What is the evidence that sound travels as a wave?.8timwfnx adkta;.;0b ej-jub8(pm j4p(fj5

What is the evidence that sound isd a ue;*5i+gbl a form of energy?

Children sometimes play with a homsxhbypqu,0 m)4q3g4 ubsf q05 emade “telephone” by attaching a string to the bottoms of 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 0 sb3up,h4yuq 05)qx4 bgmqsf.

When a sound wave passes from air into water, do you expect the frvz; qgk y.*t *d+u5b3oiamle5kbr5j8 equency or waveleng v8blua553oe;b5 +i j*rztkyqkmg.d* th to change?

What evidence can you give t:.gg4 qag,k fghat the speed of sound in air does not depend significantly onfa. :gq4 ggg,k frequency?

The voice of a person who has inhaledz+ph r56 .cgeg helium sounds very high-pitched. Why?

How will the air temperatdo *6iq3qe*t iure in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter t-n2uao ;1m08o2z lwvpobtqa 6o reduce the amplitude of sounds in various frequency ranges. (An example is a car 6tbq v o am-un2;w0ol8z12p oamuffler.)

Why are the frets on a ( 6c v(i*3w7 ;vttqu1umzo9zhxe)hh oguitar (Fig. 12–30) spaced closer together as you move up the fingerboard towahq t izv(* vo)(9 h;1t3uh67e zmwcuxord the bridge?

A noisy truck approaches you from i;h3wi4 m8o mj6tit3hbehind a building. Initially you hear it but cannot see it. Whwt33 8iohij;hmit4m6 en 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 diffraction.]

Standing waves can bfa) kq m.kl:m-e said to be due to “interference in space,” whereas beats can be said to be due to “interference in time.” :l-amfk.m) qkExplain.

In Fig. 12–16, if the frequency of the speakers were lop 69p1oyuk1- vtve zk5wered, would the points D and C (where destructive and constructive interference occur) move farther apart or1ev5uz o vppky-6t 91k closer together?

Traditional methods of protectingz3ekdr+ f vqz68e a)i/ the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noeq63zr diz)e+ v kfa8/ise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig.eg (eq3c 1xy)s 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequenciec1yeg )(x3eq ss, 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 direction, 1:bws+i6bk )e p9*m7*gc fe0ykx s lyuwith the s6:1epm7+ky)g*s 09 *xl ekwyfubb cisame velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heav/inu-m2 j xcd22+dtg , laoh6rd by a perso 22 mg2-/c hn,dxljdai6ot u+vn at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child 5.,ksclo: eu: n mrk4.rc bh;iin 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 :5rlors.e;n. :kh c 4mcbk, uiof the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening forkt+-,oo ,t pf4oimmnd(e1c*r the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s cn,rm(iotfokd - pmt 4e+*1o,after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship jusi2b4b .yu*vh st 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 15iu2b ys* .vb4h60 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in yia ,uys:k/ds9;jk- he;ah2 :jjix 3bair 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 boacmhd;ct z8p9v *6s ff(t is drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km dh*(s8cp69vzt cf;mf away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when strikz1j-. l-1ozcupe* ,xhlcrt3ujinz66 ing the water bec6zijl -*xurp-. ht3cn,61lu1 ezozj low is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to thdhjobc 3*8v.pqh. 6/ 0yj)zsty w/ ohce ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the imt/cohywjoj 6 08qz. h*.cv py/d) s3hbpact: 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 fuimq -5 .q8sjr6vv w1error made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strm5r-6qsq u8 .jf 1wvivike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain lez2 d6988e7xfwg cbqqcvel 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 intensity h:c xh qnoat/v-2,;msis $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB whe3t *x j)mmbhnh+d z7 x/zfn+-zn fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: 3zzht+/+nhmzx-dxm b)jf*n7Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally nocz 5v gt49pxh9il -(dzisy jet engines is experiencing a sound level bovd z z(9pl54c-htigx9rdering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have/:vl/qa, sj mq a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise f/v ,qmql/a :sjor each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outpanf2 -lt+ 5pqqut of sound from a person speaking in normal conversation. Use Table 12–2. 5nlqa- fqp +2tAssume the sound spreads 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 ear/yisc a: pw9h2drum 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 rate 8dunu8 +mtq;8o2jv cbd at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the+;n tbm8v 2u8qo8jd cu 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 placedo;yt* qi dc(s) 2.8 m in front of a loudspeaker on the stag( s*yi;cqd) toe.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dBfjo7 -*69lsgpi,q , 8egh mnedyc t95a. What is the ratio of the amplitudes of two sni 9f86e ltqcpe,9gj yg-7 5s,domah* ounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what facqso eg;: id*k xeu;e-6tor will the intensity increase?dek* esg;x6 ui;-o:e q Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement ampk4 zy*7jr3n j ydvs7,elitudes, but one has twice the frequency of the other. Wherdns 47zykjvy* 3j7,at is the ratio of their intensities?   

  What would be the sound level (in dB) of a soun z+:(ynw* tck )mkr*zrd wave in air that corresponds to a displacement amplit ): czk*n ym(+tzrrwk*ude of vibrating 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 100-Hz tonea1jb6kohyul- 2 k(kn7 z-7 gsp that has a 50-dglk kon61p-k s(uj-7 a72hzybB sound level? (See Fig. 12–6.)    dB

What are the lowest and highem7.5 6c:throq)a whdxst frequencies that an ear can detect when the sound lev hrd7 .6)tawqx5hc mo:el is 30 dB? (See Fig. 12–6.)

  Your auditory system cannou q7e0s +jslv0w -r/ accommodate a huge range of sound levels. What is the ratio of highest t70 +ovujlw0es n -r/sqo 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 frequen tk:/4:qkwecq cy of 440 Hz. The length of the vibrating portion is 32 cm, and it h: wk4t/qk:c eqas 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 fu-e01karni av,sn9 b0xndamental and first three audible overtones if k 0 -xb1n,eniraa0 vs9the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowin7clcj, h)2tp 7n gt/zn0p3 krzg across the top of an emp7kgp p,cn 3lhzc2/0)t tjzr7nty soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organo :qrj:v :wj,sd5 k67aa1ww hz with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the rad:a j 6r o:,5whq:zvw71k aswjnge 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 Hzh(fzmo 27f x2a as its third harmonic. What will be its fundamental frequency if it is finger27zh2f(mxa fo ed at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play Ehv9 4:tr ;vzk/hsf3gd q4z1u r above middle C (330 Hz).4vk4zsgqvurtr 9h;h/z3 d:f 1
(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 orgarrqaoic7pnt. l+w3 93n pipe that emits middle C (262 Hz) when the temperature is 2 ni +t.laqp7r93or3cw1 $^{\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 2vxvi * t,lf/z90 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hole be tx iwpfr/8wpk v;:i* .l+yg5eqhat musk i /iyfe qpv:l.; xw58g*w+rpt be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but notf kw cf6yas+ph/7o08a at any other frequencies in between. (a) Show why this is an open or a clospoaf+c/76y0af8w hk sed 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 de(vr :qx, /rcresonates at two successive harmonics of frequenr,e :xv/c( rdqcies 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 )yefj)2eh,xuj02 qr3ft:m cl2d 1oti$^{\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 th25;qrpgkn 2ove audible range for a 2.14-m-long organ pipegvp2k52o nqr ; 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 outf82ib9zja tkyah .+l)side and is closed atk a)89i.btlaz+2f hj y 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 2.0 s when trying to adjust two.pc(;ano*vbxa 1 lvm cfcwu.z+qf: 38 strings, one of which is sounding 440 Hz. How (+mf..c * n8cqu31vvoc pzwab:xafl; far off in frequency is the other string? ±    Hz

  What is the beat frequency if mi8uui8 )1tkfqpm y3 -1qy kpg8uddle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, whi opxt cv,qc9fvv.eex +qj;y h8-;xy*: le another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand:- h;xcp fcvvy.oqj ;8ey,v eqxx*9+t X.    kHz

  A guitar string produces 4 beats/s when sounded jvp o9c ;uye)9vam;y;with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational)mvae; vj c99 yp;uoy; frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned tog8k10rqpnh3y2* zac a the 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 played together? [Hint: Recall Eq. 11zng32p*hacy0 ar81qk–13.]    Hz

  How many beats will be heard if two identical flutes each try to plv5, hcb;qcwyn;(7wox 54feb2p x2 gxmay middle C (262 Hz), but one is at 5.0°C and the other am7x( hgfx25w,cw x2oyvbq 4e5b; p;cnt 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequen 12(z1 uujafpb0nf9ukcy 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 possibl ja9fuufzk 1bpu0n(1 2e 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 from ocxc sv3:/re7one speaker and 3.50 m :r /3cevcos7x 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 Hdgss7- +9x5 lqso/lgy z, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 13lqs5+g7sxds/9 lyo -g2 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+al ) f)3eesws)z)au z wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (l+ 3)a)ufw zzss)eae)Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire enginjdjjxjo )h--qlu(09 0h xn5n 4lu1c eee’s siren is 1550 Hz when at rel j nxul1)ud e4nxh0j-9qe o-50hc (jjst. What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fii ly0j69rxa p0re engine whose siren emits at 1550 Hz movesj 90ilpra xy60 at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you a+9ps6kfxr pp j6z2re : qqj3aatk 8/0yt 15 m/s versus you moving toward it at 15 m/s Are the two frequencies ep+tspqk09 2ak: jj r6p8/rfzq xeay 36xactly 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 fre e(qu0 xk4auk2quency horn. 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 hoqkuu4e0( 2kx arns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves atmm,ue di9* x;ci31 ib9 x,fysn 50.0 kHz and receives them returned from an object moving directly away from it atibyx xui3nc;e,*m f 91 s9dmi, 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a 7rft lku 7a+btduh4a7;7vho0speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat heat 7;dk7a0buhr4t+ avlou7 f 7hr in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playerr-t2f ok*thf zk:l61h d6u df9;j9lkd on a moving flat train car at a frequency 6f2 t1d t :of9rklhh dzl*ur9-;6fk jkof 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultras* ntlf/s91e qeound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arten eqe1fs/9lt *ries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using uie(cvp5 -bzz. ltrasonic 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 emih r5, r3 vbr(sa*rqdqa7b4b7dts sound of frequency 570 Hz. When the wind velocity is 12 m/s fromr(,4qab7*35 hvdrb7sqrrd a b the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its spe xhpf97)aq6zwed 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,x:bfkl6 pg58/rw )yy v fxi vu9u6i;p 2.3 where the speed of sound is 310 m/s (a) What is the an8kprfl,b5iuf v6xywv :9iu py;/g6 x)gle the shock wave 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 thin atmosphere of a planet where x we6l p+xb*3ethe speed of sound is only about x p6e*wl3x eb+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 miv + 7e*:a1bqk; hl8gcdc xr(j/s strikes the ocean. Determine the shock wave angle it pr7l: (g qhcbevrjai 1*c+8kd;xoduces
(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 0), ar7j .k/3yyl zltbsba ud-$/theta$ 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 kc-0cj2or,v very51 nc m above the ground flying faster than the speed of sound. rey-oc5c01c r v2,jnvBy the time you 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 1hm0 ms08vqd 1ptml0d-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is desi0vq0ph1tm 8 mslddm01gned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are 230 :b; p+5s 2rrhmyjvxri:gla/v jjhthere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called7yixoc:g+o3y a sewer pipe symphony. It consists of many plastic pipes of various lengths, which ar73c o+oy x:ygie 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 thresh2 m wl ze5;dci0is3er),l :tzsold of human hearing (0 dB). What will 0: 53z dielec,rltmzsws;2i) be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when aq(ig2hnh wc ro0;h7m8n 82-dB sound and an 87-dB sound are heard simultaneou7c;r(ih 0hmg 2hqnow8sly?    dB

  The sound level 12.0 m from a loudspeaker, plbbs+n( xlo(/(tdpn / gaced in the open, is 105 dB. What is the acoustic power outpb n(l/ot sbpnxg/(+d(ut (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output atc8tlb5ut1a5hgp..ys nj/u h-h l9 di 6 1000 Hz. The power output drops by 10 dB sllupu6t h8jg.i19y.-t5/cdbnhah5 at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective dexf3vattkx1gq h ;dhaq 9-fv+v78 i:f (vices over their ears. Ass-7+a;8g3qx:i1 kf 9v qdvvttx( fha fhume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communiom, qt6p s-7h)4tx5 avqjdhd ;cations systems, 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 3u0f :aria4 pcfrequency 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 tqdbdyr-49v ww+1jp, frequency of 440 Hz and a mass per unit lenqwb 9,jdt+d4r -yw1vp gth 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 i +xu4tn s 34(2v m0rsy5waobtunto vibration above a vertical open tube filled with water (Fig. 12–35). The water level i0nb5vasur(2smu+4 xt o43ywt s 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 tm1dy)mh-b ie cb6/6 u2.10 g is near a tube 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 h)emictb1mb 6-/u 6 ydfundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loisb3 0q1 onl*a7h0 zf vm/wc*lop ($\frac{1}{2}\lambda$) 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 c 97k:ma -kelwf5b gji6oming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about ankbwg i 5k-jf7 e6:lm9ad 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 conductor kngwobbh10sb.p7*5x on the stationary train hears a 3.0-Hz beat frequenc.50bbsw x 1*ghbk7opny when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approache-l69b5 g- b36l0 jeu ijndbltjs you is 538 Hz. After it tgnjd-j-biju5066ebll9 l3bpasses 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 sp bmj 6pz55n+dfzoye9+eed 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 fast is i5yn 6j+ 9 mdzo5ezpbf+t going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hfp2(j)rn jp *kz. The shorter one is 2.4n* jf kp(2p)jr0 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a , vn pe)u80ox6ovrb zs2s syh*h8. h4rrailroad 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 bpurv hy ro40sxhh8e)z b,6vnss82o .*eat 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 what behq:ap n 8ec bu9j6r81hat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the q eu9a:h8hbr86 n pj1cred 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 fle nn-.ve p87mpying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects ofn- 7mev8.pnp ef the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches ds:e:s8 lgn2,kkd 8mmgpn55q a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can8gdmekmlkn 2: 8q ,n5ss5gpd: the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpii3t;a gpfxf0 : zjh bg7u1w h ;:ymk,(sqn-(cbne village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sofa ;mgui;1pgkq b7:: z0j b yh,-x tchf3nsw((unds. 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 presence7wky5 plb pra.af,:9fg1d a( u of standing waves, which can cause acoustic “dead spots” at the locations o dg fk5,p:9ba7f lrya1(pwu. af 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,” involvqv h)nj)+q5t ges a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked witq)jqn5ht g)v +h 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(sa vpl/s94zd threshold of hearing for the human ear at a frequency of about 1000 Hz4 /(slv9adp zs 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 athe:pni ,ga)5lcq -sc28ul t z+rt-3ib Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly ovee+gtha il: c usc5ntz-)-qpr2 , 3il8brhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 5w iueai7:nrjqhz h8 y ()l8u0$^{\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