What is the evidence that sound travels asr s,da7/y:,5y5 6rym,uku qu lzwz.lg a wave?

What is the evidence that 9r uc-f7-iayhuc j +*ssound is a form of energy?

Children sometimes play with a homemade “telephone” by attachin:xhvf( ie4 9) nm2uxrug a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound :xuf r)xi4ehn29m (uvwave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the y)p tyi/yu5 1u lhu;s 6 tl;m p-7yttarl:cj7;frequency or wavelength ty1 luml7y- ulh)tt7 :py5; yr;asttup6/;ijc o change?

What evidence can you give that the speed of sound in air does not dep(x az*.n+ (+ggo +dewtysqx3 tend signift gz+x (*gynt(od.aqew 3s++x icantly on frequency?

The voice of a person who has inhaled helium s eh m6,ugkk51lounds very high-pitched. Why?

How will the air temperature in a room affec ;n .-eklcekwi +x -*8*yfp :fzfby7ubt the pitch of organ pipes?

Explain how a tube might be used as a filter to reduc qan9lx 8xok ;0*:cjdelr/u .re the amplitude of sounds in a;q ul:xo 8rcn0k e9jdxrl*/ .various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closey,r2 wd+be27lm 41kebbju r.u 2(t hugr together as you move up the fingerboard towa.m, w2 h b7krebb(ugy+2u1er4jtd2u lrd the bridge?

A noisy truck approaches you from b op3-4u/ 6kbqa/n(;2m mzypllm6agjpehind a building. Initially you hear it but cannot see it. When it emerges and magpla 6;k o-ppn(b/34zu/6 m qjylm2you 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 z3n5rb( t wggwvfe(w 0v7 (j5t -jel dc87)iuqto “interference in space,” whereas beats can be said t ftd(j )n(t3br lvj5eqicz ge 7g(u5v78ww-w0o be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowyy 7p19 rlze ty7 prrs*:9j/fuered, would the points D and C (where destructive and constructive interference occur) l 7pr1 7yj srre yf9pt9:z*yu/move farther apart or closer together?

Traditional methods of protecting t0aqv) m*yxt78fv*ze(8 qwp zb he hearing of people 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 are worn that do not block the aqyva*zx*vq z 8f)0bet w78pm(mbient 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 shojf rq h2fbm4+)wn in Fig. 12–31. Each wave can be thought of as a superpositiorh2m+4f )qjb fn of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the sd6mbu)* f+pmeoq g;) same direction, wit )qob)fm*+pd6eu m;sg h the same velocity? Explain.

If a wind is blowing, will this /;npq8/ y6bn zpwz ,xralter the frequency of the sound heard by a person at86;/yxpqw,nzb rzn/ p rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows variou 9oms/r:h:9jxnfe wq*s positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child jx9f :woqeh r9*/msn: on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length fj-p 4 xd5jcj6of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Est p4 -cj5djx6jfimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the water:g fdx6,1r kv4o:okhn i. jlj5line. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vark:. 46o rflvjg5,hn ko1j:xd iy significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavel+4yktfk -h9bmengths 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 a schoowik2 l i/fcx852e f/iwl of tuna on a foggy day. Without warning, an engine backfire occurs o5fek/i/2wx8c 2i wlifn another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes whew.idb 9) ccu+tn striking the water below is heard 3.5 s later. How high)d+ tucw b.c9i is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike then)ts k xc+;q3s;o*gon,6)iix7ul0 7jl yx vul concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and tjo6 x)t)oigsl ln7+ 0*lynus ;3quc 7xx,; kvihey are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent edy9slv00yne30yhevqe 4k 5 3m rror made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strikv043lekm evd0q0 3n5 h 9seyyye if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level 8ko4q+0wy )0nqwcp g sof 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 intenka o ox 0n5m gj2 3tpzf05(t1h(.su8dar8dhucsity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when j(e9vz:lpre rg8 po52 fired simultaneously at a certain place, what wi5ejv: ro pe2lrp8(gz9ll be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an aip3 9k ro)f7b)gwzjw.r1o w3)vsw gjyo (9lco :rplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine?c w3)gw. y7vob)ks(w z399rfgl 1owoj opj)r: [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio ez,b2pqdy)a /sjoq); 5.i3z )9 yc; bynxlcqtof 58 dB, whereas for a CD playep y)ex;j2z tq ;.s)z9 c )yybno3caiq/lbq5,dr it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking a8a 89;n+ kf6ckllye oin normal conversation. Use Table 12–2. Assume the sound spreads roughly unif9l ao+ k kf8l;ne68cyaormly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose :swn2+l 8qtx)og xd;hiv)l,c 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 amplifier B gxm k(04tnsq(is rated at 40 W. (a) Estimat(q t 4(mkgsx0ne 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 )w9w9,fj xykr se 5- iiesfg /i9ar-dug:2 w1jdB meter registered 130 dB when placed 2.8 m in front of a i--ji1xk s5,gje9ig9 : 2w)/uy fw9 drw farseloudspeaker 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 difference in sound level of 2.0 dB. Whkonq3afy ;p96xqn b9w6a) c dmq.0 3,wo4 eifhat iso iapdw;n3a4 q q mfqb3hfy)cx6 ke09,6n.w9o the ratio of the amplitudes of two sounds whose 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 the inte-x ziuw0ejus +t/9,vhnsity increase? Increase by a f+sxej9v0 ,uzthu - w/iactor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement am);( +z)l 7cfibdbnhmg plitudes, but one has twice the frequency of the g7+imdln(f h;) bcz)bother. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sounm677mf5;e w 1ac6wxe sycdgl3 d wave in air that corresponds to a displacement amplitude7e c wl5myx3m1c ae7g; s6dwf6 of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound+9qk61g,efka npt 0fk level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See 6p+1f,gk k 0qfae 9ktnFig. 12–6.)    dB

What are the lowest and highest frequencies that an 0as i6;/ivarrz mteh9z99 fg;ear can detect when the sound level iszivrz tr 9s 99aa6;ge if/0;mh 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels.01k9i+mzj( bxm oa cc6 What is the ratio of highest to low9cz0b+mmc(ko x j6a1iest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency:y: af/c k9x5hhp:a.esd pim ( 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 string :dfx/9ac.hk ph :5ep i :sa(mybe placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audibl ,6iqr i.(ljznau(q :1)6rrx/ uijt fze overtones if the pipe is ,1zu fat n((ui6jzjrri ./q xq6r:) il
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of anou j.4fz b;qwy 8q8)he empty soda bottle that is 18 cm deep, if you assumed ityhq.q48 z;8)fuj o ebw 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 witogoj ,773tophh open-tube pipes spanning the range of human heari j o3o,7hog7tpng (20 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 Hz as its third harmonicy 2fjp m2/-niuy ,m*o,*td2jo jmr.j l. What will be its fundamental frequency if it is fingered at a length of only 60l mo2imr*.*ym ujj,/t2jonj,df-2 py% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play 3si6 xs xfo++qE above middle Cxq3++ o ifxss6 (330 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 that2jc u snrp/2*iioy3d* emits middle C (262 Hz) when the temperaturiyud jpis 2o*3*n/2cre 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 at2uqhp82; q u//e wr xiehdm)9g 20 $^{\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 +xwkb7fh-m- 9zc(f2 anoq fk7 should the hole be that c7-bzm hkf(2qak-+f 97owx fnmust 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 616 Hzdvr4nkq413p t4gm3 zz, but not at any other frequencies in between. (a) Show why this is an open or a closed 3p4rvg3z4nm zt4q 1kdpipe. ----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 m;y:md50p 6s6 pjl0vuvzvz 0fat two successive harmonics of frequenciep6v: ju5 p0mfd zv0;6ylsvzm0s 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 ukmhzh0a px*a6;- 7co$^{\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 presenit-ht+ wa .af8.1 5ncdg;h:m ve mulq7t within the audible range for a 2.14-m-long organ pipe at 20 :t - awgtqal1.h;m+um7n5e.idf8c hv $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm h8o f9y pi8i:flong. It is open to the outside and is closed at the other end by the eardrum. Estimate the freq8oi f:fyiph98uencies (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 *xftu+n23k8 x. vn cgcone beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hzx+gnfkc 3u8.cx2v*n t. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz)ay/yq /,vty j)j7qk,bixfv .9 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 whistl 4vw h,lf10(yw.cyaede operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operatdl4.y e(va10 f,hwwc ying frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with i():t 6ji c:ud5idx t3zerzm2a 350-Hz tuning fork and 9 beats/s when souz5j r d2)i(t3 iude:z6i:m cxtnded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tu3ip tm-z8of7m ned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.07t pio8fm 3zm-%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middciw8pj 9f.oh*i, j k+ble C (262 Hz+kjfjbci *hip,.o w 98), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency/,gs2no al y/s 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 b/y,nslsa2g/ oeat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from ot8 n xsc-a;1 qw-(hwupne speaker and 3.50pqu(c-haxn1- ;s tw 8w m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibr0s h0uxi g7f9rating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the9is0gxr fu0h7 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 wave :xc*g5gqx2has; 2 x7kk.oqd *z7 hmhxmy 4*iolengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assukog q y czh5xd*x *m.x24o h;*i7mgaq7sxk:2hme T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when alw8*: siy+a jxt rest. What frequency do you detect if you move with a speed of 30 m/s y li+8xwsaj:*
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a (-5 nmoyd)q c;thvqw 7fire engine whose siren emits y d nvh cwq57;(qmot)-at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in freque*xpe60xu7 rmancy if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15rmxa u p7x0*6e 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. When one ie7c/m6lo:s+ 3a( 3rpbqnvzcjs 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 frej a /6 l:3(3zn7cseqbc+m oprvquency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultra0iud r25pfg-gsonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is-u f50pgi2dg r the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the:y u(bv1l 4axu bat emits an ultrasonic sound wave with frequency 30.l u(4b v:u1axy0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a ty5zqymg*,d, j uba was played on a moving flat train car at a frequq*jd,my,gz y5ency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suppo j1lj1 t ; jg4fj*::4fwcj5g b6kkpehese the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if5gwjj*6pl:jjbhj;fktf4cke14 ge1 : blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonir6)efbtkxm9 tuvlkob96 u5:9 c 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. When+hellq+l7uuh 6 r h( :uq(5bpn the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, atuel7l+rn+q 65bu: hh((h ulqp 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 o2g- 5be88w3outp -brpxpf5 tbn land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of rtz q3ffak q:d:xp 7uwm+fv/1:/ pu-p sound is 310 m/s (a) What is the angle the shock wave make3/q:f :d1 ptrzv -mpqfwu /pu a7f+:kxs 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 sound isj2i eug*k0mi0 only agej ik02imu* 0bout 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 8nw3m*u mjqw r t,a/1/g500 m/s strikes the ocean. Determine the shock wave angle wt*r3qm jgu nw,a /m1/it 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 *ksjdrczo(0yjwim6 / g .*1ab$/theta$ 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 kxjc4 5h4id 35x-u u+ 6)qw*idtxk wgssm above the ground flying faster than the speed of sound. By the time you hear the soni c6 kjh qd* 5wwxds5s4i)g-utx4x+u3 ic boom, the plane has traveled 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 sends 20,000-Hz soatnu, iq(4;1 v uc3elound 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 iu c;e4ua,ol 3( qvn1tpulses (in fresh water)?    s

  Approximately how many octaves are ne f8lk4 b*u:n/kpv:svi/bc202kic z there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a*d6w2u6fq5 ya3tsl ff display called a sewer pipe symphony. It consists of many plastic pipes of various leng26aud6y5sq lft *fw3f ths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the thresholx u*ifk.8qaa- d of human hearing* q8.a iuxafk- (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound lay;:2 9ubkz:n-s4l8x qcbq5b )ykt tnevel when an 82-dB sound and an 87-dB sound are hea-;)2l nakqb8bznqytc5k:u xy 4b :9 tsrd simultaneously?    dB

  The sound level 12.0xa brhcc(4:f ) m from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, ass4 bf(c)xra:ch uming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The powes.xk/ll;x9rhlzc cs ppk +12:r output drops by 10 dB x.lch: spzplk2l; 1xs k/cr+9 at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices ovn8eqz9y1 ddtn- o5 9cjer their ears. Assume that the sound level of a jet airplane -qo59cdt9n 8z ydj1ne 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 airplane engine?    W

  In audio and communi)) +36w wu xjfl9/r qhoqhdgfv,8ru6ications systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequency lqor638/krynb/ug p 5 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 ls7mu ilwr -)o*fel5jnr3pb; e*5s0d points with a fundamental fr m5bw l; sj3noe5di) rllf*rs0-*eu p7equency of 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(/ tur-cvp m(j tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it (c(pj u m/-vtrdoes so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is nekkiv4tlwbs;9kk :ed6w )ix; qg20 x 1d d74diuar 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 (i0 e d24 :xd;kik9;)wkgblu swiv qxkitd 7416dn its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observeb3ec960 htmsf-or ;yiqr+r*nd 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 coming from twah8i5t ;ow:juo sources. The sound is loudest at points equidistant from the two sources. To determine jti 8hwa :5u;oexactly 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 trz-1qg / g6n0sx(r mkjpain is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is tjggr60 s m qp(zn-/kx1he speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After g)9ity; q8k nofeo,a+ -x wqgl8r*tf,it passes you, its frequ9 t , i oxfo)lt+kqry-qg8ewnf8a,*; gency 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 the dii;/sgi-e;5l7 zv6kl 7lho uyjfference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency hal5ilol7h/6;kz uy7lgvsi ej-; ved) 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. The t-d+l9.uzq vg52*eue p -t rbeshort2bv gue- .zdltu +qe e5*-rp9ter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad z9txwo 4s( :u :glj.,1sadegzrs 9m6xcar as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he he ss 9g :xda91:gmw( 4sruzj.ez,xto6 lars the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.3iw4n)8y1jbqr buj7 p 72 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel )17i nuwpb4yj87rjqb 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 ce(ef,,rgvnav96 iu+1zrjh+ 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 waven91 , e6re++cjv(, uvhrazf ig detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it ./shy22p/v,7tovw utw cu) f0oan k4napproaches 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 detpfs)v0n 2 . vkwhy7ota/4,utwu /2ncoected 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 send signals from one Alpine villxady5fk2b5unptrl n / 6a( ujz405iv*age to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played ay k fnv i565 nup/(d2abx*r5j 0auz4lts 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 cav( w .t erxb(e:a*wq *ist7eb) nu5n:gn 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 2.8 m high. Calculate the fundamenn e:*7i(:nsx(.tg*ebw a tv)bwq5ure tal frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,c)yn9- x)jvg8zav3be, 1x x nh” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little)b3anx -) xcyxhngj8e ,1 zvv9 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 frequ ot *xr5x:o( lucy7kqn9 yc51pency of about 1000 x 9(* oyunr 15oc kx:7ptcqy5lHz 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 iz gd3ib-5:: z/dubs gon the ground hears the sonic boom 1.5 min after the plane passes directl:us3 5izzd b/bgi-d:gy overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1k 0- p4o7 ptvtq48utya5 $^{\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