What is the evidence tha ktmeqw2200d7r ag0hxt sound travels as a wave?

What is the evidenceo(c80;ity hjo sy+4if that sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a sdxsv*l+l6gt + tring to the bottoms of two paper cups. When the string is stretched and a child speaks lstd+6 g*xv+l 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 wdm bt.6. ypn2zavelength to chy6pnm z.d 2b.tange?

What evidence can you give tha ,m x,.txwwkhgij 3g1.t the speed of sound in air does not depend signif.tj xkx .,3,wwhmigg 1icantly on frequency?

The voice of a person who has inhaled helium soundr n* n- 4fisc2l:/whdps very high-pitched. Why?

How will the air temperature in a room affect j nip(zb8z 5q7the pitch of organ pipes?

Explain how a tube might be use. raxlj 9s r75zc:a::cpci6- l fl5kbwd as a filter to reduce the amplitude of sounds in various :b.ia:k-zsjra x5 f:7cpl ccl9rl65 w frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (F3e z9(et;m bzsig. 12–30) spaced closer together as you move up the fingerboard toward themtz ebe3;sz 9( bridge?

A noisy truck approaches you from behind a building. 2 +f5b6nss;v :moi9hu ktd ii:Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on v t+k 2:;fn9 o bs:isi5dumi6hdiffraction.]

Standing waves can be said to be due to “interference in space,” whcznfa/l+n*n8sc 2o+ c ereas beats can be said to be due2as+ nl c*ncc+ fon/8z to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers werdke3rmh y2+zn m +6xz,e lowered, would the points D and C (where desr+m,h 326dzkez n+y mxtructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in ar9cqz wa q,sx/js*xy7;eas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a rezqxjc ; ssywx,*a79q/latively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be *vlmisl s4)2ythought 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 com2yli *)svs4l mponent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directig4woz2a 3essr-tw ,h(tj/*gtk 0o:kaon, with the same velocityzoa/tg*es0 ohks3j:w w -ka4,(gt r t2? Explain.

If a wind is blowing, will this alter tw6t+1x cv +.xn g/ac*nc(xaq she frequency of the sound heard by a person at rest with respect to the source? Is the wavelength oc1+cxwng(x+/vsa aq.c* tn6 xr velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitor:tc8vl0gy84ysw 7v mz 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 for the sound of the whistle? Explain your reasonmg v7v0 84:lszyy wc8ting.

  A hiker determines the length of a16kigwy 6. oygze/ w0q 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. Estima0.w6 wiy o1 gy6zkgqe/te the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. Hzb; 0l hi2w,owe hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean abw, ozl0wih2; t 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 air at tjeox- j/-v*lx*dpt3 zg1ddv d zl:)bus(25l20 $^{\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. Wkt 9ddxkk;r.nf 3 mt0:ithout warning, an engine backfire occurs on another boat r3;fnmxk:.k9 ktdt d0 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 whwiq4)l dz2ho 5en striking the water below is heard 3.5 s later. How high is ld2hiq4wz5o) the cliff?    m

  A person, with his ear to the ground, sees a hug m)wwn.ak2fy9e 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 cow 2wn)kmf.9ya ncrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over onuoq e5g:v3ei1gfq6 f8 e mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (vq3e gi o561gqufef:8 a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a .fi+ 5y8 1b:dkl7llnpyo5igisound 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 is v)j)h7o(de9gt;ujdks xqp94 $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously at 8om (a38 kbnfba certain place, what will be the sound level if only one is exploded? [Hint: Aknm 8(8bfb3ao dd intensities, not dB’s.]    dB

  A person standing a (i )vjma * cztr6d0ksb73l bb4certain distance from an airplane 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? [Hint: A(z*3bbar j)4dcl6 bm st07 kivdd intensities, not dB’s.]    dB

  A cassette player is said to have a sig8wl7v5w8. z:vcu+ld l2n z(ety wge) tnal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratgn utc) 8 (+wtwyezdev7: 5vl.zlw82lio 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 perszph(lg:8f wc5h y5j o3ve.lq9on speaking in normal conversation. Use Table 12–2. Assume the sound9eg(l c3 :f5h.h l5vwy8opzjq spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum wh-xk; ;9i brgnkose 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,ma u0e,,wpb, g0(v lve while the more modest amplifier B is rated at 40 W. (a) ,e b up vwg00mal(v,e,Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter regi:8 p4 t1-e lwd/yawpgnstered 130 dB when placed 2.8 m in front of a loudspeaker on the stagedaew:np1/gy 4ltp8w-.
(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 diffe)ba-:a wc dy 1mhw gg,f+,q4qne7si,qrence in sound level of 2.0 dB. What is the ratioqdqw gia,+ c7 bh-4efan1g :q) ,wym,s of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a s5)pddzm ewv-+x;y aect o2o ;ba2f21sound wave is tripled, (a) by what factor will the intensity increase? Increase by ay;xme -a2 b 2co+fdwso1t5vp) 2z;aed factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal d.f sq+deb , :91vmflpm-u;sv xisplacement amplitudes, but one has twice the frequency ofbu9 mfvx1sp.e,;qfs+-:dvml the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air thsy2pma y:r/ m2at corresponds to a displacement amplitude of vibrating air molapm2mryy2 :/ secules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound levekp4 smy yie4+/qq.mu 8l to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.) me48qmy/spy .ku q4i+   dB

What are the lowest and highest7l(pw gim0 u) 9ee bon*sp(gb-yk +ch7 frequencies that an ear can detect when the sound level is 3y )kim(7 u +lce sbg*wpphb-eno(9g700 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of souniz i70r ;v*zled levels. What is the ratio of highest to lowest intv;7l 0zirz e*iensity 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 nsi :f75ajl4k9fuxx( u oz c33wq3cz7fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension 4xx( awc 7f qcl3 5ns33uzo7zj:ukfi9 must the string be placed?    N

  An organ pipe is 112 cm long. What are 3sn3 tgjhp(:qthe fundamental and first three audible overtones if the pipe h :qsn j(3pt3gis
(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 frequencim0n ei: d9.xxp qk8e-y would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed inie-dkx 0m:8peiqx.9t 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 wi*ick w* fbdny9(w1(d4 u u-iaqth open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be theiy( fw4dn1aq** 9bcik (uu-wd 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 har282ymtlj*blag;haiaes q3 +- monic. What will be its fundamental frequency if it is fingered at a length of only 60% of its originasbt8gj+a il-2y e*ql;am3h 2a l length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to plagd7b uie l +r-quzf):0y E above middle C (330 Hz). u7 i0bgdl)fue-zq:r +
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that eomfy/. .ldwc81o e*vhmits middle C (262 Hz) when tfo v8l/hoe*y1.m wc.dhe temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 2hr39f8ia/ hd630wra5w wxvk n0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiecy g(qflb, 4qf09) onu7vkr5ll e of the flute in Example 12–10 should the hole be that must be uncovered tn(5ql4 l lqkv,0y7 ) fbrgf9ouo 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 264qtl tpf. )u/*lz,v hu1 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or )utfqvzll, *pth u1. /a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is bvi(s39;x+p rie + 0kzo/3s w89 loolwojgqr;open at both ends. It resonates at two successive harmonics of frequencies 275 /rrwo8 ; sz(+9vlg9w3p03x bse+ ljo ioki; qoHz 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 izub v.0w :.mj;2v74xghd)ydd y yih 8$^{\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 ay-hcdolc+ zz xzg y/ j1h/;i/jenyf5/0ce- ,f udible range for a 2.14-m-long organ pip co//0 ,zh+jyl f; jh1z/zcecixyg/fy5 -dn e-e at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It5ne.6y2doao r9zm7jig93-zcxjny :i 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 answer dx92r6oo 9mynay3jc5:. i jn-iegz7zto the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears ockf w0, (hi hdp:(gjg;rkd7 f,ne beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the othh7fdf g 0r:(jpd;(wk ik,gc, her string? ±    Hz

  What is the beat frequency if middle C (262 Hz uuzil0u( s*c-hgb 24o) 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, whlg/;9 *:u7)ltzwdgp )xaq w;h9miy cwile another (brand X) operates at an unknown pd/ gt zwh9xgli)c9 : ;*wlqm7 uya;)wfrequency. 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 operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when smwp, ),ck2wz/d gwqphgyh1(7yj 89yoounded with a 350-Hz tuning fork and 9 beats/s when soundep(q97yj whg kgo8d ch),y ,1y/zpw2wmd with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same freque0i w1 yjwd)dj,,t wl+msi:s h.ncy, 294 Hz. The tension in one string is then decreasel,j hss )w1: w+yimti.0,jddwd by 2.0%. 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 mie:kduf: zi+ t.ddle C (zud.ki+ e t::f262 Hz), 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 of,l:l(s)sltx,ulmh a 1 5m 2neb 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounde5 (m llbua2emhx,1nss) t:l l,d 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 one speaker and 9vpi lgi; aryp74-o r93.50 m from the other-l ;p r9ova4iir g7p9y.
(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 f wmxw1;(bvo/f zz-al6p+s3 ua piano tuner hears three beats every 2.0 s when they are played together. (a) If one is v s1ab3w/ 6;zxf+mzf( lwupo-vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m an j,..5c/rbfk1+hbuczdfkm9c d 2.76 m in air. How many beats per secmhub5k,.fr.kzd 1 jfbc9/c +cond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 H3mzjh qreg7w73 be2p)z when at rest. What frequency do you detect if you move with a speed of 30 3rge 77)h b3we jm2qpzm/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire en24.gfi3peh4-ofmc z 7oxnw/ jgine whose siren emits at 1550 Hzoo-mfchin/ge4 j zwx.2743fp moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz skl ).z +9mmd6chyo1 ceource is moving toward you at 15 m/s versus you moving toward it at 15 m/s Ar1 )hk6 cy zmdelo+c.9me 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. Whejv2adey1 g/ (ln one is at rest and the other is moving t (2yvd1j ga/eloward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHp add0b+n9* -1i vodhcz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound ad* od-+pi10vnd c 9hbfrequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall ,id(1j3/h mde/fa f daat a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?hd1,fdaa3im j(edf/ /    $ \times10^{4}$ Hz

  In one of the original Doppler experimenyxl*q,;d /*ec set mr9ts, 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 frequenc s/c *trdl9,qe*mxe ;yy was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meterm c/ c6:oazr8p uses ultrasound waves to measure blood-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 expectecrc:m8o6/ azpd 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 of frequency t-oqcs 1ya)lo*xd3yhwr/4ov8 f w:i6 $2.25 \times10^{ 6}$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 frequeni0gz3 2hx 5zigcy 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear whgg zh z305ix2io 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 -zwt98m8hllp on 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 / j 48xtgnnc(espeed of sound is 310 m/s (a) What is the an jn48gt(/ ecxngle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of solcn.jn g6 0n0m sr,kn1*+dfodund isfrmd10jlns+ g6. d nnk*cno, 0 only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes bsnnnw; dv 03i 9ll4u *ncv 1xis*3rtq-p +ws1the ocean. Determine the shock wave angle it prodsnclbqw*9 dv iv41+s* 0 3-t uwsnl3rn ;1xipnuces
(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 ra t6ysdf p4,j9,5ytfan*xt ;$/theta$ 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 iytsk1j8w;j2xd k9 .w1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic bo t1w2jsji8;9 dxwyk.kom, 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 sound pulses dowp3 cl 12)yykb lqca+*vnward 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 thycp+1 )3b kqlyvcl *2ae minimum time between pulses (in fresh water)?    s

  Approximately how many octaves arwfi qyj 83l +1)ayaj(me there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewe7d 3s/*yc,v)zg y )*t 3atjtv3fnnavtr pipe symphony. It consists of many plastic pipes of various lengths, which are open on both ends)cttv, s3gjnn7at /zvyt3 fa **yd)v3.
(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 tj ang 1psssw4-q2(g w7t* *lgid;u29/ o kjiilhe threshold of human hearing (0 dB). What will be ti jqu9js g -1 7a(4 s*wk*i2tdlop/g; w2gnslihe sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level whenrc7q8d 0db6ak/-z zc o an 82-dB sound and an 87-dB sound are heard simultaneously?a 0o68zc cqd/r7zk-db    dB

  The sound level 12.0 m from a loudspeak46 d(wic7 es* ;vb3.ufuqlr hqer, placed in the open, is 105 dB. What is fluq6v3huec;q*w b 7 d (4.risthe acoustic power output (W) 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 outki*q c0 2jnpg/pret 538vk f1aput drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHjr8 nft 5k0g1pa*v2e kc/qip 3z?    dB

  Workers around jet aircraft typi 5rrbac ll 7mq/n8amj 3*pl7z(cally 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 alq lzr /3( pja75c7rabl8n*mmverage 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 communications sysr zyqk vr)-e)+ji(3)upuj r2ktems, 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 frequqf5z1tin- ff 2jwjudqp4 k9 61ency 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 vi:ya :y :r+9zxljtp/ daolin is 32 cm long between fixed points with a fundamental frequency of 440/ rxj+:lyp:d t9a:yz a Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube fille2i ozvld/6 es *1710yzhnkswmk(b+s/ vdg0 led 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 the tube opening to the water level is 0.125 m and again at 0.395 m. What 1dvg6len2ki7+osh1 mys (lz bed 0zsw 0/*kv/is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2 5xv-bxzu)r+kq :-w:cujjgt . .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 qwcj-r -5z:kxuj )guvbx+t :. to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was ob y0d qubq04/2.rrorn fain*p1 served 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 puremef:l;rsoi.k u an;8 3 tone in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant f m3a8.;f u nlreos:ik;rom the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whisrhn8.i)sr a9mhinn6. 6d * m dhirff1(tles. One train is stationary. The conductor on the stationary train he*irrmi 6). h6(h.1a nf d9fmhsi8n drnars a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches yo2 pj19yclf) abu is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)? p9f a12jc)bly    m/s

  At a race track, you ap/hr+*zs 4d wcan estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding ch*z4wrd+/ spaars. 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, produce a beat frequency of 11 Hz. The / w7ixgzy( jy5d4u d8jshorter one is 2.40 m long. How long is the u8(y /7yj dx5zjiw 4gdother?    m

Two loudspeakers are at opposite ends of a 1h c6-0g 4ccxllr+ *,gpizu gkrailroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they ,k 64zcrgl -ch0gculg*1ip+ x have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s wha12d rnn + qh5o,-u4nyvmjep 6tt 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 with mo+ jnrn4dnt2u1p,hq5ey v6-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 igvn, 9+h u-3z md9 mshou5q,khuv,c9vs 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 wave detected by the bat after that wave reflects ofh5hu g, - o mh9qdmuv9cuk,n zsv,39+vf the moth?    kHz

  A bat emits a series of high frequ9q z )hyqp52g;*ie gkxency 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 by the bat so that the echo from one chirp returns before the n;q9 yz5hx*qg )2gpi keext chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) waee; ot+/lbju+;t iw7;3bsf u os 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 3et7b;t /+lso; bwuef 3 o;uij+.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of swb-y)d.h1.v: f cb bvntanding waves1b.)yvdn bbh c.vw-:f, 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 this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “sin5lcl2 x6ah)wl++dd ztging rods,” 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, louh2)+ld tc5lwxdlz6a+ d, 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 hearbd/gcy4 gv v;x6 5wz:ning for the human ear at a frequency of about 1000 Hz is 4vz6nb5v:gy w/xc g;d$I_0$ = $1 \times10^{12 } W / m^2$ 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 M1ioo (i3 r81 j11lshqhb s,sfdach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes dis 8o1s rd b1qsfhji3l,h11 (oirectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat tk+3n f 3il2beis 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