What is the evidence that so sa.bxzde;tcg15zl +4 sg -)tcund travels as a wave?

What is the evidence that sound is ak3 d*rv0 ppa:w form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to ;l2h2 k i-6+d of ;kdvi4ihlaothe b ;k4o2+6klaf2-dvi oil ;dhihottoms of two paper cups. When the string is stretched 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 you expect the frequency or wavpa 1z5zb*).ejhb *ewiele.ahjz pe**1eb )iwz5bngth to change?

What evidence can you give that the speed of sound inzmj2w f-:/*/jadnb9ak;dlzs g7.i n n air does not depend significantly on f9 *injfsng z :;b w2dlzamd7/jk.a-/ nrequency?

The voice of a person who hwiee cs/+rl--, fem 3has inhaled helium sounds very high-pitched. Why?

How will the air temperu3 10uxvaxlim7x9 hpt0g.nk ;ature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sountesok thnxbq ;,q:134ds in variq;kebtq14 ,xoht3s :n ous frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spdp +loi9xrp08, vvj/xaced closer together as you move up the fingerboard toward the b/xi 9 v,vxp dp0jro+l8ridge?

A noisy truck approaches you from behind a b3basm *uz/lp.(: uuxauilding. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” z. */axsuabpm u3u:l (— 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,” wheru1xtlo -8pz* us0lpf2eas beats can be said to be due to sl loz1xut-p f2 u*p80“interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were w8vpw;e,h (ke w/qlkn)1 ra0m lowered, would the points D and C (where destructive and constructive interference occur) move farther apart o)er ,h;(we0aw81m w q nvlkkp/r closer together?

Traditional methods of protecting the hearing of peosae,iqf /l)zbk 2 vuui 3);s, a1svv)kple who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones s2, ) i;bfs,1u3v) ilez)vaauvkks/qare 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 ss/ltp gf9i6-ihown in Fig. 12–31. Each wave can be thought of as a superposition of two sound wav/si6 igpfl-9t es with slightly different 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 2;1 ddu+mepo ithe same direction, wi;1updi+2e d moth the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sx)n:( uka y4fyfm 1s g7roc+r.0ow mi2d8uy 9tound heard by a person at rest with respect to ty(4.frmyg 1doc2 rw m9:tf) 0uaus8x7i k+ oynhe source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitoc)z)m35cacz 5 cpu9xar 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 fo5 9)ccuza3zp5 cm ax)cr the sound of the whistle? Explain your reasoning.

  A hiker determines the lengthz7ti8 )5x k:vzucv -go of a lake by listening for the echo of her shout reflected by a ckgvi -o7:z zctux58v)liff at 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 waterline94z bj4y jyx4a. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deayyxz4 j4 jb94ep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in ooqbfm0qr; c1k5i..eair 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 a school of tuna on a foggy day. u5se 8z.hy6 n4m94c5rhd+ 5ajn fwq viWithout warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) b .h nwns5d4j my 89iurzcah65vf+q45ey the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash dxd2m1db/kf3 it makes when striking the water below is heaf2 bm /kddd3x1rd 3.5 s later. How high is the cliff?    m

  A person, with his ear to the grogk4i; m49pxgp und, 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, anx4kp4mgpi g9 ;d 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 over one mile of distance by the “5-d9low/i,(.6m:q3xizk u pvw-fsss 4xydnv8* second rule” for estimating the distance from a lightning strike if the temperatureoi v* 4ks3-6xv pq ,xu9w:/mz.lsdy8dn(wsf i is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level1t6suyeq ,wy , 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 intensityhgmv ;;tjmsv0 /s4ec; is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired sim4wppbz2z z)17s wnag1ultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensitieawpgsz1wbz4n)2z p7 1s, not dB’s.]    dB

  A person standing a certain(42)9lzfyj 8a v/.jaj 8smkqk5pt bto distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sou/z2 j 8bkaj5al( pfk.)4 mvt qjstoy89nd 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 hk s70dgqle2 7tave a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What isqsk7e 7 l0gtd2 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 sv:gw- d lvl97mound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouthw7 d m:vll-9gv. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area is t,f82dmvqb b y. um9q1$5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier s9ia r1(e0yf bB is rated at 40 W. (a) Estimate the sound i9 (0y1asrfeblevel 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 registered 130 dB whe25nk um5t sq 1m.z2oxen placed 2.8 m in front of a loudspeaker oq5u.s22kmx 5e mzot n1n 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 difference in sound level o6aqj/-bj.tpu+ (o mgwf 2.0 dB. What is the ratio of the amplitudes of two sounds whose leog t-.j6/a bjqp u+wm(vels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is trinss1t)vhzo md.,mfxet( t,6br3e5,a pled, (a) by what factor will the intensity increase? Increases53 ( rdsz .ofavbt1,tx,)t,em6 mehn by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice -l9v+r+(buw)asm w ,f vkpks /the frequency of the other. What is the ratio of their s+,( - u+wsb)f ak /prk9wmvlvintensities?   

  What would be the sound level (in dB) of a sound wave in air7(kqvm: gt8kj that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mj(kq 78:kt mvgm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tonet-ht98de1n5 , rp 5a yfyfmh)v that has a 50-dB sound level8hyf-5a rf1t , vmne 5ph9)dty? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that 1t p1)g pbresoac cp6y.-h69i an ear can detect when the sound level is 30 dB? (See19g166ip oaps-.) hctycrpb e Fig. 12–6.)

  Your auditory system can accommoda 9xdk :3s (-ko(fjpifznt *e;xte a huge range of sound levels. What is the ratio of highest to lowest int:kitxkfsfn (j3ex;zpd * o-(9ensity 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 fro; jii4/fxuk3y+ta1 yequency of 440 Hz. The length of the vibratif31 jk 4ia;+tyyoxi u/ng 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. What are the fundamental and fird)vjm + soj59gi uotx5p/0 lf6st three audible overtones idfl 6 gj+x o5m09p5u)tjois/vf 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 7g -rvy(u2uv)jt cv*s you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assvv (*utu7)s yj2v-grcumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spann bx)7a)fl8 aeydmy): :8onay:vxe/t ging the range of human hearing (20y e tyo l:)n7 e mygvaa8:)xx:bd8f)a/ Hz to 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 has a frequency of 540 87p s3;zx rt1,cniv ; z,y/ugf)ziraoHz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lengtuv3 cn irz sa z1,8;pf7)tg,/y irxo;zh?   Hz

  An unfingered guitar string is 0.73 m im u. .tx9bzvn:c53ffnv h*d+ long and is tuned to play E above middle C (330 Hzu.nv hfm 9f bxcz.v5i :3tn+*d).
(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 thq5q .ni+ry)l(n zev u17+ptniat emits middle C (262 Hz) when the temperar y(itq)nize+vn +n 1 57luq.pture 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- xtnbyl d:ud8 3s9l-k $^{\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 should the holbts 4:nnzseo8 y4dv) 0e be that must be uncovered to pl0:nz 4y4 s8d ebs)tonvay 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 zq h le/yoi761resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why thisy7 i1h qzl/oe6 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 1mfa7qh(0c u8 j5w mc,l.80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. lu,5(8fm w07mjcqca hWhat 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 3 ; v0php,)-rvktfyxi$^{\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 pres/ycpb+l(cb(jp ut58 b ent within the audible range for a 2.14-m-long organ pipe alb(pjy5 uccbt/8p +(bt 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatelyx4f vcqlkb )+; 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 of your a4qcxl; v)+k fbnswer 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 2.0togh9z:3jf i c.m9a6z s when trying to adjust two strings, one of which is sounding 440 Hz. How far off inzozfti 9gc36jmh:9.a frequency is the other string? ±    Hz

  What is the beat frequency ecd7it*s)v nmja3 o05 if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another lj4-vy o:;e7fgdhrj+ rqp 47nm/gctc, +p0qd(brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5gdp y0qjr+7qcolr+/,vgp4j7df-h ; t mec4n:000 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 350-Hz tunina8fwru*5t y1qm zu: ;eg fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the s tam;5w1ey8*:zquur ftring? Explain your reasoning.    Hz

  Two violin strings are tuned qv0aj3y;1 e toto the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recal a3qojt1y;v0 el Eq. 11–13.]    Hz

  How many beats will be heard if two identical f3zke j/w5x g9ilutes each try to play middle C (262 Hz), but one is at 5.0°C i9zgw5 j3ek/xand the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuninc v6a0oyh)+g8qytmcq* 2cbw6lnw9n + g forks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency gwqy*qb2c c68ha96lcn vmn +0o+yt)wof 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person xcf:f t* bfwh0rs839z stands 3.00 m from one speaker and 3.50 m f9fxf:8wzsr b03h t *cfrom the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tunerrwbk;i0 new f9 079uot hears three beats every 2.0 s when they are playw07f rket09w iu;o9 bned 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 p5uozk*h:wg+qgn-* w 2.64 m and 2.76 m in air. How many beats perozh+pgq* wk-g*5wun: second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freque4jxfv ,8tyv. ancy of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you d.,tyf8vx4jv aetect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire enginrufwa1i7 np84 e whose siren emits at 1550 Hz mo7r8pa1u4fi wn ves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if anx u5+afw/cjdytf 1*z 0ra/y+ 7ylpb/ 2000-Hz source is moving toward you at 15 m/s versusy wxy jfy*/nta1f7/alrbc5dp /0+ +uz you moving toward it 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 frequ*v.ufxuq w) s:x ;xx3rency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assf)x:qx3 xusv*;xr wu. ume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out-1l 3bj9bxncpe0m s+ ee n7re7d;ii.f ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 mi+e n.ienm1970bdc;-p3x7e sbljfe r /s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a walc8jxie s91be.ceon:p7u,qg8 (v+r zyl at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What freq neer ce.71+:c (iqbo,8vx8p9s ugy jzuency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuf49l ob2mmgkuy 5yu 6,ba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway9ufbugl2yy 4 k,mo m65 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 measu,imw9y5b/a( m/mgm ajre blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissuea/5,(m9/jm m bgwa myi is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves ofa g- 6 iuft27tue3+ffpzvc-c8 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. Whedi5 dgf /;2 e8dpgqzu,n the wind velocity is 12 m/s from the north, what frequency will observers hear who are locgepud, izq d 8g;2fd/5ated, 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 lanlpba)+ln) r 2yd 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 soundp(lf fe72 dlqxik (l,7 is 310 m/s (a) What is the angle the shock wa7lk(xql l2iffp7d ,e( ve 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 atc z/lvjlt fv**11 c7dkmosphere of a planet where the speed of sound is only about 35 m/zc* *l/f 1djltkc 1v7vs
(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 waheekw2-jq4p 4 1n 6v4dgdnc k)ve angle it w nh4)kdg6nj 4-ckq 1 ev42dpeproduces
(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 t)ss 5q7n/ z. jsphc2l$/theta$ 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 es/6)f7c -aiq8/cz,ni eysj82l s xrohxactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has travelc 6fah7l/ey8-, os/ s)szxiij8 q2rcned a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that pr g4z/tib(:h 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 mgt4 pz:ir h/b(, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octavrcgk5y6( :a + hiqv1uq alq/f8es are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a 93ptdkn 2,og7c zt4 fi0crmwg -mh v52display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both e-7n hgkcwzdt, r4mg9pf23mciv2t 0 o5nds.
(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 clos : 3adjdk8euy e7o1fz3qn r7(ue to the threshold of human hearing (0 dB). What will bea83 1 ke nq:oduj(yudf z7e3r7 the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when ah1,ad s er*p7pps7w( en 82-dB sound and an 87-dB sound are heard simultan1d(eh7 sw ,pp*s7 epraeously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the ope/bavq pqp79tp)ig p8nyygwn.78co )2n, is 105 dB. What is the acoustic power output (W87t)/yp8p2 gi no 9wp7 qb.ncpgaqyv)) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power +1 la iu.i/f; lzov/cxoutput drops by 10 dB at 15 kHz. What is the i f cizll1./u;+ax ov/power output in watts at 15 kHz?    dB

  Workers around jet aircraft t l s3,sg2xetx79-6deynj( ivsbb 4n2d ypically wear 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. ls tx29b7x34sveb 6,(-e snydgndj2 iWhat would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatio nzj5e2o-6ujbi aph )+ns 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 tuneddf6z2 6nz8cv-y kb*yvquh3 0 rk;dls* 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 32k*h1fd- y oqw3,sufwy)32lwy cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit length of qu2w3)y h *1oks,fwdlwyy 3-f $6.1 \times10^{-4 }$ 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 intxbacf )0((t psg4jy: pj:r:opy; *l:1nlg sv wo vibration above a vertical 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 tov a(4y( pglnrc*j;0g: l yxt1w:b pssf):pj: he 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 masap0b pl* 8gy2qs 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (igy2q 8albp *p0n its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observe0wb pf0z6. voc 0q,obq r1spi7d 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 range com e:onb-(k uw.6xxn+(e tuuxg:ing from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 ( :nt: +egnuo ukweb(x.u-xx 6m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One):z,dflndheq 3b/* ux train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the * zxluf:qe/n)3 d,h bdother train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approachx-++o6svb u8bbrtwal yf 1.i3es you is 538 Hz. After it passes you31b x-oiy+fawv8 bst. bl+r 6u, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to thkem;.ej.ql: t2vct 3t( gb yq /x(8pgve difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a c lp; /ggytqve(b..(xe8tjcqt :k mv3 2ertain 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, prodair,w dq 7f nna/ux,3 -j-nzi k7;nuh(uce a beat frequency of 11 Hz. The sh, j; d(,hqn 3fi-uz7nw/-aurx7nnk a iorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad caj8o 4+r;:wltk frqhp: j,o+ wkr as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, : +rjr,jowo+:q 8f t4;hwlkkp(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 +6h ffux1is2kin 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? Ash iffsu2 +61xksume 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 tker. x.1 wxujgc,(0c0yb -zrihe bat at sp k10u, .(xrcz0.-i xebjygcwreed 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 off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approachecnr+ /wjv6623zhnnxb s 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 dete+n h jn662x/wzb r3cvncted by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to sendkttgxr7 26j6 f signals from one Alpine village to another. Since lower frequency sounds are less suscep j6x 2trkt7f6gtible 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? (See Table 12–3.) Model as an open tube.

  Room acoustics for s/r 5z9kl ;p rzopka-1ytereo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and o 9k pz;5zr1krly/p -a2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstraykjh 7(r0ob 2uit72oltion, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is str0u y 2 rbt7ok7ioh(lj2oked 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 lt7y .+k jhb.aa frequency of about 1000 Hzbj. y .h+ktla7 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 o -(whx72ljz;c+ ywc 9+ ojb ..asrstiun the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the planil.72s c(b rwxwz .ot9j+yh j usc-;+ae’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat .cq120 md5 vl,uodnfsis 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