What is the evidence that sound travels as a wavcx9j3mg u0f rd* wl:i8e?

What is the evidence that sound is a form of enebl) 7ex 8y)+i8y rbdosrgy?

Children sometimes play with a homemade “telephone” by attachingw6fklvui 5xla2 ur(-( 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 wave travels from one cup v w-luk ula6(2f(xi5 rto the other.

When a sound wave passes fr .5*sj uhl3ozjom air into water, do you expect the frequency or wavele.*uzj oj5l 3shngth to change?

What evidence can you give that the speed6:o6npi7 ilp*m,n yc d of sound in air does not depend significantly on freqpil o7d,m:nc6ny6pi* uency?

The voice of a person who has inhaled helium sounds vucws6lys9 jtkz8 v+k )w6v3*sery high-pitched. Why?

How will the air temperature ivr /coj c536dvn a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to. 5ir4z,q).k;zujwqb bwty* s reduce the amplitude of sounds in varioq)b w tyr4*.ibz5 q;wk uj.,zsus frequency ranges. (An example is a car muffler.)

Why are the frets on a gup-xg i 96tc-uaitar (Fig. 12–30) spaced closer together as you move up the fingerboard towatp6gicu-x9a- rd the bridge?

A noisy truck approaches you from behind a build 1-4fc1v bpdu.wamg g6ing. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear m 4f -vg1db.wacugpm61ore of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be saidxa/zhr/3orq86r6w* kypdi,vrf0 m ;n to be due to “interference in space,” whereas beats can be said to be due to “interference in time.” Explain. qp 8 o/xwy3;*/krvzh0a rr f,mrid66n

In Fig. 12–16, if the frequency of the speakers were lowered, would the pointsrm qbv: pfx..q;gh :i ye45id1 D and C (where destructive and construe qbixqh: : gy.v.1;4ipdmr5 fctive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearingm-ms, 4e6 puwea3 9rui 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 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 ,3 um6- 9we4seairmup levels reaching the ears?

Consider the two wav bgbs9y90w*p2 kqdi6 kes shown 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 frequencies farther apar0k96d gwk sbpqb9 *2yit? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer moo2ks 4;tjj3 iuve in the same direction, with tk;ji23jo 4st uhe same velocity? Explain.

If a wind is blowing, will this alter the frequencyk3/b3 ie1;qaol k +mao of the sound heard by a person at rest with respect to the source? Is the wavelength or velocmklqo+ ai 3eo;/bk31aity changed?

Figure 12–32 shows various posit; jse8:a8kt *o ga.mplions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the groun l;m:ekajt sgao8 *.8pd. 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 len p7o0 4aj0hsangth of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the 0j 0pash7oa4necho 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side odpf5dyxg o6 ve c7-k w(r2ix49f his ship just below the waterline. 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 vary signific xe72yf kv 56w(94g didrpc-xoantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at e5l xxtp3 :d -f;utzg;6ozh r.20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on apf;2r,k 8vjvq/ zzd4ivn 9hy9 foggy day. Without warning, an engine backfire occurs on 98q;z vzp9,yv2d4/ihk fr nj vanother 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 when s2 d5clxvafzl*8 haoc/kg;,5bp+ j7dz triking the water below is heard 3.5 s later. Hox5pdkz j*7 ;+cv fgada2c/o8hl5z,l b w high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone su5nkm dzbm/yq7)r r 6-trike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur?/km76ru bny qd-r5)z m See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error zn5n xt*hg:,41eppb ymade over one mile of distance by the “5-second rule” fon zxp ebynpt g5h,41*:r estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound x4ys+7+ga evxat 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:tgu))6wt: f:jwtlaw3k9de*8 uqv xvy u):gn whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired s(wnwutma 21 hyn08 n4gimultaneously at a w4w yn2tghn1(u8 a0mn certain 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 equally4ervkwzb*qq q63 l( t7 noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level kvlbewqq73r tq4z (*6 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 hg2ftdr8b oyv cw5;5)fave a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the rati8;5v5t cfbyg)wrd2fo o 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 in normal conversab:1f ):ukiq e(hxre5mtion. Use Table 12–2. Assume the sound spreads roughih r f5euk(: be:)mx1qly 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 whose area is ,i o5kp1--p3i xu gxwy$5 \times10^{ -5} m^2$ (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 amy ip,dbz9 1b+9n zwo/ms:q uv1plifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to eim/:,1nz1dw +vsz9b p9uoyq bach 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 regispe3 1zx( fu8)l-pt r/qinryn1tered 130 dB when placed 2.8 m in front of a -elx f3t iq1rr nup(z/yn1p8)loudspeaker 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. Whw.rj;ukssm ;at 1p+v :at is thu w;ks vmt+p;jr:a1s .e 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 iscrvga,cb /xs4 -lg w*) tripled, (a) by what factor will the intensity increase? Increase by a fa-g cbs,/rxl )*w4gv acctor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacementews8f2 lz5d1t 7d2 vmm amplitudes, but one has twice the frequency of the other. What is the r 25d8 mt vzwfme7sld21atio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds *y ,mo7rbwi h q(wtjg0t::0osc *5mxi to a displacement amplitude of vibrating air molecules of 0.13 mm ati(mcg0 rw yi o 75x: h*ow*:mtjbstq,0 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz t(c 2swoctz- 6w gx.op+one that has a 50-dB sound level? (See Fig. 12–6 cxp+.-g owzs 2w6t(co.)    dB

What are the lowest /je2p8 bx ngh,and highest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.h/epb8j 2 ,ngx)

  Your auditory system can accommodate a huge range of sound levels. What is the yva f8tfooxi hkt8*;..km20, q6bjya ratio of highest toyv.a;6motbfh 8 0 f,y2.kkoj*a q8xti 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 ; om4t5kf nmacc+s2 2q2a-hnjhas a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass ofs-fo;na52h jqc4c nmmk22+t a 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three *v f+ y4dyx(d41:8nm ffw ybo 5e3qkwqmr5s o.audible overtones if the pow q3.e* yqs5bv1dn m k8(mfo4 rfx+:45y fwydipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of an yai2tn*v7f;b 5zch*f empty soda bottle that is 18 cm deep, if you assumed it was a nc7*i a fvb*zyf2t;h5closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanlnzw ;ng ;5rn*ning the range of human hearing (20 Hz to 20 kHz), what would be the rangewngz*;r 5nln ; of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has4xap2u i z0pks:4yn/q a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingeredp kp2na/iyxz40u4s: q at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above miy8n8hd 35s-omf; gf rmddle C ;58n8 offhsm- dgrm3y(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 opmqd:mwdse4f ( / b/9qnv5cg( s1qfb6uen organ pipe that emits middle C (262 Hz) when the fvd gqu4qm6q/b 1:wfc /esn59(dsmb( 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 a 8st/z-d f;bl,3iqgvu t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the fluo/h(djk ced-5f plj;0 8 dwb.qte in Example 12–10 should the hole be that must be uncovered to play D above middle C at 85c (wd./ohfb pe dd0l -kj;jq294 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 d54 wkx .sc/ad p hp.0pb54upcHz, but not at any other frequenc.wpaps4405 xkd ch b.dp/pc5 uies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long ag*64 lb1csap*;9xud yp pnvj;xg ) 1kis open at both ends. It resonates at two successive v)bg 6a;l*d;ckg 41jp 9pa1s*xpx nuyharmonics of 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 e5yl k/r-yo0/3qzabi $^{\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 ,ig; faf jiy8r :;u2u5 16lbokrbihx: within the audible range for a 2.14-m-long organ pipe at 20 1;yh aurffi,r:ui2 xl:jkb g o;ib685 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outhll d )/5b8,id9os hq movty)ibs /:)zside and lh:d)vqd8 omi) syz s,)5/t9ihlb/ bois 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 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 2fb+z(: y-gib q.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the i-yb(:qgz+b f other string? ±    Hz

  What is the beat frequency if middle C (26( a/al1sik,of 2 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, waf2aad6yb0:qp//dmv 3gh wi. k d3 2txhile 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 5a3v6/ f:pg2 i/0tb2awdm .k3qxdah yd000 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 tuning fork and o/ss2ay a su:wcsu:5r)p9s*l 9 beats/s when sounded with a 355-Hz tuning fork. What is the vib:ysa2u spc as*):lr/s 5 su9owrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tenqwn5gwx:/q /0rr0 j lssion in one string is then decreased by 2.0%. What will be the beat frequency heard w/ w/5x j0q0rl ngrq:swhen the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be h j.irshl (0 vvgxr842teard if two identical flutes each try to play middle C (262 Hz), vljv2irr h s0.4txg8(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 441 Hh;36lwso7k b0k+o9w,fv eiog z; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequw6,iw0l7vk eo9+obk ;foh 3gsency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A persluu19swe lzdv6 68)om on stands 3.00 m from one speaker and 3.50 m frov6)9su mu 6eol wzdl81m the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tu+p:xg5/lme 0 k6sh7ayx b x6zgner hears three beats every 2.0 zlk be5 /x+g pax76x6 y0:msghs when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m a tgkfwez7 m+5/nd 2.76 m in air. How many beats per second will be hearetmfk/ w7zg5+d? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s82pj3xcb1vd ;e :pil ls e:3rs siren is 1550 Hz when at rest. What frequency do you detect if yousi sl;rj:pe e:d823 cl31vx pb move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What -y2 si- a;hsr ou(hxalh90s(cfrequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a -2 s-ryh;9oa 0a((hschslux ispeed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency s+ud zq xd8p+d0ms9+tif a 2000-Hz source is moving toward you at 15 m/s versus you moving toward i +du+pq z mst98+dxsd0t at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are eq;byltiz 02fnu/tv 5fw.v 49aluipped with the same single frequency horn. When one is at rest and the o wnz lavftvi; 0ylt.u5 f/4b29ther is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz )- **fx)z(wwhv jas arand receives them returned from an object moving directly away from it at 25 m/s What is the received sound frehxar w)-jsa*wf) (v z*quency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s dh* f1-wnvj0k As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequen* dk- nw10jhfvcy does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dor d7u+tnug4fz 4o6v7h ppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a 4 tu7rodn7gf4z 6uv+h 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 usbe 53zzgm a+e162adqk es 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 a1qe+ 63gbz 2ka emz5dto be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves ofvy/wganrf pbi7(pkz4e3,3g + 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.x6wv)ti+ g m;i When the wind velocity is 12 m/s from the northx;v 6itgiw+)m, 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 if its speed bhoqjmmq )m/2 4en1 b*at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) Whabif--a*h *0ey 7f)f q qbedn:bt is the angle th-fy*q ianee-0d7b :h*bf) fbqe 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 thef uo. kmvl+2x w:2 f,;2jboacy speed of sound is only about 35 mfa2 2f2cwoy:j, vobmkx;.+ul /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. Determil9 g9ed8sjv1 sne the shock wave angle se9s gv1j9d l8it 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 sl72 w)rg1zzh $/theta$ 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 exactl /i+vq7fzkqe/z f y(mnic.3* ay 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a h+*f3(me /ci z v7a .nfqky/qizorizontal 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 downwar ut+o,xe29i4xnv1q95wpb iejd 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 tw19injt+iox2uvb9q54 e, ep x ime between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audiblebp2p p*3 o(diu(j 9vtn range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sw/z4z/k fu)twip59n bewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on zubk/t954p/ zw f win)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 makes6 c fjgj bu91*wnni35x a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoes? 53 g1c6w*jbixnnjf9u   dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sou/wrbwb 2;0 esdnd are heaws/b rw;2d0berd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, pjj/f oevqn vt k1 :rran2k5t*sk72 :y/laced in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directio5::q2k vjnk e1sy*rvk72a/nt trjof/ns?    W

  A stereo amplifier is rateeuu f -9rn*a)awam0 h6 ygc;h*d at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What wn 9a0-ueauh af*cg)rh;* ym6is the power output in watts at 15 kHz?    dB

  Workers around jet aircr3)u;tlp51 b1x tvvo wiaft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance ofxilb1 p t)o uvwv;51t3 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 communicationsu0 b -1b(saezubvk/( u 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 frequencyd0(6a7zcmyi za6l;gg .rdz d4 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 isozv i/ k8ypql++ lz,5qq):gzk 32 cm long between fixed points with a fundamental frequency of 440 Hk85o+q,vzl)qlq p+ g zyikz/ :z 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 vibra.:2 4shpnv ncc0lrtt*b8r l4ltion above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 nc* r r. 8hc42pnts0vt4bl l:lm. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of d) jmtz*b -:mbypqlg(e 2:mb7mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundame()ldmp b-*tze mj m7b::byqg2ntal mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to dg p97q2nb .:mbrdkg7 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 i1c(kb,kyzq47l rcnsuc vf ;d 9jm45q-n the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the twoq4 qn;cf5 vcuy-kskcd( 7 ,lb4 1jzmr9 sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conduc z3mfwp y.ck 7+js-)9 m.lxqebtor on the stationary train hears a 3.0-Hz beat frequency when the other train approachx7b c.+mlmyq)sep zw9jfk3 -.es. What is the speed of the moving train?   m/s

  The frequency of a steam pm ,ux m8efvrlsq )/5)train whistle as it approaches you is 538 Hz. After it parfmp/msxq ulv 5 )8e),sses you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed o*,gknjn-ad e,3 (bmnzf cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency hanmnakz,b (e3-n , *gdjlved) 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. Thq7 /nmtiq6btcue57+d e shorter one is 2.qit7q/c5b+7td 6nm eu40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a statn y c5* fd/aso+u)8trpionary observer at 10 m/s as shown in Fig. 12–37. If the speaos/8ct) dnafu*r+5 py kers 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 normall /ogwnwjn5s6m6 8sf86 jf, dfoy about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the gf,w5 f6j/6 msn n8jw osfo6d8flow 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 a 4l/9anx xv mur30k-llm80ucr85cpgjt speed 6.5 m/s while the moth is 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 waveclu4amr lm0l vn k89u3gc/xjrp8x 5 -0 detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of k0wzwd8-kwvbey29+i cr s2baxj 3 9f3high 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 detectej23w3b 0bv we8w+s2r zcd k9ai9xfky-d 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 Alwkg;rfy7x xi1r)z+ + tpine 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 ir1t) w+x rykzf;+gx 7is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be comprmq t9bc;fwre :4w4;yx5 w-plt omised 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 pw b;9xwrye ; fmt4 54:-lqwct2.8 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 “singing rods,” invos wlcieq5x s7:- flt71lves 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 7xt : 7eq llfiswsc5-1emit 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 f6sa4dlib1a66pv ob7+qwz 6 xz or the human ear at a frequency of about 1000 qs76dvx 16 66 4zaaopbl+wzbiHz 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 ground hears the sonic boom67d,dkooce iadllni :/2v2 n22 s+yti 1.5 min after the plane passes directly overhead. What is 7eiilil onv2d 6,d2 sa/n+2y2c okdt:the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat i 85zw*)i eh 0oizv4rcvs 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