What is the evidence that sound travels as a waa4woxb uy2a81 mu8pk, hasi,- 8t 8dxqve?

What is the evidence that sound 7z+sb 7yv, tavq) vqe :b)ps--opmqv8is a form of energy?

Children sometimes play with a homemade “telephone” by8s22weqpv9 p3zwl.gfyn 3w y) attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup,wezsvw2.9wy83 ngq 3p) p2lyf 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 water4nl cm jx-grh8jttat5m5 h8 4 kv6wp0,, do you expect the frequency or wavelength to chanl 4t c5t hav0, hr8m8m4j6-pngkj5 xtwge?

What evidence can you give that the speed of sound in air d yt eae0(;jx)yhg 7m:sfa-x2aoes not depend significfah20(ayj- exase y7;g:x)m tantly on frequency?

The voice of a person who has inhaled helium sout.;sqxb t)bv.(qf td:gj0i,c nds very high-pitched. Why?

How will the air temperature in a room affect dd6:j ks4g d t9*dw1ppthe pitch of organ pipes?

Explain how a tube might cy( :;p yq 71i99x;zf*g xqite-a ot1hiijt9kbe used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a cxht*kjtp7a y9iyi9zgifi;q e-tc; :(9qxo11ar muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you movv2f gngpaat e:9j ec6*8)jtcg2waq3,w ,b)ume up tg:tuf322)8gv ecge q 9pj b)jta*w6 w,ma acn,he fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it buts- nsz9j8qk8ir r.nn6 cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the hk zq.98 8irrnnnj-s s6igh-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interferenceh1 *m( wjeu o(l:gwh5s in space,” whereas beats can be said t u(moge(w1jlw :*s5hho be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered,4jp spptt4* y0g.qi0l3q:ty s would the points D and C (where destructive and constructive interpst ipqy*0t y0pts4.j:g 3ql4 ference occur) move farther apart or closer together?

Traditional methods of protecting the hearingf1ip)v7yg . thxlx, 6n 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 ambie,gx1vf)67. thlyxn ipnt noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thoughvupcm(a2, ct7 t of as a superposition of two sound waves with slightly different fre7u p a(vt2mc,cquencies, as in Fig. 12–18. In which of 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 move in the same dirnbw-fxj n4.c ,ection, with-xnn.jfw4 b c, the same velocity? Explain.

If a wind is blowing, will this alter the fxu/v bse8v a 11d/sfi/o z(v.lx5lk; yzl9t7hrequency of the sound heard by a person at rest wi vyi.971slb/l5t zso x/;kvv/ dehl(axf8z 1 uth respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of x0 /b jc5ndqy 9+3:eq vvc-zdna 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 highest frequency for the sound of the whistle? Ex 3db -5/jx qvn+yqc9cnd:ve0 zplain your reasoning.

  A hiker determines the length of a lake by listening for the echo o 1i;w y98wtmz/,hqj zhf 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 whq,wy91j /zimhz8 t; of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears th q4.avtc6-lvmn ih 1a*e 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 seawatertn 4i1 qca.va-hl* v6m is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengte35z co0taa ps dz4ro9/cdr7 -hs 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 dy2f419 ,i gst0qvpyeurifting 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). How much time elapses before the backfire is heard (a) by thefgty si ye0vq4p1u,9 2 fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when strs +9b;zlnf:7ix w ql:kiking the water below is heard 3.5 s later. How high is fbznw:; ikls+lq7:9xthe cliff?    m

  A person, with his ear to the ground, sees a hugg vmi1wp+a;l1l6 p, lbm 1ncj5e stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concret ;ml1j cb avw5pl,ig6npm1 +1le, 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 ma4surzyrky 92:de over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if uky4zr2 r:sy9 the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound l2pb w/yxo76z222c)g gqizyjcx 2 )c uat 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 whosem+.br ofk qa.5)dkb iek9fj6x2nqo, 5 intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers prol(+j2il(bs ft, dalq. duce a sound level of 95 dB when fired simultaneously at a certain place, what will be thef(l 2a itd j+.bsql,(l sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airdzv3 qyj6:7ii/u/td.m b/abc plane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would /by7va .zbiu dj36/cmqt:di /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-to3 9jqhgylgz (+ol c6v*-noise ratio of 58 dB, whereas for a CD player it is 9 q(h*6c 3yvlo9zljg+g5 dB. What is the ratio 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 6a qv0(mymjkw58u yg*normal conversationmv 5yqa6jm( g *u08kwy. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area iseym)r) n krx10 $5 \times10^{ -5} m^2$ (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 modzqij+nl9i:o :z (p -ezest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m fromzn:q-ejil9:+zz i( po a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registeredusxehe t 1jc 11s26(np 130 dB when placed 2.8 m in front of a loudspeaker on the stage e16c211jh pus(estxn.
(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 differenf a3 m8u7pdztm6lf4 jk6xt+;ece in sound level of 2.0 dB. What is the ratio of the amplitudes of two sou63lma 8 d f j+kt;ext67p4mfzunds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave isja1k(+85 h z bu1qyixq tripled, (a) by what factor will the intensity increas yqq+8bzu1x(h 1aikj5 e? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one.cl 8gi7g5 ump has twice the frequencyp 5g. mgcul78i of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corwz-oo0wzm4* d(-rz kkresponds to a displa4wrd k*owzzk-m-( z0ocement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what soun.z0kr +odh6r fprn95j d level to seem as loud as a 100-Hz tone that has a 50-dB p o.rk0rhf9nz5jr+d6 sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the6w .u,4yyi wsa3dg*b sht1la( sounyu 46gy ha.a, bs it1(w*3swldd level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a ho;cisn bxbem;79u. )buge range of sound levels. What is the rcbsib;e9obm7 x ; .nu)atio of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frk/zoyfo( +a5u equency of 440 Hz. The length of the vibrating portion is 32 cm, anoyzkoa (5+ uf/d 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 f8 *x ve81cjfhlirst three audible overtones if thc exjh 8v*l8f1e 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 an nx6*rw(b*ruwhao- m c7r-af tr01b)q emptycw( 0 -htmn fr7) ubr6-a*r*qabo1r xw soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipofh: ;i 3azj(c02jneqes spanning the range of human hearing (20 Hz to 20 kH; jnjqf0zah3 ec(: o2iz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. Wh 97brra wn/ai6at will be its fundamental frequency if it is fingered at a length oa9 a7wbn r6ir/f only 60% of its original length?   Hz

  An unfingered guitar string is 0r lx.es-ucy: /,kx8sq.73 m long and is tuned to play E above middle C (330 Hz)k8csly-us:/ x xrqe,..
(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 o,e zo2,x iaz)qrgan pipe that emits middle C (262 Hz) when the),eziqoza ,x2 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 zroxymf +pi,)*gxhzn *1p 8*ct 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 12–10 sh0ma gk-. f/k0jbws ..guy :nbvould the hole be that must be uncovered to play D above middle C at 2gg0n v/s :mbauf.-.. bk 0jywk94 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 3 f-lq* ln;hzmv rh7p1s:i/or Hz, and 616 Hz, but not at any ot;zv:rl3 q l-*7mf1 hproni/hs her frequencies 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. It resonates fd p+ d e5n, x9i6wadro(jnu49at two successive harmonicsnwd pdxo 94f5daj9e+n 6,ui(r 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 m )g4 slwe+)fgfph +is2y q,0x$^{\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 r /bk-fjk )g4frange for a 2.14-m-long organ pipe at 2-fgjf/ )kkbr 40 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxi-o2s(zu 9tfjc7 ky8 tvmately 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 answer78fjtscyov(t2k 9- uz to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, fc/ksw4*kv:rv z/ 4bnone of which is sounding 440 Hz. How far off in frequency isr/fn/k4 vvsk 4:z*cw b the other string? ±    Hz

  What is the beat frequency if middle C (262 Hzne +xr5tv4pq (8mn -ha) 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 another (brand X) operates .k*ksjs:i(3 yxtsze;(yo7w k at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs wht* xs:.ywk ((3s ikz o7skeyj;en 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 9 xw:t /n0j nb-(jggpi6beats/s when sounded with a 355-Hz tunji tpn-gx6n: gbj 0w(/ing fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuje2yp cn+ d)f033ulvuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. 3n+jv2c ledp)yu30u fWhat will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play midd-ercua 1p8 (zaxu5ho- le C (262 Hz), but one is at 5.0°C and the other at 25.poz18u5 ac-ax (ruh-e 0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, my*l c(7tbw38f+ f harand 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 sounded7cf*w3tb(hr +8lmf y a 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 1v1 d.svow *1osa..crc .80 m apart. A person stands 3.00 m from one speaker and 3.50 m froravwos d c.o1cv*s1..m 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 Hg0olo rxrdn 6-i/p57o z, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, wh7po/n0ogo il - rdr6x5at 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. Howe 9nracpsp07( -z 2q 4rufxs;b many beats per second will be heard? (Assume T =nzp9r;a7rc su 2-xb0s( fpeq4 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’1f ldv0+q1v80qlfyfos siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed ofq f fl0d+01vqlf8y1vo 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What 6*t d/hsk/2 yr tk2d-;mayk y, i 0gou:hgl)epfrequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed oy ;dyy6t*/ k-ad 2l,:krso e0ht mhgpu2i)g/kf 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift imfgia;9c zv1(y -uqxm t;b 6wu 8y9:gin frequency if a 2000-Hz source is moving toward you at 15 m/s uu(:iym; 1fxzb 9cq y8i;gwgv 9a6 -tmversus 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 horn. When one is p)zq9 8s+we y zdh3el+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 qhpw8zzsy +l3dee )+ 9the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves ap.r,xn s3qn-xjud ,s 2kqws71t 50.0 kHz and receives them returnsnr,x .7ds xwu qsn3-p, qk12jed from an object moving directly 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 ofr;emimx5 n 6pg q,:6lc 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in thl6x6rme;cnpg 5im ,q:e reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played onf3ia/ n4x vv;j/kznh-e, hc , beao7g; a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequa3efz h;nnvj/;h -cbgv ,ei,/k7 ao4xency 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 measure9v 6)amx)q roj(k1hi x blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat )jrix1h)q kma vox96 (frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasoni3u 3bi 9a(gafrc waves of 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+wwa 4a29gwk m of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located,ka9wwa wg42+m 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 movinyh.pf8. of jecxu( 7d6b.9f g x(3ajllg 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 of so 3( wtbqvy( pw 8qf+x,xrrj3i+und is 310 m/s (a) What is the angle the shock wave makes with thrj3itvyx( w3+ rqf qwp,(x8+be 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 pl shodc/ejki8p66s:k -1afxk(anet where the speed of sound is only about 35eds c8x 16(akks i-6jo kph:/f m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s sts to5b47eu)1 8yyhef ix; v4nxrikes the ocean. Determine the shock wave angle iy18ti)n x4veyeu7x4 h5 bfso; t 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 er 84i*fmu2ut6 rx* hf$/theta$ 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 exaqk j, e;mtro 6p)0;blcctly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic r,e)mocjbt6p;l0q ;kboom, 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 do i1ry+4cr o-9iclk rt.5 bqrl+wnward from the bottom of the boat, and then detects echoes. If the maximuicr c r+ktl+i5. ry1b94q-rolm 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 octaves are there in;cl o na.j5)jpw- nh9h the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pfnh 5e ywkb(1zat*+ k/5gqhg.ipe symphony. It consists of many plastic pipes of various lengths, which are oz 55w*et.gbk 1khf q+a(/nhg ypen 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 souv 6wt,g5ug6 tmnd close to the threshold of human hearing (0 dB). What will be the soun g5m6tt,6ugvwd level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB soun w*e v9:6ltp; yuld0snvbx8 2jd and an 87-dB sound are heapv8js ld:l2 ;*6t 0vue9xybwnrd simultaneously?    dB

  The sound level 12.0 m from a loudspef5q2 nwg p/i9(h ui..-nw vamwaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in im-2.5vn(9p/uwfhi.wqw nag all directions?    W

  A stereo amplifier is rated at 150cff,xowj 96dx0r0 3um W output at 1000 Hz. The power output drops by 10 dB af xufj,930r mcd0w o6xt 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over theid.a:k zvokk* r/fn)pr )2 glgm* 8c9qjr 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 ra *ncvrk) o8m/d9*:q krjka ).gl2z fpgdius 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 communi( xz,fcqpoz 27cations 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 frequency x6z rc7cnk/m31$\frac{1}{2}$ 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 xu, xl3u .gxh/is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a masxx3. hglxu u/,s per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with wa, jvoy y 5ton(e,ko.t;ter (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube aj ,t;yy 5k(etvoo.o ,nbove 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 2.10 g is near a tube that is open at one end m;ag0sr076k(tv mggi and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mm0gg0 a;(6vm 7sktg irode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was oslqt8rwj - wi) 6aie9k,a4q(gbserved 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 range coming from two sources. x,co wa2;c76vlbrk.eo ms0xt 2du4f 1The sound is loudest at points equidistant from the two sources. To deteoccfv 2k2l 1 4b0;m teox,r6xasw.7d urmine 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 rg ny1n7uf.9o stationary. The conductor on the stationary tyfruo.1 n7 9ngrain hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as uvlxxpk /w8+ .it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 +x8w/u l.vpxkHz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of car )e wloz)c6w)fs 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 wofe)))l6 cw zgoing?    m/s

  Two open organ pipes, sounding together, prodei b5fjf n(+qpjdm(i;tr *gto ,tp4/ 6uce a beat frequency of 11 Hz. The shorter one is +*te;t/fd tppfii (qo n(bmj 6g4r,j52.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a ra km3 n;h)qpskbs*ka 2.ilroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencihmp naq ; 2b*s3)sk.kkes of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what bio0dmd1(ozhr a nkpr7 j 4;11jeat fre h 1m1p(r7zaj1k4doio0 ;jnrdquency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the 9kscbe k/9m8mmoth is flying toward the bat at speed 5 m/s The bat emits a s9me8/ cksbk9mound 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 ox-co4emhp a*3r: , olly7-g dpf high frequency sound pulses as it approaches a moth. The pulses are approximatxdlo, g-3a:4cp*meyl- 7pohr ely 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to hv *7ng39ihpm send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G fhgn9mhi*3v 7plat) 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 d.icw4tg23y v 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 2.8 m high.tiv4wcy .gd 32 Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “k 089iwzrzgff (el,fq 1:o: r1zi(mypsinging rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,o,z 1fmrp(1 g8keyz9 : lr(i:0iqzffw” 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 threshopcf9 /rl0) tdawkr+p;ld of hearing for the human ear at a frequency of about 1000 aw 9r0fc+kr;/d )tplpHz 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 :(c -7 dbakvtxtq6c.t on the ground hears the sonic boom 1.5 min aftav.k cxdt:6 bctt7- (qer the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboapz* spycf-x9go9y 84ut 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