What is the evidence that sound tuc;4tj*nm c4 mn2-/yk hicic7ravels as a wave?

What is the evidence that so.zr5(pfqs x) iund is a form of energy?

Children sometimes play with a hlsf8dw199nvq7u /ktx omemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can ben dq9ft/usw 18vk x7l9 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 expect thsi 40q9zozc 9pv y/ne -qw 5qeoko+x87e frequency or wavel yo8i o07vx9-wqc qpke5 zqn+9zoes/4 ength to change?

What evidence can you give that the speed of sound u ot b4vj8lo17in air does not depend significant8oovjb7t4 1ully on frequency?

The voice of a person who has inhaled helq/) h v79p2vbhju 5f(olaaxe0ium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch os 4vdp4-fe sf5f organ pipes?

Explain how a tube might be usj. njkx1-6vyf ed as a filter to reduce the amplitude of sounds in various frequen.kxnv j6 1yf-jcy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together f 93y. w)jcf b.f/egy68 pynfxas you move up the fingerboard toward the bridge?eyx 8f. pc.f9j/wbn)6f y fgy3

A noisy truck approaches you from behind a building. Initially you hearvzl/rla1c14q-3:osxf k io-1evo7 d . his3al it but cannot se ler-d:q/7k41ofls1cz si v x- 1la o33aoih.ve it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats . 7du3lcssps )can be said to be due to “interference in time.” l7sp)c sdsu.3Explain.

In Fig. 12–16, if the frequency of thee3oh ;4x27s8f artsszod77j kd u 5-ps speakers were lowered, would the points D and C (where destructive and construct s;xoj3a7-k8fd7ze4 pthssr5o s ud72ive interference occur) move farther apart or closer together?

Traditional methods of mdf3k(i5 rke4 protecting the hearing of people who work in areas with very high noise levels hdk4(fm 35k rieave 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. 12–31. Each wave can be thought of as a sud .yr qr*yo,*dperposition of two sound waves with slightly differdq.y* rryod ,*ent 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 so5 4gm bk2mxrf+hy5j8am k41u nurce and observer move in the same direction, with the same velocita hm2ym+1f4g j4k8b5kum n 5rxy? Explain.

If a wind is blowing, will this alter 3cc)mny/a v5a:d9h l d0d3qq lthe frequency of the sound heard by a person at rest with respect to the source? Is the wa l 35)d9 :3l mahv/dc0caqdqnyvelength or velocity changed?

Figure 12–32 shows various posik 4/5hzrj0oshtions 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 foh ozk5r/j04s hr the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her sh0f( wb sm1n.k 43gllhsout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of h4 3bl(wm1k sn.lsgf0 the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his srno:/2y6gx wk hip just below the waterline. He hears the echo of the gy wrxn: 2k/6osound 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 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavetn +c-be+wd y)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 abo z61a z39 h0knmqvuzd-ve a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boakv6m3z z-9d 0hq 1anzut 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splastl9 eyz/ 5 z)giu,4jdih it makes when striking the water below is heard 3. /)9td ig5zz, u4jlyie5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrev/ q g) q8kdw4z+*jt/ tyh+jbfte pavement. A momj v+tjt gq4/q+fw8/b*y )kzhd ent later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made overj d frre.j h9yr.*.de1 one mile of distance by the “5-second rule” for estimating the disrd1djeyj. f.h9. * rertance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain h25) pzlyee i8level 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 sgi2+:pp3 ye p5aujcc 1ound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simult cmve75m ;++1jvg sxcai 0bz;ev 5zj8eaneously at a certain place,0ev7amjv+ 5jg v z8e;ec +c5 zim;xsb1 what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance froar :j n0r/op srr41f7om an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this pe0n / or7rf:1osprj4 arrson 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 r 1mo3cp.+w ri 9s x8npcfrq7x-ju0v)tatio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dBxi 9.1mxru 7vqj rtposcn3w- p8 0)+fc =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a pe( hw o-w8cx9sgrson speaking in normal conversatiw-c9x wo(s8ghon. 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 eardrf7u/udmng qfn6vlcj- f3z : -f*3d bo5um 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 more modest amplif3q* du5rcdk6lzxs+ xg/ 3/ykmier B is rated at 40 W. (a)l r5kk6 z3+xgcyd m* u3s/qdx/ Estimate the sound level in decibels 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 d4 y4( pn.; mz 1hwbus,2*k9daoygkkz msml+n9 B meter registered 130 dB when placed 2.8 m in front of a loudsp;humzps19 k*9lkydan, kmm bn4 .4s(og 2+wzyeaker 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 type 43 zn ut,2bpe:lfkf e9;tfc:ically detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sound ; e4 k:c n:zftfplbtef,u932es whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wwbl v :2 mibob7a(kw,h 4yhl)(ave is tripled, (a) by what factor will the intensity increase? Increase by (ohbbh w (w)m2,:a lvb47 kilya factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the bg5v 2mh;ue; .+ksc8 odyne +qfrequency 5s ;2h .du+ mg;vnqcb8e+eykoof the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds-s kw+wbyag g6pce7-:y zj:/x to a displacement amplitude of vipy:: k-+a yeg7sjc/6xzw -gwbbrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as :pwvzl y 0,gf/6cf*sy loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.*g y6yl:zw/ fpf v0,cs)    dB

What are the lowest and highest frequencies that an ear can detect when the sounjhk)jn7 wk-b :d 7n:j)kj - bkhwlevel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is thp *i1 if)6bqnme ratio of highest fbp61iq)mn* ito 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 wf,m3; tnkp9kv p5r j(w7. atkfundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the wf,7;.(a 9k5nwkk tjmpr 3pvtstring be placed?    N

  An organ pipe is 112 cm long. What ars) k2 c*js * fcadoqc/3)0nyxeth i2d-e the fundamental and first three audible overtonec e cd tif22n )asq0*c3j-)*sykdxo/hs if 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 exp ed ik+hba0:0bect from blowing across the top of an empty soda bottle that is 18 be +i0:kh bd0acm 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 range zn.g) q 2e+scfof human hearing (20 Hz to 20 kHz), what would be the range of the ln)q s.zefc2g+engths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string he0r 2wlw6dz ugofzf:f34e 9* zr46tzu as a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a le46lfuu4w23edz0rzzg t : e*6 fr9wf zongth of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to ph4 zlkqbt2q)(69 *gixg xfl :rlay E above middle C (330 qf glr)2qhi6 x z*xlg b:k9t4(Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits n xtnv6 ;aa))2vdbh1d middle C (262 Hz) when the temped )ndtx21vhva ba6; n)rature 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 20 4/ sz a24ix:cq ;jwk*pxqkag2$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Examp9mmv/ rlcx1n)ck;s k3zq)vn0le 12–10 should the hole be that muszkqsk/ ;c19nmm)3xv)v 0c rnlt be uncovered to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616am,e5vz7 l-nc.2s h ik Hz, but not at any other fnvh7 e 2kic-m5a.sz,lrequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at two succbj 2y):zgvbjosya7 4* )ek1yhessive harmonics of frequencies 275 Hz and 330 Hz. 2ag yyzk7h)o:bsb j1)* v4ej yWhat 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 5j y.qjz()tx1l -k tun$^{\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 audy/2mrhpjri)xy-.g -o-n9 8ttkdrl q4 ible range for a 2.14-m-long organ ptgqx p n4ridmor)y8-9.jthylk/- r2- ipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It isamo-c3 n dc+*j open to the outside and is closed at the other endn+ a c*c-mj3do by 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 o 6fs4jer* ycka5tyl7+ d(nzo th29gb*ne beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off 7bt4ycf*926(r5 sotey* adn z+lh gjkin frequency is the other string? ±    Hz

  What is the beat frequency if middle C:waa2zz 07 syj+qwx8 0k gvv*h (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operatk)ld)dpynm,v /4sb s5 es at an unknown frequency. If neither whistle can 5b/dsn,4p lyd))s v kmbe 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 brand X.    kHz

  A guitar string produces 4 beats/s wvz c 9d6/d4wxmpyo 4i+0voz8then sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz06o9di4z/ov +vxpyc8 d4tzwm tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are typ ;wu2*1sg .d8sviz suned 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 arp2s; ssd yw.1giu8z*ve played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes ek3 sscfy4sev.x86 nvd s*b5 o-ach try to play middle C (262 Hz), but one is at 5.0°C and the other at 25.0 ysn.4sb8svvf xc6 - o5*ds3ek $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork js 7vxl+w omfj/1uqi w+ o 7)b6ssh)i5B 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 and C? What beat frequencies are possible when A i + ws)sv+1)mbwq76luo7jxoj5/ s ihfand 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 perhd34eww1hhs-hu9 q)z+g ;kn lson stands 3.00 m from one speaker and 3.50 m from kh shw;)h4zd-ln e wu9h1q3 +gthe 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 k+ 7qmvk. ftxw *-ui8xbe vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are pk+vqti -x xum.7w 8kf*layed 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 waveibeim23 v0bq +9mi2wb/uta7zp3 1p pm lengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 20b2pmi1tpw+z03me /iqu v7m b3 a29bip $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Haiuo2 ,ue 8i4ht+b/yd z when at rest. What frequency do yohbu/ t u8 2iod+a4ei,yu 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. Wma 3y 7/pt4f9wn s4tzqhat frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speet4t7y4wan /s3z9 fmpqd of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequ *f7s wq r4yjz upfa)7:f-3carency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward jau 37s qf)4c-y: za*fwf7 rprit at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. Wheihjmoi3 v666wn one is at resmw6io 36vjhi6t 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 kHz anf4 77kac*q cio1(3l2d gdyhe7meuw-id receives them returned from an 1iogle 7wq7 yad 3ecc-(2ui*7dhm4f k 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 bavui+ ez3y; u/mfv l w/4qwam,-9w +reht emits an ultrasonic sound wave with frequency 30.0 kHz. What frzvr+w ,3ymf;9l uvwqmu/-h/ei+a ew4equency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler exb1d vcv7yt x+/periments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second1c +xvt dbv7y/ 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 ?   Hz

  A Doppler flow meter uses ultram+txpmd tny6, tu4+ht ,(a;x dsound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in hu,tt(mp+n+t4mh t,6 ;dyu xxdaman 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 y: pa,*ohfs,rultrasonic 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. cy7jqd8q cd u5,1,)mf*hquui When the wind velocity is 12 m/s from the north, what frequency will observers hear who 1u,qfj7qyc8cqu,ihd5)u * dmare located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at 204vx3zp3r/ 6j fypk )gm $^{\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 i.)w7,h8v-dl r q bz( gs,y wr)t:/kkb1msfwethe speed of sound is 310 m/s (a) What is the ansbhm7)d s )f,eywi1kt bqkgw8.( r-:, vlr/wz gle the shock wave makes 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 :j3 xs,v, e8ntag1 jew(rrml/dzu2*z sound is only about 3, s x ,zlz(rjmt /8adr:gwe31e 2v*unj5 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. Deter/wur+ .hsvf 0dmine the shock wave angle itf dwhurs./ v0+ produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle q7;kxg (c4ctso1l o7o$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhe /8k;+g ;fqwhxs5jwg xgrwg7.ad 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 horizontal dista;/qgxw w+gfj8 ;k x sg75rhgw.nce of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward froeupb2ly o5h f2u*;1dnr;te ks3ix7o 8m the bottom of the boat, and then detects echoes. Ie8* 3yd75tenbx 2lh1pusi ;f u ;2kroof the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many u9nps k xy,h/ lca7(eq,gmz: 7octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of mans5jxw j0+rvzcsj5h 0 ;y plastic pipes of variousxc +zjh0;swvrj j55 0s 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 pn7is4 iq nme/vtzm6 56erson makes a sound close to the threshold of human hearing (0 dB). What will be the sound level o mnt7vi6/ zqsnm6e 45if 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound .;pr7)i2lb z 1sk/addbo50 bymgy)ayare heard sim/ brild0m2ky. zysoya5abg; )7 )d1bp ultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 1e;9ll 7f4wfostk ip4o7w- g:k05 dB. What is the acoustic power outpu7t-f fl:s4k97w koiwlog ep ;4t (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hznsmn8-7 xp f.g. The power output drops by 10 dB at 15 kHz. What is the power output npm8n fg7.-xsin watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectivy4vs i(p eqg )2s6wvq7e devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplanw4qps76( yvev) gqs2ie engine?    W

  In audio and communications sys,zm o2jyxxwc62r:e g:tems, 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 tb:ktro1 0 6sjfo a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamentay 8xnv r4xokr6z5d+emv+ wjd,( 97xfs l frequency of 440 Hz and a mass per dor(x rx8+ wn5vzk6vdjy 97x4,m e+sf 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 filled wireqn m 4m6( v/6z qrv88 f0yscgx2zg-jth 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 level is 0.125 m and again at 0.395 m. What is the frequency or( xv6my4zz /80gn2s j6rv 8qfc-qmgef the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open ate .g,sr;igp -hah6j- 7bi)ee k one end and also 75 cm long. How much tension should be in the string if it is to pr j kr- hibaes)7- ph.6gie,eg;oduce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as on hxr/8v rncnd* s6mi*7e full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sources. Tl/h-nq h*o+ i qz/n6dyhe 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 mi+z*ih/ onyqq 6 /dn-lhnimal 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 whh/koy148 iyk9ux gid(istles. One train is stationary. The conductor on the stationary train ydi4 ugyi9oh/x8(kk1 hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you iseq/zqf *q0q2:io +l pth1tyd( 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume consthd/ :01qqy t ltfpz2oiq(+ q*eant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listen3.:yixac/ tgug/sz;f :glys ) ing to the difference in pitch of the engine noise between approaching and receding cars. Suppose the ssy)zac ggix /y/:.gf3 lst:;uound 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 together, produce a beat fre1b )be5d7eelfquency of 11 Hz. The shorter one is 2.40 m long. How long is the other?fee lde 1b7b5)    m

Two loudspeakers are atxzyd -p:glljd6pi ,*1 opposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the podxp6 gz i,l lp-d1y*:jsition 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 aor5 k(yohsg5,wim;my8* hbgx l7ta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound wavessg gm m(y5,hh;x5 kwoby*7 8il 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 moth at speed 6.5 m/s2o51r+9p i6)j(iag u i-lsprl lvdzt, 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 w)vit5ropriulz 2p(,aij6g -ld+ l 19save detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of puri0c52 j5(e/zsp n zhigh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected bsz(ru/p i05ec2npjz 5y 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 signals from one Alpine v50uk rwd4effo fz(5-eillage to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to creae-0f(ewk5ufz45r f odte deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence o8oma ) e3ew a0 t/ttkbn3(tf l,w(hg3pf standing waves, which can cause acoustic “dead spots” at the locations of the pressb a(m/wo lt33efe)03tn gtt(apk w,h8ure 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 rods,” involves a long, 3v c l)v3odamp sq2m:.slender aluminum rod held i.m:p 3d s) o2clv3qmvan 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,” 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 human ear at a frequency of b2*fq npr;hmm;joe+7 abo* ern;qpjfomb+ ;m2h7 ut 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0.0/2bfwfws,: aa9qpuz An observer on the ground hears the sonic boom 1.5 min after the plane passes 0: a,/ub w9fq2pwzasf directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is s4lb; cv4r ulm4)ll2zlqdb+zq 8ql:cfb1 )b615 $^{\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