What is the evidence that lbf w qr;v/axxf,d: :4sound travels as a wave?

What is the evidence that sound is a fozd s 15i/ulso zs*e9n3rm of energy?

Children sometimes play with a homemaw .-1tm0y (ydnu kcyh) -cx2rade “telephone” by attaching 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 sot10yn ym(h-)xrak-wydc2u.c und wave travels from one cup to the other.

When a sound wave passesr6*.cak pq qj6j/e bvo 9a ud5ds0q8a* from air into water, do you expect the frequency or wavelength kabe6qu ajvoq9*p aq5.r0c6j d/*ds 8to change?

What evidence can you give tha *qw+ z6ri0h ysd*4cert the speed of sound in air does not depend significantzwr0 dcyqre* +sh64i* ly on frequency?

The voice of a person who has inhaled helium sounds veryfzie,ee8md1 )s.e u0f high-pitched. Why?

How will the air temperature in a room affe tj4 wmyu.o/wb* ov*aa 5c3dj5ct the pitch of organ pipes?

Explain how a tube might be used as a fi68i/ hj;bmbgq lter to reduce the amplitude of sounds in various frequency ranges. (An ex8ibgbh/mq ;j6ample is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spacetmwd9 die ;xt2::a6c hd closer together as you move up ti: ;96am: d wdtx2ctehhe fingerboard toward the bridge?

A noisy truck approaches you fro jflrwb0: +c7b m+bv*bm behind a building. 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-frequencwb:bb7m*++br 0fcl jvy noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas . r*di+ypp2hi beats can be said to b yihrd+.p*pi2 e due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, w;ljbvg9rj 7s 8ould the points D and C (where destructive and ljjrgv97 ;8bs constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in area 6 ) eedrp*iw/ t.:f4p/ i u6eav)sy8pr(ixiaas 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 pyep ives86(.xiu/ai ei:4aw)apd)6r t/ *rf levels reaching the ears?

Consider the two waves shown in Fig. 12–31.j ug,5 lmvs3v )jsh-9n Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which ofmj5nv- slv93,sjhu g) the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer moveu*oyr64rw / qobiat 6/6chdq2 in the same direction, with the same veloqihy 6qc bdrtor */u62wao /64city? Explain.

If a wind is blowing, will this alter the frequency of the ms ed1/+no; f;2si jh n2qti9isound heard by a person at rest with 2nejs+ih / qdnto1sifm; 2i;9 respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various p/yfk8 e;q6s iuositions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will tuysq8; kei6/fhe child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the lengt5i9 ;s( qpsf0mm t4wp8*s7;ajh ndfki h of a lake by listening for the echo of her shout reflected by a cliff at the fanwasss9t; i kdf* pmm;5ijqp hf7 0(48r end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just be3t3q i o 2xac6hl)dph-low the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How lphcq6 d it h32xo-3)adeep 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 v jj8:gco,bt-in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy day. Wid,g u6(3qwf-gzdo s- zthout warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33)zs-d (6,qg ofgdu-wz3 . 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 cavxi76 si0l6qf0nv2zq/ :ic splash it makes when striking the water below is hearlvs0iia :0qc czxv7f662in q/d 3.5 s later. How high is the cliff?    m

  A person, with his ear to x+9aaotx+ ll4a*sn 9y the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels a9+ayon+ la st94xxl*in the air and the other in the 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 error made over one q)c5.q 4iw yve/slq83bm;mz1vf 3qkq mile of distance by the “5-second rule” for estimatm3q8 ms4qiw 1 ;bqeqvyl.3v)fk z5c /qing 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 at the pain level of 120(4hua)t u ryo7 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 gt4.aia (g. ruhqhifu8t)6 ,l $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers pr 4gjzss8t 77fm w0x(bm: p9czwoduce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]7s7wf4w90gtcm:(xmbs 8jp zz    dB

  A person standing a certain distance fro d2nl(56reumihs 7 u+im 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: Add intensities, not dB’s.] s2 +ire7n u(h5ml diu6   dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whd 6-4mmpss1s wereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB s16- ssm4mp dw=    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person m2pwxt gra5-( speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere2 tmp-xgw5a (r 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 eah;fb t.oit.)o9w md0p rdrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more mog;v;e d 1 boudh2ur5;b(fc kj0dest amplifier 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 cono 1 ; uhj ucv(rf;b;g205kdbdenected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when place6/o-o /cdr-vi km 8lpmd 2.8 m in front of a loudspep v6 cmioo-8r/lm/kd-aker 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 dBzy 1zh0u(k)ai)kd2vm . What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–zhv z1 k2ui( ady))k0m9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what facbl08sand5j 5 o0/w vk v+ni6tytor will the intensitts5v 8k /jv+on 6l05iya0dwnby increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement m3-9dh0ju(-gsqmugi amplitudes, but one has twice the frequency of the other. What is the ratio of their inte9h -i-3 guum0d sq(gmjnsities?   

  What would be the sound level (in dB) of a sound wa gp.d )h ,omq9vo1aao9ve in air that corresponds to a displacement amplitude of vibrating air9oahq m.pd1 go)a,vo9 molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound leve6 a.4toyakwca41x obb 8sei22l to seem as loud as a 100-Hz tone that has a 50-dBiaxa2 wb4oko6 b842.yats ec1 sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the ( ma+2um ie+,aic hlb+53 v1b9x icqaksound le 9qiim35aa emvbik + b+h,cu1(c+xa2 lvel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge r llok5qoy/(ef fw+bro,m7c4( ange of sound levels. What is the ratio of highest tooc5ml7 o( qw+( fb,oeyrfl/k4 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 fundamental frequency of 440 Hz. The iyeu8. 0v sq7fjwey7bc , c2t*length of the vibraj c2e. qf8veubtwy 7*,0cysi7 ting portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three gqkcu1u 7s1/ntb,k9z5ic ;azaudible overtonesqcbzc;1, 5 a/nsz7uukkg1 9it if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of mp+ gijti /a-b:k-qk7an empty soda bottle that is imajp+t /:g qk7k-b-i18 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 organyj)qqki39 oj+ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the oyj)jk+93iq q 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 540l 2d0o+oczmu 0 Hz as its third harmonic. What will be its fundamental frequency if it is uoz2mo+d0 0 clfingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string yd t,gq98g3mp44g g y6tnb;0nmc*sfcis 0.73 m long and is tuned to play E above middle C (330 Hz).*ttfpqgg4ccy3 n 4;6, bg0mnsmy98gd
(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 emc4+n9ffdsclg6 jla*+ its middle C (262 Hz) when the temperature is+4l sjlca fnf6 c+9gd* 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 atuzkm1/3 hf) co 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12qjwvi m i,miy0--lx.) –10 should the hole be that must wiimm)0-qi,. y vlxj -be uncovered to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, bsfs f63wv)n2z s2bi(nqj6 xw1ut not at any other frequenciqb (izfw 22xsf sn16jwn6v3s)es 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 is open at both ends. I jk xbxd:.a4ow )hcc+8ia; u s5tg5t9gt resonates at two successive harmonics of frequencies 275 Hz and atdoca+u gjs)t;wg5kx9 i8.c x4 h 5:b330 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 s; t/gd0g9wms,vp9ck$^{\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 a 2.14-m-long organ yqa) ,6he 3o2xvodar2u;qu,m j-/dub 7z0hfi pipe auyf20r v/uqd 62hqi ;aumhe)b,a3-oj 7o zx,d t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approx 2ota7+1xn tf9b .whtkimately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph o. ohfxbttw71 a 92ntk+f Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat eveu n yv-m5xd+j(ry 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is thxu5(m +n jdvy-e other string? ±    Hz

  What is the beat frequency if middleaooxk-0 vft,(6 l,cvq:da1bqr y:a1d C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while anothej 16x6qreco. fr (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whcr61 qf.xo je6ine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string prod z e zgb5s32h1)lnhwj2xth1e/uces 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sou gze1)n h3wlxj2etbh s5/ 2h1znded 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 frequency, 294 -6tyno9oy-vcyqvu4 4amzv/ ) ,u (qytHz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two synyot64avyc-u y q9q (v)m/-tz ,v4outrings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fl o4h)n-;8ssxj fk+)r6yjxidlutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25.0 x8ks)x4lond 6 y)rjfi;+-s jh$^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; wh a6 2 -1xlpvjxe1zr*i cbtlm7xzk)e03en A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C arex1rljc-i 0patbm6l7e13* xxk 2 z ezv) sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. bji)0e4-w kvcA person stands 3.00 m from one speaker and 3.50 m from the other. i 0kec)v-j4bw
(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 pgi r(p:frqglp 3ruh u(nww::32kc:4l iano tuner hears three beats every 2.0 s wqgwr c g3rk:w2uirn( fl:: :p4(lh3pu hen 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 wavel7/djs 7j-wmrx of0x48kyyo n -engths 2.64 m and 2.76 m in air. How many beats per se/-djw 8x4om-y f7or0 xjn s7ykcond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’unv1s j4xrh cz8/ g.7js siren is 1550 Hz when at rest. What fre.jru gs1/nhj4 7x zv8cquency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequ7 6e3y4 i .sj uhm,y-: xyd*yrvhg2qivency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speerqvgdy 4 j h6s2ym e.ix7,:u i-h3yv*yd of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequeqy9 184(r qchfd)yb :0mjannyncy if a 2000-Hz source is moving toward you at 15 m/s versus you moving towa:qc)dyq9b8 h n 1fr04jyaynm(rd it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequed w wlydl +g1s *dg)9fii0yd5(ncy horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequencwifidl ydl9wg0 (*d s1y)5d+gy the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50tk;jg j sg1b:tr5;jq.(ap 8fr .0 kHz and receives them returned from an object moving directly away fkjqafr jsj ;pbtg5r(:1;gt .8rom it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed/x ;3tj6(tm fzlv)biox7q4 xg of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz.v 7itto(3b4;j 6 lzxx)fgmxq/ What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movi-;3 gdaic t0t :w;tijqng 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 station at a speed ;gdic0wjt; ti-qt3: a of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure n6f)e9ecx* 2+khilj(9 wip yx blood-flow speeds. Suppose the jxhiw6*9 cpfenei9 )+x2(kly 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 arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequ f-h/k xf 6wqkb ,8a(hqm1bbw8ency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind vel *+sq*oj2 wsdlocity is 12 m/s from the north, what frequency will observers hear who a2jlws*+s q o*dre 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 moving4uf e+c*xonl)h3jz7p 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 speed ofg; o6c: l,wdt8yb cjn khq7c5+ sound is 310 m/s (a) What is the ang,kjlnt wyb8:c qg +o5;chc76dle 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 ouh g;uu97a v;5 (bpmxef a planet where the speed of sound is only about 35 mae 95uvxpmu; (; u7gbh/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. Determine+.l7x9picl6 :nqb wqv the shock wave angle ixv6l .:p q+cbl7q9nw it produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle mw7o/ ocz8h8o a*m 7av$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the groun570yr 2pu -hiaxagl1od flying faster than the speed of sound. By the time 1 pyxaao2 0-uli5rgh 7you 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 sonar device that sends 20,000-Hz sound pulses downward gztx pqvc 7p*p/ssq4 ,.gl9;4 j(bnvkfrom the bottom of the boat, and then detects echoeppb.*kj sg,4g(qpc49t7 ;vls x/nvqz s. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many o xjw,/32wx5ok6uqa roctaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of manyf twpr: wvx4 c7:(kjb6 plastic pipes of various lengths, whi 64tf(r cx:kw7:v bwjpch are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound closh5g pn3o p7pm-. 6-oyix2ik aie to the threshold of human hearing (0 dB). What will be the sounp5ogk yp 6ma3h7x ii-o-p n2i.d level of 1000 such mosquitoes?    dB

  What is the resultant sound leveljq46abjn/. qu when an 82-dB sound and an 87-dB sound are heard simultbunja q.6q/ j4aneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whatqcfw, m;h .x/0iynv 5z8uzxh1 is the acoustic power output (W) of the spea,yz w qx cf80n5.hm/uv1zxhi;ker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. T3b r8sv vyor(9 5va*txhe power output drops by 10 dB at 15*tx 3 8roy(sva9vb5rv kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet airvcn9r 2sg7/p pugj2m 2craft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intu 272c /pvm 9rsj2gnpgercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the b037zf1 2,ze s k2gvbi i c6vc8jdkk+again, $\beta$ 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 -fs i/a+ v9 +kpsr:dt8lgyw;nfrequency 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 fixer;u+m y11m6zx iuxx1gd points with a fundamental frequency of 440 H6xu +grmz m11uxi xy1;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 vibration above a ld(.cy,b08z i1tho w jvertical 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 i jydlhw18.(oict0 b,zs 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one endh/-tl;bkmfj l owkg 2kyv,612 and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamentamb26tkf/ h1lgko-y w;2lj v, kl mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop;wr6dq fz g 66db/od/n ($\frac{1}{2}\lambda$) 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 f,5x chpstt)q ) scci.1rom two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about ant hs qsxcip) .c1t)5,cd 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 wh 4+hnoebe x):xistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approachen)xho4xe+ be :s. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538ix e(m3l+,ymdv j yj)9 Hz. After it passes you, its(jl) ,yjmdv9 3yie+ mx 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 pc0sy yweo0ik5f2 +x0of 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 halved) as it goes by on the straightaway. How fast is it going?i5fpy 2ye00xwcko0s+    m/s

  Two open organ pipes, sounding togethe*ztecj*/lr te( 1vk+ir, produce a beat frequency of 11 Hz. The shorter one is 2.40 m lone*lctv j(e*/rt ik+z1 g. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves paij ++up zikku9)1;arzst a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound fra 9zir1+kk i) ;upz+juequencies 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 bloujgz2ksx0 ,:y(ta-bs,-wud:j on+ n cod flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound k:ds:xus, -(abwtn g c-+zjny2,o 0j uwaves 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 )eyfetg 9rx9:7znb tv+ef v6 6moth at speed 6.5 m/s while the moth is flying toward the bat at sperfgevt :)9en+9fy6 tx6vb7z eed 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 hi /qayy7 itui*d2 cb(i c826ywzgh frequency sound pulses as it approaches a moth. The pulses are approximately 70 c7/ytyw* acu28z26 ybdi(iiq .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 next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signalsu 3mz0g/s o5; 9sfk)ljk 2tinu 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. 0ogink j5z;ft u3km 2l/su)9s The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by th5 ys5ujqae(nmhv+1o + e presence of standing waves, which can cause ae( 5q 1ojnahu 5++vsymcoustic “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, gt9y41,nfy./:m egm h yb6wascalled “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’h a/gw9:s4yyfbg6ye .,mm1 n ts midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing fr+it/u xg+n0eor the human ear at a frequency of about 10+x 0i e/gturn+00 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 observeb s ueliaz8u .g1fo(.*dm;0w*g ;dno ia.:ecar on the ground hears the sonic boom 1.5 mine 1 ld;o ugiod8s* *;mu.nba: f( cz.eia.0gaw after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is fk: fc 2fh u.ts5k93fqdjg4 l815 $^{\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