What is the evidencebf,943nzqeu l that sound travels as a wave?

What is the evidence that ggc1( 3mvyfu f:r *z,s 1tgys.sound is a form of energy?

Children sometimes play with a homemade “teleph 0 7ps6mqb0nchk(d tf ujt.u26 xw cr;o1,pvt*one” 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 ottuudpvbscfh6p2*;x0o(.r0 , m jtq1t67 wcnkher.

When a sound wave passes from air into wa xzipb9adv*--,pie ql s 1t6e3ter, do you expect the frequency or wavelength tev iixes-,qzb361 d* -9tppalo change?

What evidence can you give that the speed of sound in air does*j gf b vd56+eq3esik. not depend significantly on frequenck bg5 f.i+ves q3je*6dy?

The voice of a person who hqk1 9j4q0h2v fnwi oo*w;ow j je5:h7mas inhaled helium sounds very high-pitched. Why?

How will the air tempucfrflj97p1a:0h 2u/ l;r ,alwx aoy4erature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce thetv 0x2*hqyv3 y amplitude of sounds in varhytxq 320*vyv ious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spac*x,kk0y pk g29 (a9qhlruqoi )ed closer together as you move up the fingerboard tohy qg a 9kpiu)rolkx2 0k,(9q*ward the bridge?

A noisy truck approaches you from behind a buildinm v rez),yl439cs +powg. 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 thzme 9 cl4ws,o+)ry p3ve high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats ckzl h6m-;:(9pi2y ki gklr jr1an be said to b-k1 ;lrpzilh(k29ry6:igjkm e due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pov/ 1n 9zjrds)lints D and C (where destructive and constructive interference occur)nd/ j)r 91lzsv move farther apart or closer together?

Traditional methods of protecting the hearing of people who ev4 )uwtcr ;+si+crsc(d9uf/ work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels(ucis;f9c/urdrtw )c+ s +v4e . 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 be thought of as auoi8oj1+m4 ;pvwlgay 0 y5fj2 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 coi254+8lpoygm0 yujfojv;1 aw mponent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sourceuo vq3quff1t0+e 2j:y and observer move in the same direction, wit 0eo:tfqf3u1yq+ 2j vuh the same velocity? Explain.

If a wind is blowing, wilbfwp jer1,xjr, iw1 w4h8u(4 ql this alter the frequency of the sound heard by a personjqh,xib rp1 wr ( u484wwj1fe, at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in,v 65bp nybuo6 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 c6n, bo b5yu6vphild hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listeninglsz .wv.47a; tnw j0ur for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Ejvut0lr 7w.;s anw. z4stimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just b36fod1 nt 0xcinm0l f,z30muaelow the waterline. He hears the echo of the sound reflected from t6f x0mc,ni d3t00ofu 1anm3lzhe ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 2h-h;ddjvp. ei+ /m -vy0 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy 7j w o0;.fj -wdy-tfuhday. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the f h7-f juw.;yf -o0jdtwish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash itz7t ulj* x.dofb-+7n8u ko cn) makes when striking the water below is heard 3.5 s later x7unfot.udck-o+)n* 8bjz 7l. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrvqb q*yensxm 3l89((;ti ra*d l(gl.mete pavement. A moqn ;d lr8a e3q9 v*mi(( .*gblx(ylstmment 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 theo05e7ix w* xbr “5-second rule” for estimating the distance from a lightn0 7 bxiowrx*5eing strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soun:q udf6w holo:g5t + 8/ssfpwdk)um, 4d at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level 4qhcudt -2v9i n nge)(of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simd eaqb*zdch9gp9d .uk0 cq2;4ultaneously at a certain place, what will be thp4cdg;e0abd z 2qhq.ku*9 d9ce sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distanci-ru9, yz d z+wc+we2ce from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this persz, i z9w+-udc+y2wcre on experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, rze:7hqho 27 1pvg/zu whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background no1 pv7gu:qzr/ hhe72z oise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in nor3- 7dh+aqcqwiha;sz 1 mal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered onwh ;zsdc qh3a1iaq7+- 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 x6.k0gie)n9 a)l /ed1 f w xh9wc1khyawhose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more moddn:y*w-h5 1lilm*t sv 3yv0ylest 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 co0 s *3:y-1* 5wylyl hvmntvdlinnected 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 metere2zbdf /kn1 -*a3wfgs registered 130 dB when placed 2.8 m in front of a loudf/sa nz 1- kfdb*23egwspeaker 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 detectqz * gv-burv +h+m37yj a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds wh y r-+ v+jvgu3h7qb*mzose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will th:tx s7 oec(wz4a-b)bpe intensity increase? I) b(:4wsetc7x-ozapb ncrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amwgv l:g(1 ixk -jqo)*wplitudes, but one has twice the frequency of the other. What is the ratx-*(i )jgw l:g wkqov1io of their intensities?   

  What would be the sound level (in dB) of a sound wave e5ad,bm0/8l7+z vo i 94+wq eihi/aep)hpttf in air that corresponds to a displacement amplitude of et h7,ipi8vah zi/ l)5pdt0feb+ oq/4a9+w mevibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must h7ytqb a ,+i7o mt4,vfej0;osdg4) syy ave what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. b,et g4syt omyfajs ydi7o;+,q07v)412–6.)    dB

What are the lowest and highest frequenc31h6neu,fjbm ies that an ear can detect when the sound level is 30 dB? (See 3me,n hujb6f1 Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is t p+hu ga7/5ffmhe ratio of highest to lowest intensity at+af/ 7 uhgp5mf
(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. The length o5 wg,*b rlxq/ 8bm 1xf9nq)yynf the vibrating portion is 32 cm, b xy9qy) 1bw,5m*rlnn g8 x/fqand it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112lv8vj+,+ep+dlbm nlw3x + gugx9ci/ 4 cm long. What are the fundamental and first three audible overtones if the pipbv +lw8dlx3/9+g,g lp v +xenc+mui4je is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of avzx- dd5/ldq bc. zi61;gmp;en empty soda bottle that i d/x ;dveizl6.5bc pgz;q1dm-s 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 pip2w5k8/s d i f 6f0oiv8ifcd3hme organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range o dffi/6w2div05 o38scf8mihkf 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 its third harmonic. What wi2.h:mo4 *uyscmv jg9bll be its fundamental frequency if it is fh uv sgbyoc:m 2m94j*.ingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned t ;.x ev-jz/xdwo play E above middle C (330 Hz). z .dvx;we /j-x
(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 emits o1c0v+*ot b: x-nuhfpmiddle C (262 Hz) whenf1oxtno u0-*: hcpb+v the temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at ;oovzp+eur9( e++uy 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 +f8)a 8lj,g f*g polqebz6vb9 in Example 12–10 should the hole be that must be uncovered to play D abo,lfb9 jgqba 8zlg*+8o )6 vpefve 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 piym e0b84 3nx c yza5a2steix:4pe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open orex8y zyn cme5:b4ait 42xs0a3 a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates ;0u 1fz*u:o:qgjvgy akj i/iq, o s1b5at two successive harmonics of frequencies 275 Hz and 330 Hz. : u:v gbugiy; a*0 jq51k1q izo/s,fojWhat 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 ,djxz dh 2+l+o+y6z fsf+y6 oa$^{\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 aud gnlr2em,;g0 lible range for a 2.14-m-long organ pipgel;g2 ln,r0me at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxima daskchr.ls5e62r 7w e bt u-6np))1yctely 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate u tcs1bwrk.dye57pe )6 - 2 )srclah6nthe 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 adju8tt ,o (5f(to qlysq;dst two strings, one of which, t8s;ol5((tdq yoftq is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat freymuc9x4 c,/c gquency if middle 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, while another fjs;mfi 85f(df 7-e+w/y qlpx (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(-87f i ;jypl/efmws+ x5q dff brand X.    kHz

  A guitar string produces 4 beats/s, ug-5c q9wgl4r2eemn when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrage r5ewl-g4 qc9 m,nu2tional frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same fr/ kt 5 zhe.kbo9+hhnenu3d;6gequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two g9ehbku . d nho3t5+k;nze/h6 strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try:c ewcgwv(w.zk:l 9xbxk w86: to play middle C (262 Hz)xve xw . kc8 k:clbw(6zwgw9::, but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a f .hsy81 jjjfn7 mi6ok3requency 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? s.kmi8ojhfj63 j y1n7 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 from pp)xsgqj+ g.i )o79f , u,elvkone speaker and 3.50 m from oge ,7f+p jpsi,.k9u qxv))glthe 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 hear4iyapaz 67ics17v +jqs three beats every 2.0 s when they ar4aj7zacq ii 1s6vy7p+e played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and f 7)2xfl sabbnic +k;42.76 m in air. How many beats per second will be heard? (Assume T = 20 b k)sf4a7bi;lfx+2 nc$^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 15x4u,: sj64hibnvljp8 gtimt6..aa 5 o50 Hz when at rest. What frequency do you detect if you move with a speedj.6:v bi44o,h tntpagx8 sua6il5 mj. of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire eng1sz;l0( yc *sp bz2lgtine whose siren emits at 1550 Hz mov1ct yzps ;ls*l0z(b 2ges 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 towi ;gzwlv -v wtf js9)j xx)jipkot,++:es-):gard you at 15 m/s versus you: x )e;g)jispw,jv-:j +ks +vw9il)gt- txzof moving 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 same single frequency horn * nuw7r5yj+bl. When one is at rest and the other is moving towbl7rn +5j ywu*ard the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 f2a)zu- z8 vrj: : +igq8hbiejkHz and receives them returned from an object moving directly awa2va jf z)+zu8-erh: ig:jb 8qiy from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed wk3al1;in (gudt 8 mb;of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What fr n83b;t g1w(ulidk;m aequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the originayqe:9:x qs ru*0ofp0jl Doppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railwasxjfuq *oqp 0r90 :ye:y 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 speeds. Supk;0shz*m-)qo s5 q mwsm h:tc)pose the device emits sound at 3.5 MHz, andhkows hq;05) z-qs):t*mmms c the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using l0iz4/ip kbr;v vp) m3tpw(g3q f/j4xultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound ofo7 0 iat :mmw,rzae2.v frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers 70r a2eotmm,wva:.z i 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 spg09u .njs7y:*ai3op89 crl xno-kl,-pq l roy eed 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 (a) What is 7- fkji i6ac7t7p s;tqj8c h;xthe angle the shock wave makes with the dix;t;7q7f ac7h6tjips8i- j c krection 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.powkub9+: hk .1ichp (okb-g of a planet where the speed of sound is only about 35 m/hu+ kw pi1 g9.bb c.(oh:kkp-os
(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 st;rj;p3 ri yzy pjv6qf+n/09nzrikes the ocean. Determine the shock wave angle it prvpn/6y3pi +jzf0jrn y9 zr ;;qoduces
(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 b1h6qc2z7 b+h e(lyssc n4+ b7ru *jjo$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see ikte 0v+ 0t 11qml(vfi2fz0wz a plane exactly 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 horizontal distance of 2.0 km. Sl2qv(w10i0z kev0tmti +ff z1ee 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 se )dhy4mep4h;m +m6d 45n:2ivezxccs onds 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work i5y)2d6mx:z4ehscmi 4 4 pvmon+e ch;ds 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many ocxd * p(fc-hi-d.xena:*-irct x .8gbz taves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consistso8zd e0 cmp76c48 qfk:khnz5r of many plastic pipes of variou8ek z0mqr dcochn7 kp548:z 6fs lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.09 z r5bl(lvqg4 m from a person makes a sound close to the threshold of human hearing (0 dB). W( rlb q59zlg4vhat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB soeo lwm:b7ew: 8und and an 87-dB sound are heard simultanmol:we 7: web8eously?    dB

  The sound level 12.0 m from a loudspeaker, placed in tz3 dfiov;t-s;cke jof;c) 24 xkv0s9the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in alv ;tx )jc-scdf z2v34;9;oosei tf0 kkl directions?    W

  A stereo amplifier is rated at 150 W output at 1000 ur:hvq p 65yipkfrv3 27esq;8Hz. The power output drops by 10 dB at 15 k57qurfe6 : h s3;rp8pqivy2vkHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears. .yt,vpvrz0v. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30r,.0.v zpv vty m from a jet airplane engine?    W

  In audio and communications systems,r; 5-4xmgt myc 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 viotlbt.pz5q m0f- e5,kn 5qdh r*lin is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long betwee+tggzj ,)*vb;tm bj );oehkskl)x9 5hn fixed points with a fundamental frequency x)bg)*t9s;o,jltb; +hz k 5 kgm)vhe jof 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vi2f6l h f e)-cnv1c1jclbration 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 watern2hllf cc 6-1)cvej f1 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 neartu1v(n c f+j)-hk)dbn cw3w .j 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 fundamental mod j1)hfc+vcw- w tn)n(buj d.3ke) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loopj.xszcqnl* 0kmcppe;0;ng 1 5 ($\frac{1}{2}\lambda$) 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–a.opt3zy lkst 1*a, .k1000-Hz range coming 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 and finds that the sound lev.3atkak*.y lzot ps1,el 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 v5f)ou)tun2e conductor on the stationary train hears a ) f5enu2ut )ov3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Afte5(wti9+hz g8-lwfm5bv idt f 7r it passes you, its frequency is measured as85dli5fzgbft-ht v 9(i 7w+mw 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of c6rvl5ld2 4/e fji5p chars 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 5rc/65 lvl24d pfhj eiis it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency u:wx2 v8t1 zf/1fo hmzof 11 Hz. The shorter one is 2.40 m long. How z/uvof :2hzf1 m1xt w8long is the other?    m

Two loudspeakers are at opposi9r lomx8q 8btxx6q69wte ends of a 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 beat frequenc8bq9mxrlqw9x 6t86 oxy 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 h- b mp+x5sl0tbeat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected s0hlx5 bt m+-pfrom 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 f +t)vr3 f fucoamc;w7/0jn)5 ky -hzsylying 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 detect)zymj usf ;voa)nh50c3wk -+/yrt f7ced by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of higptsv 8jdg j*p3:a: ;wfh frequency 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 mosa3:v : gf; pdw*pj8tjth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38j0wz4+9bdh zod 7jd j. j:1b56effkoh) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, thedz9+j5:hj ebzh .jfw4 d6kd0f1ojb 7o 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 b qpm0.y, r8cnqe compromised by the presence of standing waves, which can causeqnp,c .y8 qr0m 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 qj-j z6or 2rf /eow7qdq)-w98c2 yce .qlqcc+“singing rods,” involves a long, slender 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,” o/cej-2 cw y9.z7qrowr l 8qqcce oq q2)+f6-djr 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 he-j7 i lrg9d/dn+oo3ooaring for the human ear at a frequency of about 1000 Hz+rdn3d9 7 -g loojoio/ is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on tqe99-zx-t zdrs7 s:b gjlj-g;he ground hears the sonic boom 1.5 min after theq-j :blr z9g de7x szsj-gt;-9 plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat z:maaz 2. +nwfis 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