What is the evidence that srxe v29),7e t:fjw+jp qjd u/jound travels as a wave?

What is the evidence that sound iso)dw;d i+oa7 /tl v0li eiki(* a form of energy?

Children sometimes play with a homemade “telephone” by attaching ay.jbq0 ,fyp3 wj kwiu);5f1ne string to the bottoms of two paper cups. When the string is stretched and a child speaks i;nj ij1yfw.f3) 0 epq5u ,ywkbnto 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 water, do you eilz. o.f o3lj1xpect the frequency or wavelength j31lo..oiz l fto change?

What evidence can yo hv 192:8j.jwk1oa f3vpaoxbm,wrc k7;a 8 bwau give that the speed of sound in air does not depend significantly on frba .p mk1ajoj82cv 1o9kwvb3hrw, w; xa:fa87equency?

The voice of a person who has inhaled helium sounds very high-pitched. Why? fjz)*k rs:zp8

How will the air temperature in a room affect the pitch of organ pipes+ f4yy-jg. wki?

Explain how a tube might be usedz 1e6 5ecl:axw as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muf5exez l6ac: w1fler.)

Why are the frets on a guitar (Fig./oer xmr0bsu ; qlrx6jy 26d;4 12–30) spaced closer together as you move up the fingerboard toward the bri 66b;x/lo me;2drrxr 0sq4jyudge?

A noisy truck approaches yol:hqu61bt wt d5-:u 1a qxc/c tu-+fgqu from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the:5q aqt-ufc: 1ug +cdlw-uh /6xqttb1 high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “int5fn6zzf78 ovterference in space,” whereas beats can be said to be due to tnz6o5ff8v7z “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pogymg ok pru00c;*,va0aqr*c /ints D and C (wherg*v/aa 0crupmr0cy*k 0g,oq;e destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hor0(2ru)cpt l earing 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 te)ctl0 2 pur(rochnology, 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 fu:.775b jpgiz. 8 k2 uazydl-tk z(so+c zsx/thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are thea/bz28szd(fu+ py-xcls. .kzjz 7i 5 : ok7ugt two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer movnjc 7/3s0nb nmc p.7qde in the same direction, with the same velocity? Expnd7nqnc7 3 /.m0 pscbjlain.

If a wind is blowing, will this alter the frequency of the sound her1- ja1netss, ard by a perser ,- anjst11son at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positi4n3uztshinbrqyh **01 /,bqm 0/r9ex5 qytok ons of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound o 3ys5tbor, i q**r/nmb 0qx9htnz/h 4y01 eqkuf the whistle? Explain your reasoning.

  A hiker determines the length ofgt8 3g cx,3adgc53bgi a lake by listening 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. Estim3t5ggc3g ,xa8 dg bci3ate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just brd+:hol a 6 1k+5sk8ted-rp tpelow 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 spa8lodr kr6de1p+pst t: k5 +h-eed 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 a6 /em4:ttp-ip *wz+5gkfrxg mt 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 tuna on a foggy day. +pymma)7gf5k y*r //qjeix9e Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. qi9fgy*pee jy7k//a )r5xmm+ 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 splzdx1;pd m38sau s-i3 iash it makes when striking the water below is heard 3.5 s lat3p3m1i;sdia dxz -su 8er. How high is the cliff?    m

  A person, with his ear to tontyg 4: m*cc6he ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from theg yc:o6n4c *tm 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 :nty79ug+o(yo4tu ix; . geeoerror made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature isutn9 ;og(o7og etu4eyy:ix. + (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at dr0zh 2r*q yv r )(d;hheph-w/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 of a sound whose intensityp9dlg f)s 0:v1 1m3.v1pzqplx.vu pyz is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB wh:;xb(w 2h26t:uw qprw:ojlu al3 qhqcg1fj25en fired simultaneously at a certain place, w t:;blruqgwjoww a3 :26:qh1h pq5l2(cxjf 2uhat will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an air.r 2cnnes.kls ,9;6rrjtiv m7/s anb,plane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engin/7jcbknarrs;v,29nsl ie,.nmr .s t6e? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, wh vtvp ,nz2;)gx(exue ,ereas for a CD player it is 95 dB. What is the ratio of intensities of thev2pxev,ux(tzgn , ;e) signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the pow ronnay,n0g(qt-v( o (er output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. o (0ot q(v(ngnny-a,r$\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose 9vha8p n(;,ue upwr j:a- fb)5,f3axemdzx6d 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 Wjcd*2/dj/n qk , 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 /*/2k cjqdndjto 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 whrrgv a9(kv pp/v y ,h*;y/i.faen placed 2.8 m in front of a loudspeaker on the sta//gar.yk v(f, y vv9*pi;haprge.
(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 typicl028havwbh9dhr1 f 8 kally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels didaw8brhfh2lh1 k0 9v8 ffer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fa 5l)j022vsa,jrpj5 fm -h ocjactor will the intensity increase? Increase b5m 2j5pjjljfv02rao-) s, hac y a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, butf2b 5(ppamu u0 one has twice the frequency of the other. What is the rap2up5b( fa0 mutio of their intensities?   

  What would be the sound levh wngr-31c h-zel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air moleh1g-w hz-c rn3cules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound le4zx,n hfqujnfp60jd* kojz,l2 9hn*3vel to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. p4, ,d 9fuxfjhzj*z32 *nqnolh6 kj0n12–6.)    dB

What are the lowest and highb(e *wize;d7nest frequencies that an ear can detect when the sound level is 30 dB? (See dn( *z weie7b;Fig. 12–6.)

  Your auditory system can accommodate a huge range of so+vdfz+dc) j i)r /nzb.c+f2 ,qxfww5eund levels. What is the ratio of highest to lowj+5)dv f+ exf, +.d2iz qzcnfb/wcr)west 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 f t gw 2+cl2u4h.gy1b5km,dqx brequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.k 2gtm5+cg .b yb,2hlxqw 14ud35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundame7wsa if07c*vo3 *ycdsntal and first three audible overtones if the pa7ds o7 * wsiv0yc*cf3ipe 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 blowjl,t1p 6.t xniing across the top of an empty soda botip.1jt nl ,t6xtle 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 organ with open-tube pipes spann(h0m.jgaa25ywgu kv -: czgu8ing the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes:wam-05k. u g8v h2cjg(gzayu required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 5kq;3b 75vlw vnjmys;340 Hz as its third harmonic. What will v 3 qv;jnw5bl7;ms3ky be its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to pla(yc */v exdpu+y E above middle C (330 x+ yedc(/v p*uHz).
(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 oryzky-0; a(hcggan pipe that emits middle C (262 Hz) when the temza0(khc;yy g -perature 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 2stputcrt e fb 4t1t)a) tkp7a/.,i)- y0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiew3ye; 4nm:y199 cnox/nv sk wnce of the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 Hx 3wwno9 94ncm:;esy/n1 vknyz?    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 61m aqa4u44og0 s6 Hz, but not at any other fr4qug4oa0m a4sequencies 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 res jm83ljq)ixxyy*k ,i06ox oa5onates at two successive harmonics of frequ*lk36xix m 8xo5q, yoja)i0yj encies 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 b6bej65c9ujb n6 fa6r$^{\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 audibleu6x e9zx02-pcxjsc)5b1d gci range for a 2.14-m-long organ pipe at 200- jc9 6ic2ud5sgxzpxbex1) c $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is appy n**vd 8jgg4yroximately 2.5 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 g4y**jy ndvg8. 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 strings, o8(y.t qkzc+ ;hfvo,hw ne of which is sounding 440 Hz. How far off in frequencyqty.w;cfv(h ,8 +kozh is the other string? ±    Hz

  What is the beat frequencyp u:fepa f(04..8cpsnq1e tcl 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 whistlesk 9fc/k;z x l yofr-edr)01h-k0pgz9 operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whinso-9x9fre) y10k zd rczpk/-ghl0k ;fe of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when s .t(yapr7yr 6sounded with a 350-Hz tuning fork and 9 beats/s when sounded with.r6(ayrpt 7s y a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in one i aqe i:gyh(u(wdi(+aixf *0.st h:a(.(+di i0aeif* xi(wuqgy ring is 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 each try to plav-t9a5y (/mkrpe0on k y middle C (262 Hz), but one is at 5.0°C and the othektv (er/9anm- pk0o5y r at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuningyxq p 2/d);c tqzch6ebb )g7q7 forks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequ7gtqq)q7c e by xz2h/6;)d bpcency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded 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 lg:l)rlo9oqj31wxsr uhjm9s) ,i :*jfrom one speaker and 3.50 m from the other lj9imj,9jls 3lo)row xs1rg)uh:q:*.
(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 bmdbi m7 a:a+fs2 y-o0be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played togm a +smoad-072bf:yibether. (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 2.76 p /5lt z8dwrv-94ul oy)eq qc*m in air. How many beats per second will be hz9ypw )* l q8qu/v5 td-cr4eoleard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire tjbh6c d. lp6:engine’s siren is 1550 Hz when at rest. What frequency do you detepc 6:l.jhbtd 6ct 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 fire engine who.l8qy5c/q drcse siren emits at 1550 Hz moves at a q.ql5dc/c yr8 speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency c4dn1m+:zwjyl:1qrs+ 8,n p(nigf bhif a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two freque pqlz:1mw8+j1, (srigcbn h4 + nfydn:ncies 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 wiwqu2 b;(d fv16byajzybfr5 * 3th the same single frequency 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 hornsf1r b(wzb;b3uyd2* 6 q5yvfja emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and rekeprexgj .w5+,,;y6 sm:n vzjo3m6xn ceives them returned from an ,gwnovj, mek3yz5xp:s .r 6;jxm +ne6 object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emi0 v.gakqt*p td2q v ;-fwo3oj2ts an ultrasonic sound wave with frequencyk2.jooq0t3gpv qta2dfv;-* w 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dozsbk+e, s3 dh7pes*,zppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second ident+,b3 szsdz* hkpe7,seical 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 ultrasound waves to measure blood-flow speeds. pypxkoc3d3o,s s plj- k:+ c,:Suppose the device emits sound at 3.5 MHz, and the speed of sound i kpc :,y3j,d+x- 3sclpksoo :pn 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 ultrasonic waves of frequenc7;9vuog+ pux hy $2.25 \times10^{ 6}$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 the wind velocity is 12ok-h9k ;s4dfo m/s from the north, what frequency will observers hear who are lofs9;4kdo-h ok cated, 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 oaajv4+5 wqy x;n land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the06au96wlj4b. p ml7dxsjvmk3 speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direcausl4bvl9x 6k3wjd067 . j mmption 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 the speed of s m1np0z/ cwgy6r,)xlv1v a4aj ound is only about 46vpzygxc1 ljan0a wmr )v,1/35 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 oce fg)p k4)px8 y2tg,yhban. Determine the shock wave angle it prodf)48g pb2kpyht)x, gyuces
(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 ,: efuclb17w y$/theta$ 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 km a 8qfxlvaev 2o*u+lj35 bove the ground flying faster than the speed of sound. By the time you hear the sonic boom, thef +82xlvv3ealqu 5 oj* 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 o2gx,4 kjy,6bcb7cmp 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 is 200 m, what is the minimum time between pulses (in fresh water)?4bm2 x,y bk,o 76ccjgp    s

  Approximately how many octaves are therye ern6 u9)qepdxe5(* x b++jke in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It cons8 leq:x 0qu2edmxv77cists of many plastic pipes8dqmx:vul0 exqc 2e77 of various 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 5.0 m from a person makes a soun4yaggcfw 44v2hy3c1z(x ep5eb. 0x lcd close to the threshold of human hearing (0 dB). What will be the sound level o.hp(xceg c4bw3c4v l5 4zf2 yagxy1e 0f 1000 such mosquitoes?    dB

  What is the resultant sound level wheldk .- s5xb5x19s,ysutm; :asbo:jovn an 82-dB sound and an 87-dB sound are heard simu xab-1 ju o 5vs,so.t5sb;:9m:kdylsxltaneously?    dB

  The sound level 12.0 m+1sawqs o1 ;qn from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates eqn1ss wq+1o ;aqually in all directions?    W

  A stereo amplifier is rated at 150 W output at 10o(1yw192 z:u dzv;2riir-ks aot jw5q00 Hz. The power output drops by 10 dB at 15 kHz. What is the power ouaivr:ryw1 ot( 2zdo 1zq -su2;9 5jikwtput in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their eq8 pv(px d;7stars. Assume that the sound level of a jet airplane engine, at a distance of 30 mxq vd;s 87p(tp, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systeg58 d/wg/,ydx ,seb v3jlgl c7ms, 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 frer+-k e f,fliq1+m fu0ioh0 va9quency 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 fun iy 5zzg;90nxeukjr0 6damental frequency of 440 Hz and a mass p0z 6gru;j05 xy9n izeker 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 open tuplm)ec z0g(2nz ;vh 4hbe 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 thencg )0(zhzvlp2 4m; he 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 2.1dl4hghlg )+g4,( dx1hx vki1 i0 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 fundamental mode) with the third 1hg44khi (gldxvg)x1,dih l+harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop (6m 7s/ b(+0c fbymlugm$\frac{1}{2}\lambda$) 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 500–1 t;cv+ *cmmdf4*u 4sdh000-Hz range coming from two sources. The sound is loudest at points equidfc;tvmd4*m*d c+shu4 istant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on dm1niwe 9b6m,f m)4w+ +kunpd the stationary train hears a 3.0-Hz beat frequency when the other e), ubn6n f+ d mw4dkp19m+wmitrain approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you z9w.9 ufp1tjm is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (9mpz. tj19wfuassume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by lp(c l:n.9b axev0)0 pbalq;ywistening 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 oct0;yp bwqx.0nb apce (:al)9lvave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding togeqyni1zfpk51.x vq b, a,rd7ix0r.sq+ u2kvd0ther, produce a beat frequency of 11 Hz. The shorter onbfv2zia7 x xy +5r01.i.10 d,q,vkqnupskqdre is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad caaoeg- 93hpw 7gr as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound -pgeowag h7 93frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s wfcy noomw8 - 58zkssll9;iw+, hat beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected fosm;lzw98lc 5 +sfiy8 ko wn-,rom 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 thi..9zwq 7t;egb awwm ,e moth is flying 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 afte97q.emz.g t;,wwbiawr that wave reflects off the moth?    kHz

  A bat emits a series o70i9qhcc ob :xf high frequency sound pulses as it approaches a moth. The pulses are approq9 bc0ioxh: 7cximately 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 returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send pd mz- n8nay)(signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The m p(ay8 n-mnz)dost 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 )ml2nn*/oiybu x9ai . by the presence of standing m 9u a.ixniob *2lny/)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 room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing d, k4fbr9 bjila:ydn0z)q*)8es i c(mrods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked witcq0mn8 z)4*j:li9yf)s rb(k a ddi,ebh 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 threshold of hearing for thefds5 uxiz8/,gx k e09b/cnjx51srml : human ear at a frequency of about 55xszxid1,8kxmljrg:s ne/0u /cf b91000 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 observer on the ground hears the sonic boom2lc o(enb a bxxz y6./t+mn0u1 1.5 min after the plane passes directly overhead. mlx.(0a yb1oe2bz nc/6+xnt uWhat is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat :2p 7bdr 1yulh,/zlucis 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