What is the evidence that sound trau4 hjr 3(lz9ilvels as a wave?

What is the evidence that sound is a form os0en8 8)xuth o4 v5tku8bv.sof energy?

Children sometimes play with a i80 2juz, r): bps(a :ectcjgkhomemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child riaj,:jksgp (2c:u0e8cb) t zspeaks 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 into watert(zh75on 1rf c, do you expect the frequency or wavelength to char1ohz(5f c7 ntnge?

What evidence can you give that the spee6 j r(vzxo0fi/d of sound in air does not depend significan i o/6rjxzvf0(tly on frequency?

The voice of a person whd a8mei,8ohy0,d ts2do has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room ani8*wdbwoo qvfunueq9 ;) ; 84ffect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude9wb w5agh;:lhv7p ogr** noy * of sounds in various fre**ba; 9hgwh5vl rg*o: yo7wpnquency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig,,s ,sfj*0m7zjg6v nx o4i-htyqc6r r. 12–30) spaced closer together as you move up the fingerboard toward the brid4 f,r6oxc ziss*y7 h6- tn,vjj0qgm,rge?

A noisy truck approaches you fro p9u+ 11cmw0jfjtnq j5m behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is sudd j1wjtq9+1n5 p0cufjm enly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference is4gqah(h :i. +dito7gn space,” whereas beats can be saidh:+gqd.hi ao gs74(ti to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequenckfvfhgl9r-. i,w 4t7ty of the speakers were lowered, would the points D and C (where destructive tvk7r- 4til.9hf wgf,and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the zulced2m12rri*;y e( 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 head *2irm ce1; zreu(ly2dphones 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 wu;s zwpiw6;. thought of as a superposition of two sound waves wwz wiu.s w;p;6ith 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 obser7 tp-gwezu))63eq r 5my 4scgdver move in the same direction, with the same velocit7ec3m46)ggrp d 5u -ywsqt)zey? Explain.

If a wind is blowing, will this alter th*l :cbz4n /sohe frequency of the sound heard by a person at rehb4 /:szcoln*st with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positionv n,moar:v r01 1i:asws 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 chs1 ovairn:v,m :w1ar0 ild hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo 3wl9z1y oxcq, of her shout reflected by a cliff at the far end of the lake. She hears the echo 2lx3qy o9wz1c ,.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below t s59safadc8f (,jz :yahe waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the oceans ay5c( sa ,f9zdjf:8a 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 i l.xdlncf1c 14n air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of*w2pk 3yuu2 ut3 wwm(s tuna on a foggy day. Without warning, an(w suy2 2muku*twp3w 3 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 fish,    s (b) by the fishermen?    s

  A stone is dropped from the ti-h:7y f(sqxx op of a cliff. The splash it makes when striking the wqy ( -7ifhxs:xater below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pgay 8 j7 u-cl;ng1s3diavement. A moment later two soundlnia;3g7 1us jcy 8-gds 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 byf0i,l- snqsa- 0m+seq the “5-second rule” for estimating the distance from a lightning strike if the temperat,siq esf--al+s0 n0qm ure is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at t:z1zn,bfjj-ly v3-sd 73 7zja, hwa xkhe pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensip lp02b2camt8ra2 f 8dty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a-7f:u cdqynr7 sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensit-q 7dyc ur:nf7ies, not dB’s.]    dB

  A person standing a certain distance from an airplane wit s18koth /ktb9h four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sk18 t/ts9b hokound 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 a signal-to-h9/b j:+ dy-g 3bl gy)rim1koanoise 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 for each devicky :log)m1rgh-/b ibyad+3 j9 e? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound rn (giah3;c+q from a person speaking in normal conversation.rqaih3c+(; gn Use Table 12–2. Assume 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 eardx o vi5g2fijno*1 5/cqrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 25j 0 yomao*w8u46 a+afb0 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 eaay0*8 +owa bjf ou6m4ach 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 p3buxn24qq5p 130 dB when placed 2.8 m in front of a loudspeaker on the stage. xqqp5p2nu3b4
(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 dB. Wha h /***n kxt+rr)coskcfgog) )t is the ratio of the amplitudes of two sounds whose levels differ byfr*h)k crxs *k o)g*)g/n+co t this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave fmdxols+eijg*s:6; k ;4:nl ris tripled, (a) by what factor will the intensity incr:*g;6sro+4fsdj l: e;ik nlmxease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, bue2npi:axaza0525/ad my 6zmldc s2*h t one has twice the frequency of thehx:nz6 *d2spaa /yzai05a2 e 2mmd5lc other. What is the ratio of their intensities?   

  What would be the sound level (in d:on:e7mbq1un kynl+3 f k*je:B) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at+:u 7e nbnk3kq*:1:yjneomfl 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tt6xl,*cor ;naone that has a 50-dB sound level? (See Fig. 12–6,;rnclxo at6 *.)    dB

What are the lowest and highest frequencies that an ear can detect when the sounv3i3q3rgf:sy- ek .hy d level is 30 dB?yevys 3 .iqghf33k:r - (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound lew(b/xuef., r,3d8pqt8 -ur ut+ pzhj ivels. What is the ratio of highest to lowef,tw( ber,+x qu zp8i uj-8rht/.u3dp st 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 fundami;it 5.p5/gfngf6v va:. tcap ental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a massa:.a5 ;ptfp5n c/gt v.givif6 of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. Whaz/4*lcmvzdh:0bhct, p; * az 7 a5dmpat are the fundamental and first three audible overtones i*t p a:5z7h a bhavz/dc*;zmdp cm4,0lf the 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 exphag;i8hdmivdttp+ ;l b(ws t w3175 sr.vs6/rect from blowing across the top of an empty soda bottle lm daihsg;tv tiht(8 srsrdp;5w/3v+716.w bthat 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 organ with open-tuklx+nk 7/rbuq6a42 cd(gzew . be pipes spanning the range of human he7z.2 k6un/cx lkg+ (4bq erdwaaring (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as qw:)my-m/b6 cl e:dpmits third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lengthm6el:-/dmyb: c)pm wq ?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abov .hb.m2kfljzevd e376e middle C (33m.6 3kelh .7zbde2fvj0 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 emits midy)yz/cafvh ;* dle C (262 Hz) when the tempera/h ;cyfzvay*)ture 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 b*8fqmfp 9mmnv 2 o62w20 $^{\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 h7) . bwhuw;esgt/o ;snole be that must be bw)g;7 ;e ushots /nw.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 61emkk 6 6-pc5.b/lb( svsg-lm6hh6hm i6 Hz, but not at any othih khmpkl6cs 6hm/(--6.blv6sgm5 e b er 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 1.80 m long is open at both ends. It resonates at two s;c44cmtsdm5p8 uhkx37s*ta v uccessive harmonics of frequencies 275 Hz and 3ksm7;4a8c*5vcs up d4x3mtht 30 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 .* ii50ifz +vs( fge1 ) sjcb umfbt1v-(w;fsx$^{\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 rangoj twu3139mf ze for a 2.14-m-long organ m3j31wuzt9of pipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately ta h-pxqv++ va61qs4o2.5 cm long. It is open to the outside 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. Whattav+ 6+4qvaoq sh -x1p 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 strings,luv (rz(sp;b 5 one of which is sounding 440 Hz. How far off in frequency is the other;przl ( v5u(sb string? ±    Hz

  What is the beat frequency if middle C (262e n, . s2cq0p1-unyw40zjv gls 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 kHk epwx8g2 (eu-z, while 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, estim8g(xuwkp2 - eeate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork andqmdzw; ror+p /32 axe: 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.+2a xpmwoerr:3 qz/; d    Hz

  Two violin strings are tuned to the same frequencys 6 50-lo*ak-bjbkt7amejj 6x, 294 Hz. The tension in one string ix 6lj5to b6a js-0ekamk*bj- 7s then decreased by 2.0%. What 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 identical flutes eac zmzek8s8,dxwgm3r 0. h try to play middle C (262 Hz)z w.80xzrm k8ge,3ms d, but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuningl)383rpl ywx. dcvy:ni oywq/9+i jz2 forks, A, B, 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,8jxpcw2 o r:di q)yz lw/3y+ 3y.nlvi9 the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apartkd pptb2x(: xi6:ey-,*d tosc. A person stands 3.00 m from one speaker and 3.50 m froo6p*xy bcse:dk d2 ,(:x-i tptm 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 7fvwo7(h xq gs3rm17a piano tuner hears three beats ever 1(homvaq7sxf 77g wr3y 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wava1u3r y 4;a zylnw6c(oelengths 2.64 m and 2.76 m in air. How many beats per second wo anl;4(ryyzu3a16 wc ill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz whec5glht 9 :b 8z)aegf6en at rest. What frequency do you detect if you move with a speed of 30 m/szahl ec5g8 :ebt )9gf6
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whoswr7zqlimo 1m es+ n;. 5larm74e siren emits at 15501 7 l ;se.i7+qza5mrnm4om lrw 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 2000-Hz sour4;lr awo/k7 6djv e2rece is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the teaw4vr2dl 6jok/7e ;rwo 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 equip9 tdh3i* deluqo4 )lg34*n7txqplq,m ped with the same single frequency horn. When one is at rest and the other is moving toward the first thdg3 qmp 9do* nq4l)i*qlx 3u ,7tle4at 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 ultrason4iol qi +o0l(tic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequency? (to+ 4li lqi0o   $ \times10^{ 4}$ Hz

  A bat flies toward a ow80hmej bi+ 3wall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave w8 3h0 emi+jwobith frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tubthkagf yg /;; ;byov 9/zt*mf.a was played on a moving flat train car at a frequency of 75 Hz, and a second ident/*vzof9;my kag.;; t/byfthg ical 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 uog4eg pzg8w)i)j, -a lp4g4xeltrasound 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 arteries at 2 cm/s directly away from the sound sou ga w48l)o-jez ig)exp,g4g4p rce?   Hz

  The Doppler effect usu xgz;cl5 ,ajqg)4 m9ring 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 emits sound of frequency 570 Hz. When w6nwe qwh8gf9x* r 7:zthe wind velocity is 12 m/s from the n78grw n*9:e6wzf q xwhorth, 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 speedma0fzu;7r k2z 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) Wh.e/p7o wydpx* at is the angle the shock wave makes with the direction of the airplane’s motioe p7w.op/y*xd n?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of x d n7wk(541*n zpa1vcat/awz sound is only 1* v4/zazwx( a1wnnd7ktca p5about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determindb-;bi:,lw t8rw5yje)+afytrm w;x 6e the shock wave angle 6wr:i;xwt+rjb ; )efwy -,t5 md8by lait 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 x ph1jb9zgrjd39c:+t$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see7-b+vpoz q v5)v/ e 4ir p-(bz-rkrlxx 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 trav 5lp-bx(-qv/prv4or rixzbze 7 k+-v)eled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound puls6ii 0,hi2ws7 blxbzh/ es downward from the bottom of th7xs,zbhhwlbi i0/ 2 6ie boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human axwi i78wp34vgzqi as vvx w +*.y90qb-udible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewereuo)w3cd1u58un p4 nt pipe symphony. It consists of many plastic pipes of various lengths, which are open on both ends. on1 d)3 uc wpunte485u
(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 mc,*k d b1xkcg8 from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound levegk8cx,1ckbd *l of 1000 such mosquitoes?    dB

  What is the resultant* vb7 l0bbdu/v sound level when an 82-dB sound and an 87-dB sound are heard sb0 *bv d7u/blvimultaneously?    dB

  The sound level 12.0 m fr 7a,f besg+5s-qyi. oxom a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of5a x,-.s+ qyoeig7sbf the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The p /basi7cv4l p-ower output drops by 10 dB at 15 l 4abic/7s-pvkHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices hv1.3gfp 7 ulaover their ears. 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 unpra.lgvu 73fph 1otected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gai-d.vvv.*, 7ai w cz cu80djncgehw*7l n, $\beta$ 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 freqi-xc5(3o y jlsuency 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 po j1eej blrfw-- pq 1dg56ka 3z,ku07ncints with a fundamental frequency of 440 Hz and a mass p aw7-5eu f p-dlcqb11zn6e3j0kk gr,jer unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical openwckr2pn ) ;px984dwt v tube filled with water (Fig. 12–35). The wrn tx 8k9v dc2w4)pp;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 tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one h:cw6i dqc1u/ enduc/ch:1 dwq6i and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resona)7+jcrqu0*rg 0ytrn fte as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sources. Thg:x)hr;k )jl8g t db9je sound is loudest at points equidistant from th;) lj db8xh9g:r ktj)ge 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. Thgsko5x6 .x.mmv wviv .5ipsq4u5d ,x .e conductor on the stationary train hears a 3.0-Hz beat frequx,dmxgk 5p 65v. vs.5qswiu vi.xmo4.ency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistqi6 is*qryov 6wz0 82x.)qxxd le as it approaches you is 538 Hz. After it passes you, its frequency is measured as 48i rq.6v )x0 *z26xqqoidwy8x s6 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the (p1vzmo+mjd -difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequd-om +1m(zvp jency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together6rg dtk)(1p jw+ka ei6, produce a beat frequency of 11 Hz. The s+61p( tjrkda6 i)wk gehorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pash,dm4z(( nb ,yz4w t3wkhnqc6t 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 observern4,q4t hyw h(k (n6 3dcz,zbmw 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 bel t+9a/x7i v ne3gxt hm*+)mdvat frequency would you expect if 5.50-MHz ultrasound waves were directed a+ i7 m +*mtd)/vg9veht 3alnxxlong 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 ew 8 s/gp0cch2n2owj5the 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 wavp/e w02woc2 5 n8ghcsje reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approis*h:s re launa*,i73e6 qz*saches 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 bat so that the echo from one chirp retuu *7iaesh sr*:al3n6,zqs*e i rns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signae aw1v 7ik)s5lq9 bmeem0j-(zls from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns bi)1s 0jemlqe(w em zk-v5a 97were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening m bomjt-ip .br/ 7t*q1can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this m7 otq*mib rj1 p/bt-.room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstram4) u mayk:l*o4t*s5kh3dh.h z pevv+ tion, called “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 toyth43eva+uk mdp)* s:zh4h ml5o* kv . “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 rj5+)(fbt*uwyr iu /3j5carx threshold of hearing for the human ear at a frequency of abou53tr*brfw +i xyrca5 / u)jj(ut 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An obs -0 2wfrdce,rderver on the ground hears the sonic boom 1.5 min after the plan0-rd 2 fe,wdrce passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat i1wiol* 7b n nzp/ung34s 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