What is the evidence that sound travels t74tee uqs:-(zwnz g6 as a wave?

What is the evidence that sound is a form of enu 3 nx5e7r,/ . qgp/)inwqlzhsergy?

Children sometimes play with a*p,/49;z oyml tpzt pm homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is str,pzmol/z9t 4;pm* t ypetched 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 u o+hf -dqel,(-v1phs or wave( 1qs lvf +p-hehod,-ulength to change?

What evidence can you sf2 uqx o,9elyki-r x5lr5c+m0d9rk6 give that the speed of sound in air does not depend significantly on frequefc,isy2ro r5 9q9eukl05- x+ lrmk6xdncy?

The voice of a person who has inhaled helium sounds very high-pitth/ k+s n0ofb,ched. Why?

How will the air temperature in a room affect the pitch of organess0)b.vaz3 c 1el k-z pipes?

Explain how a tube might be used as a filter toxd2kg i +st*1m reduce the amplitude of sounds in vg+mts x2k1d* iarious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar hnb ;b.9f3xmg (Fig. 12–30) spaced closer together as you move up b;ghnbmf 93.xthe fingerboard toward the bridge?

A noisy truck approaches youkd23roe y+c3 bji 0xu5 from behind a building. Initially you hear it but cannot see it. When it exj ud5 3roy0+k3cbie2merges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due( hfl okfan4+o--qja2 to “interference in space,” whereas beats can be said (h-f2-loa aqk+jnof 4to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, v9rafkprn*x10s/;i xwould the points D and C (where destructive and constructive interference occur) move farther apart or closer together? a1i rfxrxp90ns/;vk*

Traditional methods of protecting the heat39jqzl) y9csot0pbm; ) m)tl 1lzjv3ring 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 ambient noise. Instead, a device is used which detects bz0jq)3)vl1 pctj l )s;mt9m9zlo yt3the 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 showkw 9z) 9rhc 2qljn:0ofn in Fig. 12–31. Each wave 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 component frequenr9 0)hzqc9o2lwn :kjfcies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observy*a:v+-,d imj +o wquier move in the same direction, with the same velocity? Exqu i vjy++madw-:,i*oplain.

If a wind is blowing, will this alter the frequency of q5eo.szua 7b5 the sound heard by a person at rest with respect to the source? Is the wavelength or velocity changed? so qe75a5u.zb

Figure 12–32 shows various positions of a child in mod 4dyi:l*y7h rq b*wl/:ev;lytion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, wq el7h/ ;yw4yr bldl:y v*:i*dill 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 2sv nqv,.4l08kpfsbm6koe :eof her shout reflected by a cliff at the far e,f.e2bmso e:qkl n4v ks0p 6v8nd 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 waterline. He he6cpm,lbyk wcsk30.c:e: cvc,z4 b s-oars the echo of the sound reflected from the:,4op0mc 6lbcvsy,s.-ck:zwebkc3 c 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 indx7( e)kvxf4 2 zg3jh-opwffb)y+ 0dn5pxm3x 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 aig-ig t 1lqb3- school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–ilt- - g3gibq133). 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 w 8;/6jku( hytfv.efpfhen striking the watef/y fekpu( tj8;.h6vf r below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to th *9gnb( k/+y7 otpf-7rg1obr oi anr1qe 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 th(t1 -g1yrn+rfb gr*7a9n/p oiqokb o7e concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent ;,od;83to nop3 w x2wiz p+y4ljrp)xoerror made over one mile of distance by the “5-second rule” for estimating the distance from a lightninyrno p o4j t)od3p2i o3+;w lwz;8px,xg strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity vr z**4/y.r*r bwhcr8kd 1 uehof a sound 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 of a sound whose intensity:+; scr dq sigwf1+dx7 rm;9zt is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simu ljqyanh67(o/k yh-ib w 1ap:3ltaneously at a certaplbhkyw 31a:hqjy a/io6 n7- (in place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally *d9 5i+i:te:ybvdtk q noisy jet engines is experiencing a sound level borderi9iyvdd itb:*tkq :5 e+ng on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas pr4z(b4vkf b 8;/juyzfor a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each d4jkb;z (p fy 48uvr/bzevice? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal convere9g79 rv(3fi94jwk kvfk0ee msation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on thekffk(7g90r9wme4 v ejkive 39 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 area 5uo3t)3g m xg56rjkz iis $5 \times10^{ -5} m^2$ (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 w 1/ :aq6j46bqtcovnz more modest amplifier B is rated at 40 W. (a) Estimate the sound le6/:wnaq1jv qct oz 46bvel 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 meterr jj/zq6unb f) zpa9(n+ud*r + registered 130 dB when placed 2.8 m in front of a lonjubajf dnpz +q+/ 9(rz*6r)uudspeaker 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 iz1 7kkxaado+rm v (+p0x;a0thn sound level of 2.0 dB. What is the ratio of the amplitudes of( 0+tvax0x+d1kz kmh 7aar;po 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 wf/qvl nj(l ;exx6atv4ku4x6rxg 1n -al (ux *7ill the intensity increase? 41 vt (fux-4 x u7g/ra(xl*qn6x;6xvnklle jaIncrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but 4lqhnw5o8 6xo 9a0n/ ry ypj,rone has twice the frequency of the other. Wha q6jao0 r 4on 9p8rlh,xnw/yy5t is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in aiyc, )rnt m;0ccz8w1evr that corresponds to a displacement amplitude of vibrating arctc; c8z m01vwn) e,yir molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as exn*q+ffpkp0 d0*yp/ loud as a 100-Hz tone that has a 50-dB sound level?d/yqxfep nf p*+*0 0kp (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can de1kr l.m vbkiwoi11//otect when the sound level is 30 dB? (See Fig. biv/moi1 1o1 /wkl.rk 12–6.)

  Your auditory system can accommodate a huge ranga)1ym*d bi9ff zv+p 2sx3 5bdbe of sound levels. What is the ratio oi)5bd92 b*bvf3+dxp mzs1ay ff highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundhshc w.2ono;3amental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has ao no3ch;.h 2ws 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 fir7dm3jo)pcmbg4pe62 r st three audible overtones if thegob 3pd pjm7r 2c)46em 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 iolidgn7ps3*-,p xp9 would you expect from blowing across the top of an emps ,g*3i nopp p9xdl-i7ty soda 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 46m9q / 9akhbfoqmd- bpipes spanning the range of human hearing (2dq /9m6bkmohq -4a bf90 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 harmagx b)n/lv,eade ,l;mnm5oi/f3 x:* eonic. What will be its fundamental frequency if it is fingered at a length of only 60% ofmd/ nee ml,i:n5v)/;la xbfxo3g ea*, its original length?   Hz

  An unfingered guitar strdzhgb e-u(/pm1r:r0iing is 0.73 m long and is tuned to play E above middle C (330 Hz)./pe-mhi 1bd ug (r:zr0
(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 opee :i0gks4flk6n organ pipe that emits middle C (262 Hz) when the temperatu04: 6eigkk lsfre 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 w v09b.szk nb1$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Exampl+yy2 id/anw3r e 12–10 should the hole be that must be uncovered to play D above middle C at 294 Hz? r+wda/ni3y2 y    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, 440y( )ape2ixi0d Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed padei (2x ip0)yipe. ----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 endsoyn--yl:z; kxutpd-8 . It resonates at two successive harmonics ;z:--udy 8kypn- lox tof 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 n *8qf3zljxsk).7el63eyjh u$^{\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 li +-gjx;2vw ra 2.14-m-long organ p+ri;2w -lxvjg ipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately t,-p(lhe 9mi g2.5 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 wavese(,-i 9tgp mhl 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 one beat every 2.0 s when t ce jw9g6d**8 j jeo,vdy(sep*rying to adjust two strings, one of which is soundingo (pg wsedvj*y86*d,ecj9ej* 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat freidrg2a;1epj v)s9n ektu *wmdu- l 5)+quency 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, wh: aj5lk :gyab)ile another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of freqkjyl:agb: 5)a uency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuni tjbr (t0-iu,tng fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational 0ittb-,(rt ju frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned f5qi/ ag +x3dsm0.pnd 9nuz 9eto the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%.zddeufi/ng+p x0 n.5a3m9q9s What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will bm/af pvlw a yf *5n-r,2wxk(o0e heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the orf,2y*m kpl /a0 wofn-(va 5wxther at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, any*bf;/ jc0p ahd C. Fork B has a frequency of 441 Hz; when A and B are sounded together,0 ;a *phf/jbyc 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?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 mp 7,3 -fued:nwuu;jod apart. A person stands 3.00 m from one speaker and 3.50 m j opud ,fedn:w u;3u-7from 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 p;j 0kdm b6f**qws cif 0/yfedheaijc4v1z 7 5)iano tuner hears three beats every 2.0 s when they are played together. (a) If one isjhbdy4 fm ack16 )wv/fc * jd;fiiz0s0ee*5q7 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 2.64ziw5d wtu ;ai ; wvc097pe3j8zw03xsb m and 2.76 m in air. How many beats per second will be heard? (Assume iz0 zce893a;w 0w5uv w jp3tsbxw;7id T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fgz by,8q2vcq4 jj. xf j 3m+wv.)+vr.c2w vdgfire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move withv 8.gqrcb q2mvg2 3jdj4+ vyfv x.jw)z+.,wfc 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 firea;r r/joqn2ub4h*o/ z x qwjtx2;,ds +v6iwx4 engine whose siren emits at 1+or xznx6 ,rhqdbo2s/;4tuawj /w ;*iv4 2qxj550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency j od.je0i)b-xif a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two f)b- j0ed.oxij requencies 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 s8ul , .*t 8nvukwl/eskingle frequency horn. When one is at rest and the other is moving toward the first s neu.8/,tvl8kl w*uk at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives t9j.w) p+ry5wivm )xm(e.wka c hem returned from an object moving directly awrjak5m) p9+ . v.(cwweyx)mi way from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a w)ry zj3ci h0f(all at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frzr)03fc( jyhi equency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original djg(602rd; y( xzekwcv++ uhgDoppler experiments, a tuba 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 railway station. What beat frequency was heard if the train car approached the z + (x(h c+ddv6jkge2uy 0rw;gstation at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bloodk vg2w;rqg c+v9g,y9b -flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg 9ygr q2gvk+; 9cgb,vwarteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequenv;mvpb s g8n.idw)8n5qb.2ty cy $2.25 \times10^{ 6}$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 frequzj 9/p5wa8 svlency 570 Hz. When the wind velocity is 12 m/8 spa5jwvl 9z/s from the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land usrxke-s1f c6y204f3ls foa: 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 Man,ve.pyk eelv-) +z7 gch 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction o pzg),+7n e ve-.lykevf 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 ti5xmahc 4 l- -8bxj fe0(nps3uhe thin atmosphere of a planet where the speed of sound is only abou4hu3 asx-li(j ce0-n 8 5fmxbpt 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. Dete*w zyzyhp6 n.*rmine the shock wave angle it phn*zy.6*yz w 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 j9 n6en.8sqhqgzj 5. h$/theta$ 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 exactlt :bb pzt1b(qh2b*m7ey 1.5 km above the ground flying faster than the speed of sound. By theb2*em 1p7 (btbz:qbht time you hear the sonic 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 sbg;9aaw /;jtd l9.qqconar device that 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 wor9a .;bl d9;t wqq/cjagk is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible rn0-be+ixp/at zbdu2 k: szp ,+ange? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe s -jvrt37 j:qfwit;5vaymphony. It consists of many plastic pipes of :3-vi7j 5v qr;fttwja various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes 3diqbh4 yru -qj5o5i6a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquito i3o4qyu556i-bd rqj hes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB ghmq r gg88 nm xpk)a*d0ns/a)s jr(p77hm3r-sound are heard simultanqpss ap-mxnh7r*0g) 7rm )8m/n(rkdh g8jg 3aeously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, isk) 7b ;x f3k+mhrs/adm 105 dB. What is the acoustic power output (W) of the speaker, assuminrakf7 h 3;)dxmk+/sm bg it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The powe4fok o6wuu;ciz5(qa o1u t7v2 r output drops by 10 dB at 15 kHz. What isu z72 v5t;owuk ocof6(ua41iq the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over th0 (pqqcv )fxe,eir ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engipxv)c0 (, qfqene?    W

  In audio and communications systemf5kp5y ;yg8utfm 7.jks, 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 tbn o8m6;j *h2ne(4ovhcs2 e zzuned 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 d i;ir/w )ph-e 85cjzmsp: 2ooxl.0hafixed points with a fundamental frequency of 440 ma2/wl: ;cohszi h)x8.j- 5eip 0 ropdHz 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 a2sagtkb m p620b7ao95 pw *amwith water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again0672bapatsm92aa 5 b* ompg wk at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of71/v-e kcxqjy kea6v9 mass 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 produ1ve96-/ ek7 c jxayqvkce resonance (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 k71fj b+q ke8.l.l, gq8m gwpc($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two s6gjvn3vau 7e8ources. The sound is loudest at points equidistant from the two sources. To determag3e j6vu7v8 nine 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 whistles4ael bxr igxakr)4p;7 v, 24ql. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. r4gl pl7rqx)xi4 a 4,;bkv2eaWhat is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After vn16 eb qis9r d.bx58faa1l7rit passes you, its frequency is measured as 4867 5.deqb ivar9 sbr68 xl11nfa Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just) njw 6jz1dkd1 by listening to the difference in pitch of the engine noise between a n1) wj6jdkz1dpproaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, prodbnhe, j q ou,:bk;7e+suce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the ooebhek:;, us7 q+, jbnther?    m

Two loudspeakers are at opposite end hajj .44fpmq/s of a railroad car as it moves past a stationary observer at 10 m/s pa4qj4 m.j f/has 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 have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what ne sz,y4cxe.1beat frequency would c,1n4 eey xsz.you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a 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 flys. 4 g3km)oos5z5d tp;xkf6mv ing toward the bat at sv5ofs)mtm pg.4oxkd 6s;k z35peed 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 bf:vbel bs f8-u 0z3r;frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected lb3bsfr vu:; b z-8ef0by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) lu+ah1ypr r-jt/jbd.( 6gb 6n dqb/5rwas once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.)b+.(ab qgjhbu/ dtnj6 p5-ylr d1/r6 r Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence kf a)0u)w3xh pof 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 fundamental frequencies for the standing waves in thisf30whpxk a ))u room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rodu.xazd 6t29yms,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, l.2mx z ya6utd9oud, 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 thresholdad rz p*68,px3aoqx19sw h d/fpzo l/4 of hearing for the human ear at a frequency of about 1000,xf3app8 6*4o or/h19/ pql azszxdwd Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the grou:qt9xc dx wqz6y; x5a7nd hears the sonic boom 1.5 min after the plane passes directly overhead. Whatx :9t;a5q7w zx ycxq6d is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatzst s3j.9ob; o is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h