What is the evidence that sound trav:) 5pyb*cy73)l7cw2lzno ;q kc-fos6ww lzux els as a wave?

What is the evidence that sound is a p.b dv*zs+ivk3dnct2o : 1( . ;abgjcnform of energy?

Children sometimes play with a homemade “telephone” by attaching a stlci. ykbb:u q q53i a3.y/u:zjring 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 othe y.u5b/kji.z:a3lq3i y: c buqr 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, ztgwb) -km(ima+;c 5ic (d5icdo you expect the frequency or wavelength to ( 5gk- cc);i adwic5it+zm b(mchange?

What evidence can you give that the speed 4u9a+v 1mbyo:t5 6 s iezz-8d.trkm saof sound in air does not depend significantly on frequt+ 4at: adyuk s8r ms91i65zmoeb.v -zency?

The voice of a person who has inhaled heliumb3y2*-.lmymo fyigaebz5 1 r1 sounds very high-pitched. Why?

How will the air temperature in fo 1y *n;b,d/o6gpmrda room affect the pitch of organ pipes?

Explain how a tube might be used as a filts 4vtpq*.dn/ ger to reduce the amplitude of sounds in various frequency ranges. (An example is a car muffler.) g /dt.sq4v*np

Why are the frets on a guitar (Fy qk.6z 3v wypq,w*u*jfn1 .vmig. 12–30) spaced closer together as you move up the fingerboard toward the bqmuk *16pqfv3vyz,.*wy .jw n ridge?

A noisy truck approaches you from behind a building. Initially you hear it but g9o7g gb+7gukcannot see it. When it emerges and you do see it, its sound is suddenu9kg7b+7ggg oly “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 “int 6bf)4b mdjlt:,eq9f perference in space,” whereas beats can be said to be due to “interference in time.” Explain.bd,jffm lp9 bqe )46t:

In Fig. 12–16, if the frequency of the speaxpz tm dov p2e6u1t -h oi(v1/eo6gy6;kers were lowered, would the points D and C (where destructive and constructive interference occur) move fartheitxtd/66;1 uzy6p2po1me ghov- o ev(r apart or closer together?

Traditional methods of protectiq;l tnntzx+uvcajd4: )9)d w 1ng the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce nois) 4 1v:9)nnq j ;dxczwd+ttluae levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thouti6fkx e57xx me r/i0s7z k,dm8c-z6 cght 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 the two component frequencies c06cd5ez7 x-t/ix 7 mfk6rxze kmis,8farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observe.lq bk gh-s8t3r move in the same direction, with the samk.hq stl g8-3be velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a p5qith v.7ysa 9erson at rest with respect taty v759sh q.io the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a l,ty0o 3lomz+n z/pdd o; .n9q)bxvj/ swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Expz 3x ;),on+obmo nldzvqj9l.p/y dt0 /lain your reasoning.

  A hiker determines the length of a lake by 66yl nd rm3*eqlistening for the echo of her shout reflected by a cliff at the far end of d 6yeml6nqr3 *the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears thee:+y kse 7bky5 echo of the sound reflected from the ocean floor directkeeks5+7yy: b ly 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 airo k rb(g/5(zhd 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 dq;b -0m4* j+ s)sweakicx2b jabove a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33)m*ji skc +0) desajwb;qb4-2x . 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 ofy.q*d6frgmy.: h/fd/spk wy3 a cliff. The splash it makes when striking the watrypgd/w sfmk36y.*h f .q: /yder 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 ch dzbc)hq*jl5* :df+-nvkgd; . ug w7concrete pavement. A moment later two sounds are heard from the impact: nuv* ;:.hhfkc+-*gblqw 7cj)d5dgd zone 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 efimm /)n 6fyx)rror made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperatu )fmi6/mfxyn )re is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain lezdapsxs/*w /.qw k) h3vel 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 int3 9b4u m w.rgla3d 2xt6qqe8akensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 9e;8,wdodm) s4c tp 2va5 dB when fired simultaneously at a certain plac d8awpev4m2,)o d; scte, what 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 1 xz:llwn8j1 tairplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 z x11w lj8ltn:dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-n1 wyn0 3 4(kq,n.ncuv9-uoxs diyk7 bwoise 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 eb.wn k7ciyu,u vo1 349y-(qws ndxnk0ach device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a9g0 pw ,1vle.yzcse tg4s-3sc person speaking in normal conversa -sgwegss.lz91ve,34t0ccyption. 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 eardrum whose area ip0 (qfj*yj (x.x03g tqocicd1 s $5 \times10^{ -5} m^2$ (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 modest amplifier B is/tv)y-vvq+ut0 m u wj:a/:lte rated at 40 W. (a) Estimate the sound level in decibels you would e+m :jua-t qwl:vvtetv/)0u /y xpect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB whea8ft.n pd3g/x n placed 2.8 m in front of a /gfxa nd8t p.3loudspeaker 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 typicallioe i1::27npn 7j+omyy,rqxs lz;f (ey detect a difference in sound level of 2.0 dB. What is the ratio oi(ylq 7nnp7ox:1ej;o, 2z ym:eif+ s rf the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a soun 5.klm 4f,mgdnd wave is tripled, (a) by what factor will the intensity increase? Increase by a factnmf,4.ml5 gkd or of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitrh/x5(3ew ycd udes, but one has twice the frequency of the other. What is the raticdx5w3 (/ery ho of their intensities?   

  What would be the sound level (in dB) of a sound es+2x8jk0 zzl 05anbn wave in air that corresponds to a displacement amplitude o z8l+jxnaezb250 k0nsf vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must h-j qsk 6+p ba ro-x)j6q-clla:ave what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6)-jrkcpjlxq qbo :l-+aa - 6s6.)    dB

What are the lowest and highest frequencies that an ear can detect when the soundn qblndo:0cfa7bnd u+3s) ;/ d level f/n bol ;nd u)dd7:b30aq cn+sis 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate 8m1 de7jv*:d tana9psa huge range of sound levels. What is the ratio ofa9p dv 8j:a*smend71 t highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a aira7t*(g7jr f zrs6 ,fundamental frequency of 440 Hz. The length of the vibrating portion is arzra7j 76*t,is(fgr32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental anl24mxdhr8sm g q0 kztfj1n3w47a0(myd first three audible overtones if the pimnk4jlm3m7f0 0h18yx2rdgwsaq z t ( 4pe 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 ofr3f8vz at8/ct3fu (lp an emluap(8 z3r v3tf/ctf8pty soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the 4v3tu /yba f43yd0 pr-kw*zrorange of human hearing (20 Hz to 20 kHz), what would be the range fp3o-ay4vur0dbz*y r3t 4 k w/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 its third harmonic. What wi bdl s-dgh4m f(3*q(*fruypjl;x up( +ll be its fundamental frequency if it h r(dyj u-udm l3(4p*;(pqx fsbl g+*fis 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 play E aboa xlx7 ;+7j0 4oclupwfpt0ir :ve middle C (330 Hzc7p4upwxaxf0ltr +; 7 0iol:j).
(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 middle C (262 Hz) whe2s1cihxre,i e +- krxbu;x v/id7) 3wnn the temperaturexs3ex b2 ixrch-k/ruwn+,iv17) d ;ei 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 20cy8i,5hutbb8z s0k 5 s $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the e g1qw,ekc.nk8- wbg ,flute in Example 12–10 should the hole be that must be uncovered to play D above cwkg- w1,.ekqe gn,8bmiddle 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, vafu,3knj/,l4fucc 8 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a j/3a ,u4culvf kc,8nf 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, q:7p )qpii1nx/7e f fptgs+iuccessive harmoniciff)/,+ i nxq7 tppgsq7ei:p1s of frequencies 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 c l+a0 o+o-hrr m vq96pth1p22 gm8cbl$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-/w xzt wc)4vn15o -crwt/3vza long organ pipe ao zxw -vca cr31w4/5n)wztvt/t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal ,vxwi-btg20 ais approximately 2.5 cm long. It is open to the outside and is closed at the other end byvtx,ba2i 0w -g the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adj2m a)fnkv.uc59jr bf6ust two strings, one of wvbnjcf)mua 692kf. 5 rhich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (+.y ,hz8is c: :*e) +7tkxrygaq9bz4rjcw saq262 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 operatekug fve63,p,n s 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 whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of,k, e3up fgv6n brand X.    kHz

  A guitar string produces 4 beats/s when sj(:bois8w (2tw* y gafounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reawig o b*:f8j2ts (ayw(soning.    Hz

  Two violin strings areuqiw7+y( z7e*w1suv k tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. wikseyuu v+*7q( w 1z711–13.]    Hz

  How many beats will be h 7qlzl(f*o i3l. flm2keard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0 f. f*l3l(z2 lqkio7lm°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hza8;gnw5xqe),w t gt4 n; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequenxwga) 5n;4 8wnt, gteqcy 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 from one speaker and 3tdmh*7 +dx7n s.ms*7xd+dt n7 h50 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tunerneg-p db 5,d0tpmld; 9 hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, whten9 5p-d0pb gd,; mldat 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/ ierpq u38g9k.76 m in air. How many beats per second will k89eq3rigp/u be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency omir9 ,na 9ve4cf a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move wi,r9 mi49 ncveath 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 djfr i23y+ hp:;ujid i(etect if a fire engine whose siren emits at 1550 Hz moves at a spfih3:jryipu2(d+ i; j eed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you at w.d m8k ,z zd,onz,k4nk+3hm h:kyz(wo8sim, 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they okim3z:+z8 nnhz z8o,dh,myw( k d., k,mwsk4 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 hisk;u7xbs j,k/3 cn h.orn. When one is at rest7xkunh .b;ssj kc ,/3i and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHzu 4tx.icbyid* 2/mw+ hxz6 n)r and receives them returned from an object moving directly away fri urh b2m6)/+* d4xzycwn.i xtom it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a7iag p0oi2qv2w/91kkh0k x , qsl bg)b wall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wavs0 kq/a2 g,g21q9i0vh7kxli)o p bb wke?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played )yk+l e;atx5k 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 railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?ley+tkak )x 5;   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flol7 qfu8lxga53e 2ebh q(/.yam.)wv vzw 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 expectedu )(yh/la. .vf 5ez3bgx7av2 mq lqw8e beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usinwo1tf u+qay6*g 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. ,: qmcr-t 8n3k;jgfvkWhen the wind velocity is 12 m/s from the north, what frequency will observers hear who aq3m8- cvkrn, ;ftjkg:re 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 mo3fjh :m( cvc3gving on 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 the speed of sound is 310 m/s asmuq (hv.z +.3j-gwe v;k6 xq(a) What is the angle the shock wave makes weqm-xga3hwz ;v s v6 u+jq..(kith the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet whe*zibi4uviqc 321 til ci s*-6yre the speed of sound is only aboui 4 b sv*u2czli c6tq3iiy-i1*t 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. Determine the shock w-c mjj0 jf.ncyc*a03 mc2d+a qave angle it prodd fcm jc mq.0ca2jc+-yan*3 0juces
(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 w)3jf3m r9 hrfzye4h(n f1v4hmib* b* $/theta$ 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 exactlyyz2 5j1xedu0 n 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. See Fi2u z5jydx 10eng. 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 devimb) b5(kizwn ++5*pcfc ndrl)ce that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If thdz*cb5) nm+fnlk 5pbw i)r+ c(e 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 octc +v8 evtaeb;z/ l+l8paves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symb(;l .n,* naz lgej j*b,2xhpsphony. It consists of many plastic pipes of vg eb;s2 * *bjzln jp.h(lxan,,arious 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 sound close to ,stn wk ; tok,k/,ff;,ne:ze fthe threshold of human hearing (0 dB). What will be the sound leve;,n/,fe,k,ow z ktt: fen;ksf l of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sd0(s/+vi: zxr0 m i n6veixf-found and an 87-dB sound are heard simsrm xi+xzv06 e/ 0(idn:iv-ffultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dft+ jqt4dxls8b 4o -*xB. What is the acoustic power ou*fx8tt+l 4sbd4- oxqjtput (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The po 45mw5tw* mdv f6lqzz bo)u1l:wer output drops by lz5ww54o) *vtfmb:z 1dm q6ul10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over c8u t* gmq 4qwov+ ,9jq8/exovtheir 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 unprotec9*coqj +wq, 8e8v4xou/ vm gtqted ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems8*sp 4g xn9uzp, 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 aihdh/y qqfmim2)j9h*a2s 7*s 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 between fixed points with a fun3vay kgjdk:sqho2 bitx-o5b5h:* ,2 yb 7s di4damental frequency osjqo: 7vi, as doigy2bd:h *xb y532tk4k-hb5f 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 vibration above a vertical open tube filleylota8z h 4pmsi 9h-87d with water (Fig. 12–35y lt8so a7z-p948ihhm). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of m7hm kvoann 21g4l7d ,eass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube? k1ngo7evn24h a7 dm, l   $ \times10^{ 2}$ N

A highway overpass was observed to diui0tb) 2e2u resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the veti1s- m8 byf(ajswrw5q /12 do-1pp 500–1000-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 level is minimal at a point 0.34 m farther from one source than the --r w w/p5(82fo1v yaqs1p bs1jed imtother. What is the frequency of the sound?   Hz

  Two trains emit 424-Hv3o.(7ig(xivwh;ifsuw3v; j z whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz of3 v(ixiuw;(vs;.whj i37gv beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train ws sis1,npvx r13ul.3tz 5:hnhhistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving zxtr,nsh5s p3li13 :s hnvu.1(assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just bwm-vq x5m (6znd*kb;vy listening to the difference in pitch of the engine noise between approaching and receding cars. *mv-mw;5 zdqv b(nxk6Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding t +om2i0hq.h drw1+ zvjogether, produce a beat frequency of 11 Hz. The shorter one is 2.40 mmvq2d+ o1.h0wh+zjri long. How long is the other?    m

Two loudspeakers are at opposite endrwzw;gf l zqx+i8 9+8ds 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 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++8dr;wg9iz q 8x wflz hears the speakers after they have passed him, at C?

  If the velocity of b0 1uvnmdm+w/llood flow in the aorta is normally about 0.32 m/s what beat frequency would you exp+u nv lwmmd0/1ect if 5.50-MHz ultrasound waves were directed along 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 moc(er-3, -s8 ymvehx itth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. i x3,vc-hre-yset 8(m What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency syai+h3+ ku;if ykcj: i7zwp.*ound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns befof3icyiz.yj:au;k*w+ ph 7 + ikre the next chirp is emitted?    m

The “alpenhorn” (Fig.*s dnyr(+ov s ms,v+d5 12–38) 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, the alpenhorn must be blown in su+(rov*svs,nd+5 dy sm ch a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be comprn. ftksfieba / 6ot5(/sa/gj;omised 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 (b ajsn 6te.i5ktga/f; o//sfthe fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves p2ms+:u, r 4 q3zedkzdw 7tw:fa long, slender aluminum rod held in the hand near the7 pw, :rz smezqk3f+t4d2duw: rod’s midpoint. The rod is stroked with 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 bg,u(k 9dug(c for the human ear at a frequency of about 1 uubgd,(9k(gc 000 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 observeoe, +pp4i nx7eov6qm-r on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What iso4 -p+eeinx,7 m6op vq the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboayfka.usx,jo;gg/ q( c-rcyfv 60l,t5 t is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h