What is the evidence that soundp+kj/aj7x5r)zdx - ca travels as a wave?

What is the evidence that sound is a form of ene pframcigo 5l 1717g6trgy?

Children sometimes plax/tj5j i (bth3ga*i j9y with a homemade “telephone” by attaching a string to the bottoms of two pijbtgxh*j53 /9 (tijaaper 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 to the other.

When a sound wave passes from air into watec qgfeog0cx5egq8o* a0:x(.er, do you expect the frequency or wavelength to gq:gq.0e eoxa0gf(e c5cx 8 o*change?

What evidence can you give that the fa 8fsg4l688 w)o lhxdspeed of sound in air does not depend significantly on frequency?)g8dw a6f8hxl8fl4o s

The voice of a person who has inhaled helium sounds very z b3eqxn3, -erp8 ;guvhigh-pitched. Why?

How will the air temperature in a r/ u0sfkrbx8a 6oom affect the pitch of organ pipes?

Explain how a tube might be used as a nafao:w,tvy8 z/myi 17sp)b 1filter to reduce the amplitude of sounds in various frequency rant/ ,fan8a)o viy7 p1msy1 bwz:ges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togek-sls nvls;wy()k/j 2ther as you move up the finger( ys 2lws/snk);jv k-lboard toward the bridge?

A noisy truck approaches you from behind a byrpf+36bw cjj b6 y4w*uilding. 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 diffractjy *wcr 4b3wfbj6 +6pyion.]

Standing waves can be said to be due to “interferenkzg +a vchtzc4m;1* vbzs+3n;ce in space,” whereas beats can be said to be due to “interference4bztz3*vz;nv+c;g sm 1 hcak+ in time.” Explain.

In Fig. 12–16, if the frequency of thhsk5kd q(.mbn0t 4m2pe speakers were lowered, would the points D and C (where destructive and conk0t5(sd2 mpqk b.nmh4structive interference occur) move farther apart or closer together?

Traditional methods of protecting oz-6zu9ok bsdoee :zj.y584 kthe hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a rely:z k o uo sdb94.86ze5oejz-katively 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. 12–3 ;fnnj*5a6cg5hk ,pin 1. 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 hgi 5fj 6nn*5p k,;canfrequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same fkyu f -/ u6bnu4cx,t34nj:ww direction, with the samwu :3w tn4/un,ujk by c-6f4xfe velocity? Explain.

If a wind is blowing, will this alter the frecf++r nyz7b+p9dm/ i(5jb(blb k0hf rquency of the sound heard by a person at rest with respect to therrd/+f5b( y(pk9zbl hi+ j0f+b 7m bnc source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of r ahzxm5wv/g0/z-j+ ga 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 the child hear the hirj x5m/gha- v+z /w0gzghest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a wnrxl;t, yfw n -9o,lqsw/5h(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. Estimate the length of the lak,whn ,-s 5lwx;try(ql9 o/nfwe. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just b mw*0b/cp s;ke)-/fh9 omjfuoelow the waterline. He hears the echo of the sound reflected from the ocean floor dirj/mocw p)9/km0uff*b;hes-o ectly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20 t cgw19ul)yon7;; nv 5v)xaf4r,xysa$^{\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 driftf op3kf3fh*/yztl s (4l qu;/fing just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33)yp3 ( qso/;z4llf*hf tkuf /3f. 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 stri t jd:xgl3+llor26e,ln 3o4jd king the water below is heard 3.5 s later. How high is thej n3 +otgj6,432xl del:llor d cliff?    m

  A person, with his ea pq4(2ql 1m,c0lgdko13 juhelr to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the dll10q u m oghcq k,4(j312lepair 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 mile of distance b 9 ,ojorad eibo)h,y*3y the “5-second rule” for estimating9ea o ,)y*,r3h bdjooi 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 tc l+rwk:7nkf9mi2/xa 6 k)ruq he 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 wr uit,48vjg p;eg0 7pis $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously jjzcy6ys 9io-a6.)nn5c nl9hacl 90mat a certain placn09yc) j6.lnlaoy5hns 9m6j-i ccaz9 e, 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 foqshtx3-,7g i/ nzt4sdur equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level wothxinz g t3- sd,sq4/7uld this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas f v+az2 ajq(0pwc9kjv y .i6:u8zsfd (dor a CD player it is 95 dB. What is the ratijvzysw9cu6ida8p.qv+2(z k( jfa d: 0o 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 spwh(b fgwd 93q.*- vfbiv-pzr3 eaking in normal conversation. Use Table 12–2. Assume the souniqdz39wp hvg-rbv (bf- .wf* 3d 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 strikesi9(5e f3uz9cc b1jiz g an eardrum 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, kd;3a ds 42xzhwhile the more modest amplifier B is rated at 40 W. (a) s;d4ahxdk 3z2 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 m h0) (ogafn wxehc0q q7-ou88veter registered 130 dB when placed 2.8 m in front of a loudspeaker on the stagq xe87-0noqa0)uhow(h8 vg cfe.
(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 typicj( cce/ep.h)ljq- k88 vn rav) )4bvehally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ b jv) cvl pr qek(hhjbna488-.ec)e)/vy this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a so),/9qps0 easoxfz6;rox u k8kdy35we und wave is tripled, (a) by what factor will the intensity increase? Iz,6aye/03kdqs58xpo )x ukswro; 9f encrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal display c9hteh1z i01ia10excement amplitudes, but one has twice the frequency of the othehxyte91izai0 h1ce 01r. What is the ratio of their intensities?   

  What would be the sound cxj)/dp*2q*a sd;mh v0 vk2q9x8i tjslevel (in dB) of a sound wave in air that corresponds to a displacementv ds8s v)9;x2ad0i2*tqck xjpjq */hm amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that hg+ousb;/zk 1has a 50-dBg/ksz u b;ho1+ sound level? (See Fig. 12–6.)    dB

What are the lowest and higidsscd2wh9e)* ,xuuc7ol 5q f5omo 83 hest frequencies that an ear can detect when the sound ls,3e x *5fdol5mo2qdu8usw )ho7cc i9 evel is 30 dB? (See Fig. 12–6.)

  Your auditory systemo (lz(0 p6 zhv ,i,j*cdvy+t ulxux54n can accommodate a huge range of sound levels. What is the ratio of highest to lowest intensi h6z(c4n u0xtjvlx+*zpd,ivyl ,o(5 uty 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 len l: s w-vwi/kh,j/es/ .rpgk.mgth of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be pla,.sk-ve hw /: mjlp./gis/kw rced?    N

  An organ pipe is 112 cm long. What are the f2c+rzr, f7m uiundamental and first three audible overtones if the pip7 zr+c,m rif2ue 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 ofd/hzyr+t v/k h8bocc06y h- p9 an empty soda bottle that is 18 cm- yc8zvhph/+k6d/tobc hr0y 9 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 pipaq dy:9u+ yhzx )ldhh ctc0(),e organ with open-tube pipes spanning the range of human hearing (20 Hz d)(quyt9x ahzh 0ly)+cc d:h ,to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has u q5y*ik- 8jou- br/:u:lhpa: ia2gus a frequency of 540 Hz as its third harmonic. What will be i 2uk i::*aur-aqgus-oh/p 8lju5 y:b its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned th 01)/m. z jtst8niur0jbtd-fo play E above middle C (330 H1stf0tzju ni8dhb /)0 j.t-mrz).
(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 edf1,70mb hle hmits middle C (262 Hz) when the temperath,mld f1b07he ure 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 rkv1ui( y(fw9at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiecesmz(9 0lu;hin of the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 Hh;n 0m9 zl(isuz?    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 lppw7ue1a+ q *Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a clos u*qe p1l7pa+wed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long7-jostgm 4 6lvs7x aq2 is open at both ends. It resonates at two successi6qxltv2m sa 7j so4-g7ve harmonics 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 i12mw0g cbrhq,wrua6 /of 8m+$^{\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 mi, 7 )fgw9qqtrd)+k urange for a 2.14-m-long organ p 7d+ q,)qt)ig u9fmwkripe at 20 $^{\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 outside anmf3n-7r q;8gzkzk,s rd 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 tgq k7 s;zrz,rn3m8fk- o the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, obe )4(j*bm rsane of which is soundia)4* sbrjmb(eng 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequelov3cgzf11x .ncy if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, whz 0qdhc:brb5wrx .tc0g,. s 2iile another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when playbh0 205bwstz icx,qgd .c:rr .ed 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 sounded with a 350-Hzr:gladzsqv5;aa6*g- 2 cx9h xhaf0o: tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrati*hlr:: 90;2 a5qhvaga-xoa6d f xczsgonal frequency of the string? Explain your reasoning.    Hz

  Two violin strings a ;gz,sac3* xg5 fxn)ajre tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. ,axf5az;x3 sjgg)*c n 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middatsgi2,*xeth0- rs 5w2it* z dle C (262 Hz), but one is at 5.0°C and the other at gw d*z5i *tr- t20htsseai2,x 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forkh(*y3(eifhvn/-r l yv gwq79gvi)yo5 )uuq, ls, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible wwrq )y efliv(iv-5h7g /,l)*y h3u9ynou qg(vhen 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 akn c5 .rgl/j8hqwbc7;part. A person stands 3.00 m from one speaker and 3.50 m frolg 8q7nw j;/rhckb .c5m 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 so1ox34:pnd rg(rc ; twkze y10upposed to be vibrating at 132 Hz, but a piano tuner hears o:gned(cp1kr3r4yt01 ozwx ;three beats every 2.0 s 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 and 2.76 m in air. How many beats p- ok d9.f(epkser second wil. f(kke-pd9o sl be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire eng9l29ymxe-+k r ifmfg89+ i fkqine’s siren is 1550 Hz when at rest. rfi9f8x y 9kg-l+eiqk9m+2fmWhat frequency 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 frequency do you detect if ar9 yism;*p)ms xs;a 6rgdr11 i fire engine whose siren emits a6r1;;mr *rss1aximdp yg9) sit 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frfos21v 1y cby5dmb1 8uequency if a 2000-Hz source is moving toward you at 15 m/ o215ybs bmuy1 8d1fcvs versus you moving toward 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 frequency nyg .5-h6hakn1yc l2y horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest ln y61nhyyha-.kg2c5 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 soqwcp)15aizdv +1vm+*nkz kt) , tu;stund waves at 50.0 kHz and receives them returned from an object moving diresz5 t;)avp +1n k )vw,*+uqidcztm1tkctly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, t pcdbb3h4 :gy5he bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency d: hbc 35gyd4bpoes the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving fl7v,uyot 9*btv9 kn y.wat train car bvo*t,y9.y wv97unktat 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 of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flowp6 ;c/zwaxn8 o speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected b wnpco/6xz a;8eat 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 nf))x 1 z 0p 8rg3zeet ;,hzw2s8ox(mnw8egm e$2.25 \times10^{ 6}$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 freque1 80 4o7cniwqqy ecl:incy 570 Hz. When the wind velocity is 12 m/s from the north, wha0qw: 4q8 n7ce iclyi1ot 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 atwhr -27 j7)bbin kfo3(py zkc+ 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 of9j2uk .3gfu qwiev +9n sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motion?i3w 9ne gq2j+ vku9fu.    $^{\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 2wk3 l4 -bltzxx vr-bay(ul04a planet where the speed of sound is only about 35 ml v xabr2ll4 30tw-4(yxu-zbk /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 smuidpgk ua57gm vb 3 g-)mwt +2)p+m;strikes the ocean. Determine the shock wave angle it proug5m3uwta)g-mmg;) + v2 7si dpm+kb pduces
(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 avw587.1vx ef1wid7 heh gd ;b$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overheao /u i-gdktq-8d and see a plane exactly 1.5 km above the ground flying t gudk8/o-q- ifaster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward zhbm rf463o4x; momp: xt1x+hfrom the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m x4txmpm hzbh 36;o1xfrmo:+4 , what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the hum7n;(j f oe,a(rmihsr -an audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sympswx gn)zg:ok-( vx 9nc,sw; (jhony. It consists of many plastic pipes onsx zs (:c9oj-)kv,xg;(gw w nf various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound clo 7kebie +dtu7jz9):pcse to the threshold of huzp9tc b)eku+j:7ei 7 dman hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-nezue) q j) w;y,+n2badB sound and an 87-dB sound are heard simul2)ae;)nq u b, zejy+nwtaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is ,o 0/syl :wkq 0szqif8105 dB. What is the acoustic power output (W) of the speaker, as,sqz wos/ykq0: li08 fsuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output;-v l4,mmfsgy at 1000 Hz. The power output drops by 10 dB at 15 kHz. my4 f-;sgl, vmWhat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear proteco+1+a-f aufjvr e h4dh1*4-isn :jnlctive devices over their ears. Assume that the sound level of a jet airplane engine, ac1-4n :rfnf a*ohlve-j +a4uh 1+isjd t a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the ga3m 1tp9hda:x oin, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequency s0 krx))-j0ko/ t4 xc(stwtsp1$\frac{1}{2}$ 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 beov hirz+xytg7 b7h349tween fixed points with a fundamental frequency of 440 Hz and 93hrbhxi47vt+ z 7ogya 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 vibratio;/ otw3,pale 0l) hyyb+fo q*aj6yjn. n above a vertical open tube filled with water (lw qh yabj l j0n .3,f6oe;+ypyao/*)tFig. 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 is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2okfgre6p+ksyei n;ax hyu;j+k; ). +;.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 fundamental mode) with thk ;s;;i.jhk)n6apof ue+ x egkry+y ;+e third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obse-p (osidr999h0rhlzm rved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz rafffgo9dgx2bzw 6 wm7 mh37o(.nge coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves abou3gwg wxdf76f7z(o 2 o mmh.f9bt 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 stationaz mpsa5f/ p927 awht/bry. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving tra/95tp7b2 aa zm f/wphsin?   m/s

  The frequency of a steam train 5t -zqi.t7 wzgiu nw5*+9po(bvetl 6lwhistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocigi5(9 tw-nib v65twue 7t+lqz*.lz o pty)?    m/s

  At a race track, you can estimamtx32 hipjz:sb;u 1 r4te the speed of cars just by listening to the difference in pitcrix m b3t2:;hps14uzjh 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?    m/s

  Two open organ pipes, sounding together, produce a beat frequency z; ;h1 fs,ffo 1.qxxpwof 11 Hz. The sho,s;; fwhzxf o1px.1fq rter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as ls58j0s ogl k1it moves past a stationary observer at 10 m/s as sh5gko8l j1sls0 own in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 8*qnhvtyanlyh/fz- +;8c+t am/s what beat frequency would you expeqnay 8-n+at ;tflhh/+c*8vy zct if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a 0w 80s1;fxdq kuiljt/moth at 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 wave detected by the bat after that wave reflects du qi0w/t1 ;skflx 8j0off the moth?    kHz

  A bat emits a series of high 58kxhkm8vtn 1 bat2ij7 jr,c.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 mothnvxh1mt 8baji t5,cjk2k8.r 7 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 signals from one Alpine /cr de(qcf l 5mz,7jz2village 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 le(cmq7 dc5z/2 j,rfz 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 lykkob 9y 7)7nv 7urk(40gs udthe presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Conb ykvk7gdsu)7 9u4 lrk0oyn7( sider 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 “singing rods,” invju/;gq- iuavx9gd5 3rolves a long, slender aluminum rod 3g ax ;ijr/5 vq9u-ugdheld 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, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human,mcxdlm o70trupv) 0k,t,tw5b53f wu ear at a frequency of abo rt,7wfmtxlu0ot 0v 55, dcm)bpk,3 uwut 1000 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 a8y c bnn 0tm,,4coxeq9t Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passescn0bo9 emxq 8y4 ,,ctn directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbbf,g3qf z5/ bboat is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h