-b6p4m*cofvn ld of human hearing (0 dBb 6c-vm*n opf4). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound an4 u:vt d/e,. vjfx(vejd an 87-dB sound are heard simult,/ej:d4 uf. (vte xjvvaneously?    dB

  The sound level 12.0 m fgyot4* d:u/pz)*krr jrom a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in al4g*jk do/zt*: r)r puyl directions?    W

  A stereo amplifier is rated at 150 W output atu1ry uesu4i u 0zo5c62 1000 Hz. The power output drops by 10 dB62ro1suy5u ucz0 ieu 4 at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective d1e rzdvlc6uhc/m c4/)pt9kx z-.eya +evices over their ears. Assume that the sound level of a jet airpla+ey1-9.aemlk)zd cx hurc4/z/ cpvt6ne 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 systeb-.zj iz1)p 5 zgcmr v8qqm;-2 klzu.rms, 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 frequency y (-h;j s.mxndu gv*:(odwl/m1$\frac{1}{2}$ 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 betweeny,/pswf86z w.mivkx( fixed points with a fundamental frequency of 440 Hz and a mass per 68v pmi ./zwy(xs, kwfunit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube fille/j dkcd7v q**u2nkni83mp-1pcy )p xwd with water (Fig. 12–35). The water level2q7c d1*nwcu3 kjpmvpk )xy/*n8-ip d 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 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 ts;ppj mo(4me .ube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fpj(o p. sm4em;undamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observe5q3 ,zv .bra 86 j56gbkznwoved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sources.e , s7p81wq jypq/hvz3 +nz(j:;qhxe y 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 than the other.q +ph,(q ez p;yh/ej vs7 xzj:3ynw1q8 What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One to( 2f5hduor )k3 n4lvi9 qk8mqrain is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving tnqv93kfl4)5ikm q8h2 or u(dorain?   m/s

  The frequency of a steam trawdf 7fms+d,: rin whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast w+rfmd d fw7,:sas the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate thz q6n dkypnm4qef06 9,e speed of 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 itk9dmq ,q0yn 4e 66fpzn goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding to(duii8 .vu+6oy y eh9hgether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How lyie9 yh u.o6uhv(d+8 iong is the other?    m

Two loudspeakers are at opposite ends of a * g0s4iixrurmiw /,t: railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the be gimus,*i/i rrxw0:4t at 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-,fvbttqd r0 s;c4ta,suqs1p3-l+ a bat beat frequency would you 0b+t us pf1qt,t;cq,sdba-a -3v4sl r expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a m: qv(pce24/-/npqntufg c+ ko oth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s/n(tvngof2:e4 pqc+ / ckp u-q 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 approachgr9 gy4 c )k)mowo3h9 vmg3uf9es a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away coo 3w9 h9 k fy4vcgmg)m93urg)an 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 onctc/t d5kf+ lr2e used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open dtcrf+l k/ 52ttube.

  Room acoustics for stereo listening can be comproi 0 fety6;vk60y/shoemised by the presence of standing waves, whyfht ye6koi 0/sv;0e6ich 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 for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slend eof +zor/0w:mer aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little o0rwfm/z:+ eo 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 o3z-aa -pk y*yrf hearing for the human ear at a frequency of about 1000yp yk* zr-3-aa Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An obsead7t ifv33* xnrver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What isvda7 n3fi 3t*x the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 vxsj nnlxza, v, 3/9j88sjbp 8$^{\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