What is the evidence that sound tr;mob-3t t1x 8 u4hje2pe n1rwsavels as a wave?

What is the evidence that sound isn )v( gksh 3eh.h or 8nvip8w/jb8k8f4 a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to th4 -6hp 2rjizfse bottoms of two paper cups. When the string is stris6-r2 4zjfph etched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do yju+lw (0kz b9k*oq ezuj8pl/ 5ou expect the frequency or wavelength to09jz(uw5l/+*zjbkoklup q 8 e change?

What evidence can you give that the speed of sound nj/ (yfkxeg 6s4coix w::a8p5 in air does not depend significantly on fpx8/ eg y6 wis(:5cxjkona4f:requency?

The voice of a persol g utfq)9n3(1 fyoumcmp/m5 -n who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room;)s uw5j4rl) ymmt a .r67sorl*p:p;mtjx u(x affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplit(37fb nycpx:6lldl: tude of sounds in various frequency ranges. (An example is a l6tl pd7 y 3nlb:f:(xccar muffler.)

Why are the frets on a gu*di2g :c4c/ an)z bofv nnaqwbi0 i.5:itar (Fig. 12–30) spaced closer together as you move up th b2 :/ao vngcc b.:fw znaii*d0i)54qne fingerboard toward the bridge?

A noisy truck approaches you from bes- b(c6 qbfl-ie*bns 1s/re4ihind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is sud 4sbqn/c-s(-i bl sebe1*rif6 denly “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 “in.pwdnt -5 b5xnterference in space,” whereas beats can be said to pt-5bdnx. 5nwbe due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speaks1;bgdge+skd 2ke j y::k8mo.ers were lowered, would the points D and C (where destructive and constrsy:12jd oseek:k8b;+dmgk .guctive interference occur) move farther apart or closer together?

Traditional methods of protecting thejh;;bdhn-p7b (b;v-8qmuyao hearing of people who work in areas with very high noise levels h;-buv j -;y8mp7hnha bb(o ;qdave consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–32oy1ra :gtkflud*f 5 71. Each wave can be thought of as a superposition of two sound waves with slightly diffud :tf1y52* rf7klog aerent 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 observer move in the same directj ctv m6rmh7or s(y,-:bf ;eu+t-i.urion, with the same velocity? Explaint j(rb.m ucm+euhr,-yf7;ivro6 t- s:.

If a wind is blowing, will this alter t -/l/hq jpds(0lrmy8ezb5v1vw h t2b8he frequency of the sound heard by a person at rest with respect to the source? Is the wavelenvj-s/p8 dqlm1wbtb0hv / y5h8 l(re z2gth or velocity changed?

Figure 12–32 shows variou lt: n,xpnu6-h4)ln tvs positions 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 of the whistle? Explainnt ,6nllx-ph)vn4 t:u your reasoning.

  A hiker determines the length of a lake by lmq-xyss1 f2l0t ux,4wistening for the echo of her shout reflected by a cliff am-xf,s12 4 0xlqstuywt the far end of 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 w7ormkvxh4f- *h wzupd -0un ,z*q7(qs aterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1w-h*kvru zn,* p q dmuf470 szoh-(qx7560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavexry/r+0nu0 c o86 7eoabljj4e lengths in 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 abkgptnj9wun,3wx1o0n mu 5kg,9vfa+5ove a school of tuna on a foggy day. Without warning, an en,mgku j n1pux5 0 3,n+gwnv9wtf o9ak5gine 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 frhlhaky, - +jwz+ d)i+bom the top of a cliff. The splash it makes when striking the water below ,yzbki+l-dh+ah )j+w is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees .l; 6ckvww2*lqn8qlo a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in thel vqco2.w8*lwnklq6 ; 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 maedn8h xu i 91u91 wvcx5cowm*.de over one mile of distance by the “5-second rule” for estimating the distance from a lightning str8ecvo1m .xx dnw *5i9uwc uh91ike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain l-s7s0+msi;a7ub e*kj w, ymgkevel 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 intensite y* b .ud7sr* 2aqpfil tqv54pqvh7-6y is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously d+bjnz/ a 6)a7 m6xry-v wshx1at a certain place, what will be theyaab6zj) 7 xm1n vs-xw/6dhr+ sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from at ;hvb7c/2 pq en4skg,n airplane with four equally noisy jet engines is s; 4 h,engb72 tkpcq/vexperiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, wherqs xj5 m/e.1-clcx ewbf.c2x8eas for a xx 8esbj2cc.qmxe-f w.cl/15 CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound frome6 ra0/ ;phdes a person speaking in normal conversation. Use Table 12ahe s e/d0;pr6–2. 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 stri grk(n*:su+o, gt.i hqkes an eardrum 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 250 W, while the .ftyju( (:nijck we+4tyd0+zmore modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibel+f.0wynut cjj((te iy+kd4:z s you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in frontfyhlh *. 8nu,(r0e2aam fn1nd of a loudspeaker on y2,f *mhn aae hnn81d0u(r .lfthe stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a dih zl/;mvqt +:e qq-e-gfference in sound level of 2.0 dB. What is the ratio of the amplitue: qgm/ e-;qql +zvht-des of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is triplegc0mzm/*p,4 hv,+ n jzp/ vdqyd, (a) by what factor will the intensity increase? Increase by a factor of ,4hy,jq zm0pcv/d npmv* +zg/    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one ha;.bg nle-q1 zcs twice the frequency of the other. What is the r1nq c.eglb ;z-atio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds tom 9)qz3s5bcd l/:kq9til,jplnn.f0bpvas32 a displacement amplitude of vibrating :vp9l,n)5j33ibs0/lmp2b9fsanqkd qcl . tz air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone 8mh slvfxb/zn29 b* b26)pner that has a 50-dB sound levem/ rse 8p fv2nzb)*l96n b2bxhl? (See Fig. 12–6.)    dB

What are the lowest c j:c huk0ird9+vjm::;.vp a k6inb/a and highest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.) k+u6m apj:i9dr/0.v:ic c ;n kabhj: v

  Your auditory system can accommodate a huge range of sound levels. What is xjam-3+l g scv(j:1dtq k;e 3uthe ratio of highe(1+- tecxvs:au3jd3j;kq m g lst 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 fundamental frequency of 44;g)4nffb4ap p 0 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placedn pfb)fpa g44;?    N

  An organ pipe is 112 cmu/kh3gy.ycg b 1a3 pe- long. What are the fundamental and first three audible overtones i/y1g phya-e 3bgk. 3ucf 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 expect from blowisffdr*p/0(t p u hc(k9ng across the top of an empty soda bottle that is 18 cm dtppfrk9f0*/us cd ( h(eep, 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 organ5di3vrzo. vh3va2 x:t with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the ran:v.x25dira z3vvht3o ge of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 54)rl8l 7zyzsgxol 0 eb,3+n2at 0 Hz as its third harmonic. What will be its fundamental frequency if it ex btrs+0,lazynlzg) o7 382l is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string i *:p485r hlqdiquvc6nwo8c 5 ns 0.73 m long and is tuned to play E above middle C (330 Hz).qdor6*8q 8c 5 hcw4nnlvu5:pi
(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 cp gu2b-a /ye8emits middle C (262 Hz) when the temperaturegceua/ b8py2 - 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 vbg(qif tp -:220 $^{\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 sh wtw4*k . /v;va8owbyqould the hole be that must be uncovered to play D above middle C at 294aw vw .qw/ko84;t *ybv 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, ( nn+bkorpej; g8z 8*g440 Hz, and 616 Hz, but not at any other frequencies in +n*pzn; g( k8gobr e8jbetween. (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 resonata1rjw c/rnx4i0th7/c es at two successive harmonics of frequencies4 /rw7j/0r 1achintcx 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 :v4zw3 fk ad ki17.sc4ba)uou$^{\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 go )n/:ye3 oh2hzj;hsaudible range for a 2.14-m-long organ pipe at 20 og;)23 nho jy:ehhs/z$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is jhy8ir:t0+fh approximately 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. What is the relationship+0 yjh:rf iht8 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 whi(7t/p madbz 0en trying to adjust two strings, one oizmap0tb/ d7 (f which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) an 9 id*w9x-fb7nkw wow:d $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, w94a)(eznl kvom7 sv( thile another (brand X) operates at an unknown frequency. If neither whistle can be heard bkmt e974vza )nvols((y humans when played separately, but a shrill whine 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 sounded with a 354ryucek*do+)+ 2ys , ev lwv5db8j:qi0-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Exp s4v*idow:+cej yuv82b+k ,)yqledr 5lain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz.taq s/ddr 1ryh)qxz71 -td65z The tension in one string is then decreased by 2.0%. What will be the beat frequency herd t6zr-15q dz/datqy)s7 1h xard 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 play5eio .gl * 0(0m:;g iip7iwzd1tdhgho middle C (262 Hz), but one is at 5.0°it gwd.ihiigg:7 ( 0eo 0d5 opml;1hz*C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A,z;x lz+,pz erfo/;sd+ 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, the beat frequency is 4 Hz. What are the possible frequencies of A andozdzl;s;x f +z/epr +, 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 perx(3oxf c.p h)jbb04x4.wv pikson stands 3.00 m from one speaker and 3.5bp(khvw 4oxcf ..0 4ijx) xb3p0 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 vijbded)s ;n,x tj28 mj+brating at 132 Hz, but a piano tuner hears three beats every 2.0 s d2 8) ;bt+n,mdsjxejjwhen 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 wavelengths 2.64 m and 2.76 m in air. Howx(bp ( 7/z2qwjpvh ptg(j1 0fe many beats per second will be heard? t0hbzp1v2jp((/eqx fjp(w g7 (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren ish (zo6tv16t7zj k lifuq)( 5qi 1550 Hz when at reskz 6 q(ovl 1j5iqhz7tu(6fi)tt. What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do y c-lon6xq qf- 2wn)d6you detect if a fire engine whose siren6 2-6)c x ldqnyfowqn- emits at 1550 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 source is moving towh3tjtg;3fhq;r:i() k7lrx5dtodxb6 ard you at 15 m/s versus you moving toward it at 15 m/s Are the two frequenciqr)5 x3dh3dtt;:6lbi;g fhot7kx j(res exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn.szs0ebl 4 x1ne xmy75. 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 isles 0exxyb15z74. mns the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonigcvq 4+ a(mrk8c sound waves at 50.0 kHz and receives them returned from an object moving directly awqmvrg(k a4c8 +ay 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 fr)ij gmq *.z 5q/wv(1jqe1kialies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency d em5jrk.izaq)/1 1i g jqwqv(*oes the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler c) 3ekrfkmgjasad6z /6cicd 7y.1g8(experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the sad k(ia.gcy rm63c167j)cskzfae/d g8 me 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 mk7cndjvfy / /q.0 ybi/easure 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 source?fck.dyq7 j/vi nb //0y   Hz

  The Doppler effect using:vvkj s owoth;0z.f. : 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 x,n+ u6v3vr9 o qc/tbfsound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear wu6 qvbv nt/f+,or3 xc9ho 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 ityk,jxiga* q)c mkday1 :ha29ppw4h20s 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)khsgkcob9g r051u 8x/s (a) What is the angle the shock wave mk b )h91go8kru0sg 5xcakes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of sola n,: 1k5kfhaund is only lfak 1h:,kn5aabout 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. Detyt. il48uq af+xqk6t;ermine the shock wave angle it pr8+tk6 ifl quyt4q xa;.oduces
(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 0y0t+;epw.:ry vky odh tto 8c38gw6 d$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly over s l7ila7i6h9m3cfg/rn(mq4 ohead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horimn qc9/hiamg673o fls7li(r4 zontal 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 fy. x:j0+qmrt/4x. zfan qk.bqs ,pt4that sends 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 pulses0mysft,k+j/zrx taq.b p :n4f.x q.4q (in fresh water)?    s

  Approximately how many n3k7 y a0:lyeroctaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symp0ja83x hfd ,9,quwjh b8fb8jqhony. It consists of many plastic pipes of various lengths, which are open on both ends. xhqf098jb jbua, fw,dq3j8h8
(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 (:,l- xuwyevtperson makes a sound close to the threshold of human hearingutl,-we :y(xv (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound vzct , :.vy;eyare heard sim.t:;, vyz cvyeultaneously?    dB

  The sound level 12.0 ua;( 8psxl*k kg3b ,som from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equas,loa bkgsk xp *(83;ully in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops g :0wvwunqnp89bz8+ l by 10 dB at 15 kHz. What is the power output in9nnl+ 8pg:vqb w0z8uw watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over th3r 5+7pgedfa ; -skymleir ears. Assume that the sound level of a jet airplane engine, at a distance ofyl7kga-sd ;3e pr fm5+ 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatio6h ,e2u,vohs kns systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequ y /5cy,pni 8lka94tkbency 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 fu1 .(y fw9.: l9g tus:i5qbfyxjz(r zrfndamental frequency of 4rqfyt:xs9w5y(ui .lzz j1f ( gr:.bf 940 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 vertica q v:62tzhtx b )a2xhvl++u;qfws 9a)ll open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water lev+69 x + qaxbvwl)v2qh2th:a tz)lsu ;fel 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 tubefb fej-vrpq3s-511ao 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) ev1-jq bsa1 -3f rp5fowith the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass wa(xte- 6wh7z s btoh+4ps observed to 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 500–1000-Hz raao/ dra w:;w8 0u6nj*v n4sfuqnge coming from two sources. The sound is loudest av:*wa ndj0fus8uwnq ar /;64ot 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 other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistle2ddw5eokdfadjc 4z49 v0w e0) s. One train is stationary. The conductor on the stationary train hears a 3.0-eafdj 0 )z vcd20k owdew4594dHz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a s6xnnh vr/el /w8hj 17tteam train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velon1 x re /lw7h68tvjn/hcity)?    m/s

  At a race track, you can estimate the sx: -q y,ro y(x(x.loujo d/hk4peed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car droyuxoh q/ jo .y,r-4l(d:x(ok xps by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sound(k 69sj ;eosj6q7m(hqz r1 htcing together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m lqh97okq;1jmsr (tje(z6ch 6song. How long is the other?    m

Two loudspeakers are at opposite ends of -;m xnqq t ydau84,n5ba 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 i-,nuaq b dym8n4;5q xts 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 s 5 j)-umkyqq8in the aorta is normally about 0.32 m/s what beat frequency would you expect 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 q5u)y-s8j q kmspeed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth 46 /- riprfc,wn8kx4u zt;zpyat 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. What is the frequency of the wave detected by the bat after that wave reflects offkz n,6frpryw; -p/iu4 c8 xz4t the moth?    kHz

  A bat emits a series of xom .tsdp95l.ic7194tesc e1q0qoe rhigh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How fd1r1c 0.7tq.lms i9 pcotexo5eqes4 9 ar 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 awwh+5 c*wjhk 2a*t p7used 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 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? (Seea5pchkwa72t* jh ww+* Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presenc ,::c/konmae ke of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Considero kcke:m/:,a n 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 9 k/bpb ka;.ha2kgf+y “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,”b/khgy+a kf2. b a9p;k 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 the hum *x(ixw .k:/z -ocku g4-t0ouec; qdjuan ear at a frequency of about 1000u 4gxq:wek uj . kozt;c0x-d(/*co- ui 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 y06u. o+bwv15 l+d egnte4 fvlground hears the sonic boom 1.5 min after the p4etfnlv1g .o+ by0u +e5wlv 6dlane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedb xyd z;ocui:6;oat 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