What is the evidence thas vms8vx 1/grvu v,m*mm 5e9,qt sound travels as a wave?

What is the evidence that sound is a form oql-a k8tv 7 fytwd-*;vk pvt2xy+-wh7 f energy?

Children sometimes plal+bjbun9( g-uav, e5( mgnfn4y with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a c vn+9 uflgu(m4e(anj- gbn5b, hild 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 bdzsnuwg34t: /v/8o 2lj ab t7into water, do you expect the frequency or waveleng7agwo v:t/b/dju23 8ns bl z4tth to change?

What evidence can you give that the speem./k 74cpqaru, ed* ubvr92qhl -p ex:d of sound in air does not depend significantlu:.b - apq*q7ex mcev9ku d/,ph 24rrly on frequency?

The voice of a person who has inhaled helium sounds very high-pitchzf6o : 0 efsgf8bip0(ba(z n4qed. Why?

How will the air temperature in a room affect the pivxmc 3j m;5s7stch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of souy + 0kcotz--gw1b qa,unds in various frequency ranges. (An examplog+1w-baty-zu k 0q ,ce is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togeth/,yfyuoa 5 (,dmp3q:3tecfwm er as you move up 3wyt c/y 5,,d p:fu(3mofeamqthe fingerboard toward the bridge?

A noisy truck approaches you from beqpq ;bdtvu(4bn) :o, whind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “bq4v,(bt):w; dp bunoq righter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be(v md / tli+-w8wk):qaswf/d e said to be due to “interference in space,” whereas beats can be s v/fd(wlw e+/w)tm:8 ka-isqd aid to be due to “interference in time.” Explain.

In Fig. 12–16, if the frel+y-vb.hhbb w/nu :c( quency of the speakers were lowered, would the points D and C (where desv h :b+/nl(cu.h-by wbtructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of ubxn vy*n, )a1people who work in areas with very high noise av)x ,u*nny1b 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 in Fig. 12–31. Each wave can 6*oang,ghq3 7dl q:da-vxc t;ew s- e:be thought of as a superpositi s:wdg7g q36,ct:q l- eanxdh*;e-aov on of two 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 the source and observer move in the same directpe r3ro.h)1meion, with the same v). r3 pore1ehmelocity? Explain.

If a wind is blowing, will this alteetkis-51sn b/ tpx,+p1eh0 dq r the frequency of the sound heard by a person at rest with resspqxh e i,sp0tk1 de/t15+n-bpect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows variouu .ckurw gb395;nuac5s positions of a child in 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 reasoning ;9ba5wn3g .uckuucr 5.

  A hiker determines the length of a lake by listening for they n c8ncmq3sy84ofz;s 6bc.dft47s(h echo of her shout reflected by a cliff at the far end of the lake. She hears the echo .d3q8cs yn8sbfm ;4cszn7y46 thfco( 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 waterline. Hetwav ,e2nw3 5 in wlv(8mbj:l; 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 t 2a85 en(vn3 mibwllj;vw,w: (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in airfk5w (x5fnzc +qgoc8 / 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 ab5,yth s9* mopbove a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fbp 9,m5to *syhig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped fro p8m*5uit s0xid r,:jkm the top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How hi kprx i:u,*sj50t8dmi gh is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the cm,in+n7zfx p7 z+sre.uj nu wh59x2i:oncrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other imx7s if:nez9+uw uh2 n,zijr + p.5xn7n 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 distc8ol h g k+8j+ul-et:kance by the “5-second rule” for estimating the distance from a lightning strike if the tckol 8jul eg+-+h:tk8emperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain levelmf2 b1f7 t9:bfly5b we 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 ob3wxz)gz *axtha n /99gr-p.whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produc +pr.ml* vv(bihjfk i:t,-;tve a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound lfl.hv tj-b*k,+p: iirvmv(;t evel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certt2uu:psev)e ( ain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add in (euvspet2) u:tensities, not dB’s.]    dB

  A cassette player is said to have a st/ * l5ng-+dyebjrgo(wf)-x lignal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the -g*w 5)+/x tll(ryeo -djbngf 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 spx/jz/ 0diu8p p4x8afewj2 sz1eaking in normal conversation. Use Table 12–2. Assume the sound spreads r4 0d/esi zjxp/xf j2uz818apw oughly 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 eardrum whose area itw p0 9hy./et2ovm8c js $5 \times10^{ -5} m^2$ (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 25f0eki8a-+ d:j d4pzes0 W, while the more modest amplifier B is rated at 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 d-0d :+4ia f8ezjpeks 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 i3*rc fkhf6+ xqn front of a loudspeake cxkr*q3 f+6hfr 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 2e6rb;j;y)kp/i lh2 ahv x-e o8.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? a/pxej hl - )o;e i2yr6hkvb;8[Hint: See Section 11–9.]$\approx$   

  If the amplitude of az )f gpa99cvf0m8.xyf sound wave is tripled, (a) by what factor will the intensity increase? Increase by a factor ofp vz).f8 ff09gam 9xyc    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the fg,9ut urr/d-m requency of the other. What is thtdurm-, g9r/u e ratio of their intensities?   

  What would be the sound level (in dB) of a sound c qi7k7o02lkmwave in air that corresponds to a displacement amplitude of vibr0km7co72 ilk qating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 4qml8gydwwcu-(f/ +e 100-Hz tone that has a 50-dB sound q/dle8y g(w cwuf +m-4level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies thatieznxd(i j h2uwj 8y 05d9/2wy an ear can detect when the sound leve09n 2eij 2/ dhxw(wj8uyz 5ydil is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sounl /d3jycy we 2:r.wj1id levels. What is the ratio of highest to lowest intensity at :j 21rywy celw/3dij .
(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 Hz. T 8b qea2t3p)do g98hsrtos z,2he 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 b9sqgo p,3s od h2tz)t2ea8r8?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audiqq:j f gd*uc-4va 8uq:ble overtones if cf:q :*qja ug-4du v8qthe 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 6e+j) dtqld*v k(rsuhpb l* m;; yls::expect from blowing across the top of an empty soda bottle that is 18 cm deeb)*; me :rudltj;6(lhlk dsyp :sv* q+p, 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 withtr7+bv0m eboz+ cn96p4em gh 3 open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipevg 0+cm eorzb67 b3p49e mtnh+s required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. W2+,3j2yskm j x pes9 5 w-ssrzecuj7s-hat will be its fundamental frequency if it is fingered at a length of only 60% of its o--,ej2s wekx s57rmy+z sspj 9j32csuriginal length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to f sb2 ;si9mq)nv- h*xwk lsmhlb7)/3splay E above middle C (3323m;i9 mf ) nqxssskbl-vs h/hb*w7l)0 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that , /fhcv k0i3h 2rljesv6dv1g0emits middle C (262 Hz) when the temperature is 2 / vhhsfci10ljek3g0 rv,6v 2d1 $^{\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 wcl- 4x f,2ca7icm8zmw vz5 42igvm)nat 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 should the h jdai6r-tx 1vrwg//xs 49a jv.ole be that must be uncovered to play D above middle C at 29416 gav-r xjwv.ix 94ts/d/raj 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, 440tm *s t2 .9nr(moe/9xzkewvo1 Hz, and 616 Hz, but not at az2x( o m.9*9 n/m evtswk1eortny other frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 2grkbq t+;j(sg0la,k nps 6v71.80 m long is open at both ends. It resonates at two successive harmonics of frequencie ;kqt 2p bv(r +s6n0ljg7a,ksgs 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 g, 2gde(8;kypl4wn c9k 2wrrl$^{\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 iz t.yfspa;4nj .srh0ay87yph:w i*:.14-m-long organ pzrs*:.a4 .nyyhp8 i jt;7hysw 0p:iafipe 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 outsiwh/rrp6lxq*t e 7d9o9 de 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 informar/6orx w* 97dhqpet9ltion 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 )wf 7 hhx(e1cgwhen trying to adjust two strings, one of which is sounding 440c1hxw( hg)ef7 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) anaub nsk30 1n9u ry/hj,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 at 23.5zjwkm5+d,i wf6( g 6wp kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine oj , 6+pfgdmk5wziw w(6f frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and 9krq,o(f y 7zj)m y53zs beats/s whens,7qk 3rjyyz oz5)(mf sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. Thyt qr8 6+ qmhw-n+cv2ie tension in one string is then decreased by 2.0%. Wc +2-qwqhy i6+t mrnv8hat will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identihnj1 9hdmtes7fzgfm82id5 73 cal flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other ai3t7 de m2fhjg9f d7s51 zhm8nt 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, 2angjsn+r d4-loqw08 and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are 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 togethe+dng s qr0a 842-lnwojr?$f_A$ =    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 frou*c4l,q tnk:r-s9 faam one speaker and 3.5q:,4f slu-9t akcna*r0 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner heat4y;sh k ks3.wrs three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the4wt k ;.hy3ssk 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 bea5q -:svblshx- 5jjyd4/t y kd)ts per second will be heard? (Asj5 kd4vydtbj-y ss)-:x5 qh /lsume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain c 6 gdg3-p()kcvnxxluc+ 5ojtmw:;s1fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed owc)xncmtulg- jcvd3 51 +gs x6:(p; okf 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you doa,,q ;m0j tbc1)5p habg2zh setect if a fire engine whose siren emits)tp s2c0zbha;o aq,1mg ,5hbj at 1550 Hz 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 2000epf;; q;cs je*-Hz source is moving toward you at 15 m/s versus you moving tows;fpj;qcee;* ard it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horntf nc0o37djj/*(a u la. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emi fa30(7u o tac*n/djljt? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonzo3t ba32v kb5u3r s8u-fmt.o ic sound waves at 50.0 kHz and receives them returned from an object moving directl .ov 3z2 b-a3msto3bu5r u8fkty away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits anjijj:.xweo7:f 3y,xs ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in ty ,xfjw j.jieo :s7:3xhe reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was pladrb,np, g lkiulbp()z,;sw ;;yed on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at r(b ,;lwkn d,gslb) pi;rp z,;uest 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 s bmsdxg,w6yuin.x . l.+r1ev,d fx7+q peeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue i +w.,6uxq.+ niyf e vdrl,1bmg.7sdxxs 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 usingx0lnv/mz67r1/ cwqvgx :lu m-f( p3rd 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 emxmkt3vq16ouh5 s: 9wlits sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear w ts6o:wum5h9 13xqlkv ho are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its spee0y ojf;dlu mm iu g jx)8k18o/no -9a8e/3ilked at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s f6vlb g c4l5-a(a) What is the angle the shock wave makes with the dir5vfl a-l 4cg6bection of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet w) 58-dej.xanl a2tg ywhere the speed of sound is only about 35 m/s djtegyw) -5n x l8.2aa
(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 ocean5r:(pwfzl wdu 49zqp /ku-i7c. Determine the shock wave angle pr dz-u5:l/9qkip7 fuwc w 4z(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 ; de9n+ (ia:rg6 mckvkoit 23a$/theta$ 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 exaceoiqv n)zj m-,8i u/6b r:9izetly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizonta b6ini)-zr qm 9vje8izu,/:eol 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 20,000-0hwfjc i5-oa*lto w0 vn9a ).nHz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is desi.*vca fa-9njnt0 5o)ww oli0hgned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human ajqz ail;jm5/d:e,y o s8ftv((y9izp 9 udible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer,qno l5 8byuu* pipe symphony. It consists of many plastic pipes of various lengths, which are open on both ends. q8 yulu n,*o5b
(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 togdgo9r 14/ piq the threshold of human hearing (0 dB). What will beg491 orgq i/pd the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dBe4tnh7e9n 64ons/m, mcjz(o t sound and an 87-dB sound are heard simultaneous neo6/4zonct 9jm ,(e4n7tmh sly?    dB

  The sound level 12.0 m from a loudspeaker, pdamu)0 iysugo:xk,ex9,l, v6 laced in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all di,x,gi xa0uydk,6ul:)moe v s 9rections?    W

  A stereo amplifier is rated at 150 W output at 1000 H,f8tq. j7o h)uuox 4cjz. The power output drops by uq78. 4tjcfujox ,h)o10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over thei;yqd0+k.;etuy 4 vz tur+wdz0 r ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that th;0ryv+ .+0zku yz4 ud;ewttqd e 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 sjufc7l2no mvo/x* * 2nystems, 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 frequenc(ahhsnxx( s/6 y 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 fundamental ;rnkyh /+ar3b frequency of 440 Hz and a mass 3/+rbnr;kahy 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 vibram/.5kr ylrcrfzw v;u)b-u8/ 1ty6 ilktion above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the 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 8k1l/ c iuy5 l/6ruvyftz r;wrk.m )b-tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is opel*c kmm17s-oi /pg5vs: mu0cftu-mf8u 9x1ih n at one end and also 75 cm long. How much tension should be in the string if it is tc - pv0 f-mt:ucmluku*m8i 1if 9mhgx7so5s1/o produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed (q:+ hqsn2usmto 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 comt28;(ac xhwdf4ezsg 29en v -l 3i/nhaing from two sources. Theghl i2/83e n(2v 4-h t;d9szacx efnwa 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. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductorc5afw)i vm zp jb0ez;8y.1 ;lc on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What ; m ic e80yf5wj1l.c;bzz)vpais the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches4 ufz h67m.dqx you is 538 Hz. After it pasm74 q hu6fdzx.ses you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the 3 bh )xva46n (b9v6gzpzczssgzvg395speed 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 it goes by on the straightaway. How vgg hzzb5z bg6z)96 sp3x9snva4v(3c fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beaxok,8u5u jii 3t frequency of 11 Hz. The skouui 8i3 5j,xhorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a rai,intc- f5in5 nlp9l:g 5aq)i olroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer 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 afton,i5gi9lcp -:in5 ql) 5 anfter they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.325zk8aa -jqw 2z m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed zaqz2a85 w- kjalong 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 toward the b .y6x/lrvi s(tat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is ts.x6vr(l/ iy the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequed/wn1 lm;dqj .ncy sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the batw d1l m;qnj.d/ so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine vi,h b1fo uo v)qy+)bo2nllag,b)+ny1 obvoo)q2 u hfe 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 tube.

  Room acoustics for stereo liet ,z*sex r56gstening can be compromised by the presence of standing waves, which can cause acoustic “dead spots”6g ets*ezxr,5 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, t5 -tm a05 vu)mts2bi nie8oo8slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,u05im2 8sbnei to8atot -mv)5 ” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at axc lhgy/x 0j+0 frequency of about 1000 Hz hx0jx lcy /0g+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 atyco4f b/a;*t i Mach 2.0. An observer on the ground hears the sonic boom 1.5 min a/boa;4ycit *f fter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboiw,:cbq 7 h 7obhpgc4+at 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