What is the evidence that sound travels as m,t. hon .vu4ua wave?

What is the evidence that sosg yv8byp3tm+bd 6n 18und is a form of energy?

Children sometimes play with a homemx8:mpxyd4d m -.7o5b ip 6/d mgdey+sy4i vry.ade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks inty rm m pbpdyd6 io5isg4:8 v+yd/dy-xemx47..o one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency o91d5p (qqzkgl r waveq5qpzk 1gd9l(length to change?

What evidence can you give that the a9lx 09et(ne;zv5xm+seza( f b(j s 1pspeed of sound in air does not depend significantly xzea mbf vs+e0aj9z(5n e1sxtl(9(p; on frequency?

The voice of a person who has inhaled helium sounp7hsc* o4w-qu 4rxs 1a2weu7dds very high-pitched. Why?

How will the air temperature in a room affect the pi4miyj x4 f 7t,eklbf85tch of organ pipes?

Explain how a tube might beyoga;m28 1 ns5,u9lc -da(ugkac q p 7yamr2a5 used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a ca7 c5 y52rc 2 -a 8aola9g1sgkdmnqypau ;,um(ar muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as*kkifvye)p(n(dtu m)1*l z,x you move up ti(vy dfmt,l 1p* (kzu)k)nx*e he fingerboard toward the bridge?

A noisy truck approaches y)x ;gyeyhf xz58rw t29;k4cizou from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more otri 98 xzhk z4f)yx e;gcyw52;f the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whek/g- v6k-y 5cl imlo,preas beats can be said to be due to 5gik/k-,vc- m 6plylo “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would ri fxkso-05 fa2k4r9ithe points D and C (where destructive and construc45afkxir -fki9 0or2 stive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas wvf1tn789lx a xith very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise.9x 1nf7tx8l av How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wavel a.3f ;c4-+sy:uttzzc,:be nijmo6y can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two componyn:; cte.:-c6 fmjzaobi, sl 4zu y+3tent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same d7vxkx:sg +k0 (yu:x tbirection, with the same velocity? v7x+0 kst:ugxb(:ykxExplain.

If a wind is blowing, will this alter the frequency of the sound heard pa3w*f4oa8zh by a person atfh* 34awop 8az rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions ,k::sf hbn-qg 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 throun,:f-k gqs: bhgh E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo 2ml1u)h cks;o of her shout reflected by a cliff at the fsohkl 2cu; )1mar 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 sid.q is+e5bq9fbe of his ship just below the waterline. He hears the echo of the sound reflected fromq b 5sbie+f9.q 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 wavelengths 6g+kk5lb saw7ga m a):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 above u/ zg . 6pm6pr lz*u.iv*eqba0a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfirbp06m r/ uv*g eiz* .l.puq6aze is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes whe ylidv9ohkj psf:ep1). 8o 3a9n striking th:kaevy 1 hf 8lo sp9dpj)io.39e water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear toh8*7xdm*vrnotv2sp t ,-7 tiq jo(rp) the ground, sees a huge stone strike the concrete pavement. A moment 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 apt *hp2po7mds rv,tj8* nqo r)v7xt(i- art. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mil and 0 .hc9zncr:+s/uvfrq (t/e of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) qv9afc+ u/rhz/.ds nntr:c0 (30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sou1f/t+r oby 49 wgylwh6ge0a eh)d6lx.nd at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level gl- ;gbwb;hm +of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when q) )m5-wfp--m79yjrwbnvk k2 k fs5fbfired simultaneously at a certain place, what will be the sound level if only one is e5b)mvk w)qf 57myw2fpb9fn-j rk-sk-xploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with foue1:xs;n dre/fytp5 /k04iyie r equally noisy jet engines is experiencing a sound level 1s0;5/4ie t rp:exy/ie nkyf dbordering 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 s ps est*xlba6 5tdj761ignal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each devicetjb6 se5 ds7pa6x1t*l ? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a perso1or0u v.s7fbmxih, 2 on speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly omrs7 x. ifuh0 obv2,o1ver 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,iz ( gc6:sab8 b,*ryhz7oubs 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 rate,si9nn2hd ip sl8b2f xj,st2a (*.uqgd at 250 W, while the more modest amplifier B is rated at 4i 8x9hpundq2tsjsf i.b,( g2*n ,2l as0 W. (a) 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 dB meter registez(1mgix5rs6n / waafuu+39 b ared 130 dB when placed 2.8 m in front of a lou19ib/rxu+n3z(a fg5uma aw6sdspeaker 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 typically detect a differen9*g7x)r+k d r bq3z.; qfhi9 cxuytv*cf*cl)rce in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whosec)qh rlr;.gr9fxcb+d ctv *kzuxi7y9 f **3)q levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will t w8d mev0a9a /t*dnqyj +c vl6z,xak5*he intensity increase? Increase by njyw +*m z9kaa0*/l vdvet,a5dxc8q6a 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 freque 3r0tc sdst27htpbqg+ / /tc(sncy of the other. What is the ratio of their int0ps (7bcd c23srs g//tqt+tht ensities?   

  What would be the sot r(c*ohnq,7/,1jnlbg-l .*n v d qedjund level (in dB) of a sound wave in air that corresponds to a displacemen,7bhndq.* rj ,gdj*olc- ql ne/v(t1nt amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have whae . t.21, afdndhxmvq9t sound level to seem as loud as a 100-Hz tone that has a 50- 2.f .qe ,nhddvt91axmdB sound level? (See Fig. 12–6.)    dB

What are the lowest h axmjv,z17j-4co 2 qgand highest frequencies that an ear can detect when the sound level ismgv2 7q-1 a4 zjojxhc, 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels./pn3vkj8-)gam6qjfu What is the ratio of highest to lowest f6j3-kg qmj8 / un)avpintensity 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 440 Hk.araqml2*6 dd)o( orz. The length of the vibratd6 )arl kar(2q .od*oming portion is 32 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. Wha ugs5guso ,ab/ 446zw1mxco i6t are the fundamental and first three audible ove1z4s5c,smw/6ui64ouga x o bgrtones 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 expect from blowin25i/ies b p8cig across the top of an empty so5i/c 28 esbiipda 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/g:a7 8 9jnto1sw ;g-qxrdnda spanning the range of human hearing (20 Hz to x7gw/da- jdq9snga ;8: o1tnr 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string haswd0m018t1mcil j:j9a cv oucjr; ..wh a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if iw. uajor lj:0 t.19dcvmcw;jm8c0hi 1t is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar strivt + zhjq54xbiq0 q5;yj7 o+/ru/rng fng is 0.73 m long and is tuned to play E above middle C (335 5fitq+o+vgjr;n r j0qz7uxby q/h4/ 0 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 or87q+e j qs(4hx-e pqyrgan pipe that emits middle C (262 Hz) when teye (qr7qh sqjx4-8+phe temperature 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 k9x c ype2+x tce:x-t55 iyr-d20 $^{\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 shouldwocbaylhu xz9u:4.62-o c h(y the hole be that must be uncovh4 ylwbaoo2 9cux:uh(y-c.z 6 ered 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 canu7a:opoga d x;4j6z/b resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies i 47da g:;ox/6apojz ubn 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(9m iacna x i0rpt fj,)(ct:i+8nqa. v-7xhk j ends. It resonates at two successive harmonics ofp8.) , -irtvh(7xxi0ia c( jkntnfmj9 a:+caq 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 a db.s9v- bp ;9nsgv8p. djn/b$^{\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-long orf1syv 95ho 02au5zmdmgan pipe at 20 oy szd9 uahvm51f520m$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to gfw k7:z s p8gzf97wx,zw4rc)the outside and is closed at tsf w w,zz c kg)7x:wf8gz4rp97he other end 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 (vg)swb,d- rhone beat every 2.0 s when trying to adjust two strings, one of which igd(- bwh,vr)s s sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middleu/5 ark; hy e,2g9)zi)wlonkp C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates ./vm6 v;h* m 3oorgnv3j * 46tjdchxdyat 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by * yhcj vgh d 6o4/mo3t;*n6r.jmxv 3dvhumans 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 beatslc)+/f :w6 hbrgy7s qs/s when sounded with a 350-Hz tuning fork and 9 ssgq6 :b7 rlc/+ hfw)ybeats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Ha5w 9d wxobru2y(x(x 9z. The tension in one string is then decreased by 2.0%. What will be5a9ox ydx 9wwrbx( 2u( the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if tm4 )tvx a9ha/a6 pegn76 v4xogwo identical flutes each try to play middle C (262 Hz), bux/ o4) gpahvt 7ea6mg 6n9v4axt one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, :nbp cirv)*z5xh8 g,s 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 and C? What beat frequencies are possible when A and C are sounded together? 8b vh *,)gxriszn:pc5$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m aqk6/apr*ysl, d1ne v *part. A person stands 3.00 m from one speaker and 3.50 m from th */r l,kdev 6y*qpa1sne 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 fi21ab t-f+vcxbk nktm- , 8jvh61xu0be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they arexcbj vkab x6ni-81 0ktt -2+ ,mvff1uh 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. rn1o3j 1sb 4dhHow many beats per second will be heard? (Assjs41hdnob13r ume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren i*,4 u* p,okj nmgo7ttis 1550 Hz when at rest. What frequency do you detect if you move with a spee*mtg,p*4 7okj,iunotd of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whi+q*l-*yj(:ihlha d xose siren emits at 1550 Hz (l h*i *qjiy hd:lx+-amoves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency72-h oxu wpq0s if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it aux7o sqw2ph0-t 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 equippopfehs(3u7cl f9d )9oed with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What ie)(fhp3 ousc79 dol9 fs the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 9 e rjytd27fue 22adr*e/3e1vcf1uxv kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound freq* y9vuxv7de3 e22f 2ceu jafrt/r11d euency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an g4uv 4uvtjq(5ultrasonic sound wave with frequency 30.0 kHz. What frequencytj q 4uv(4u5gv does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moi 7 mx t9icmh-:jlpxe0upx*,c 9eh-i;ving 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 ixm7plj,xx0c: -9ehhuip- 9m cti;*e approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speed xjkr z+d5u03bs. 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 xb5z3udk+r j0 beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic w++*0bl kgicyeywy8s 3 aves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the g wwx fikfu 96b z+50*3f:zahlwind velocity is 12 m/s from the north, what frequency will observers hear who are located, at ref 9 zufxgk6fwab 5w3:i+zl *h0st,
(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 lanw:2, f,nbtqmtu 3 pc1nd 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/kf;zgpf1-9 ats (a) What is the angle the shock wave makes with the direction of thep;t-g zk1ff9 a 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 so/gljazyo9qel(9 y- h3und is onlylz3 99yqh o-l/eja(gy about 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 wave ang(wx03fon/t8 xhz, tq *br4mfd le it produces txth x8n bfr(f/m,qw304o*z d
(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 nwcls7e+;oi1 grz,e kfkd4m-q1p +n($/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the grotnhjk utzbc;2 ic +998und 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.8in j9utzch +9t;c2kb 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-Hzc;2a,ny( evdv sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (yaed,(; n cvv2in fresh water)?    s

  Approximately how many octaves are there in the human audibk9ie rh0o-icn p*bfyx42m 6q 6le range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dispmts*hca 2 5h*blay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, whicb h *5htam2c*sh 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 the thre 3+e* y t2eenc5yulzsuj25ft0shold of human hf 30z2c yeuuy ne+tjstl52e5*earing (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 are he ddb3vgve4la -z42t:iard 4v2bdd43a levt - :zgisimultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed rmw ywd+punk7h7 *(h1uj2/ vcin the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming7/hpy7um1hu2k+j rw*wvcn(d it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drm 0;ar )vnzx,gzxe5jj;p b+) rops by 10 dB at 15 kHz. What is the power output ijzjvberm, xap) )x;05gr zn +;n watts at 15 kHz?    dB

  Workers around jet aircraft typically wen4 ho;ljz x5i6ar protective 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 ;h4jx6z5 olin unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain,d0l:y pjei mlu e1.8z( $\beta$ 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 isu+2 1/vjpeyfxn7y- 1mtq+wqr*s7w vr tuned to 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 pointho x/:vs9 esz*p -qwd kl2y*f*s with a fundamental frequency x/ pfwzs*2ko eq9**sv:h-y ldof 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 filled wit:s78xw lkmad/h 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 whenl7/8xadwk:m s the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.1xj .a-e 2uxn9sgtz: 6r0 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 resonanctx-aenzx u6s.r 2g9:je (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop (;5 g htb2wg.( 2jqmfuu$\frac{1}{2}\lambda$) 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 500–1000e+4dni h-)(s.v .ha xo2vs(9kjra mcl -Hz range coming from two sources. The sound is loudest at po2j li)a9(or4.axn v s(hh+ems-.c dkvints 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 whistles. One train is stati(kk sx5up;g* dtv 7ma,: dw5lu4ghz v2onary. The conductor on the stationata m4huku zk;w,5vp (dx *s7l2vgdg5: ry train 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 hxfawd.(9ll6e8et5wuu(s + yit approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant veloci t8(wflhasewye5uu6(+ .ld 9xty)?    m/s

  At a race track, you can estimate the speed of cars just by listening to t) i4yyc+bc 8qc mdg+v .vts2h*he difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octa 84gs+)ycbct m.vdc y+i qh2*vve (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 frequency of 11 Hz. Tau p99ad /vlls: )riio)l,. vs)irw .lhe :.sl,wr)vl pa9/d9 )o i).l saiiluv rshorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it mr+7q4vhlan(3j*a8mf n (h etyoves 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 hears the speakers after they h(3q( t*hf lymnav 4na +r7je8have passed him, at C?

  If the velocity of blood flow in t/ xdia,2y1rahmdn4k- he aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-dk-1dn,ira/ hmyx 2 4aMHz 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 moth at speed 6.5 m/s while the moth is flying toward thcrebg8k9pgfrm uoo7 hh:61 .4 e bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the waho:h.gr o14upgrcm8e6kbf9 7ve detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pckg:6ov+.v -qxmwm2rd nbw) 2ulses 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 rv. w:) ngd2mb+qc6xo-wmvk 2 before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once use6g oz z,f mck,o5;xj4exx .l1ed 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. 1zcz ,4. e,5l mojxekox6gx; fThe 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 of ;l ;v jn*7ihu -y9 -vwb(qscubstanding waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the funbl7q-(;*sb ;w9 y nu-cuvi jvhdamental 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, /d nr*i2ylz:k, wr,.arwc;xw slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. * wrdlr,xw2iz:/ crakyn.;,w 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 hearin4qey(n) f gf e hpt1ea8e+y9s/g for the human ear at a frequency of about 1091yaees+epnf8qt4)/( hfyeg 00 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/bc r(au 8a8vety+gk5 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes /u+ekcrb5a v8t 8(gy adirectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 ex el5/qph7lc+9t+ qd $^{\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