What is the evidence that sound travels as a- c e1sp8mrw1qpl/d(y wave?

What is the evidence that soun7ow0,j lmf:alb0yjd.cv-zjh8(6z nrd is a form of energy?

Children sometimes play with a homzyu75ux/wm y 6pv9 b-nemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks int6 7/pw9 nu-mxyuz 5vybo one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, d: cj) 4 jj8zs oo7egdy2jqb1c/o you expect the frequency or wavelength to change?c:oo )s jjdjjb2qcg 71ze8/4y

What evidence can you give that the speed of sf;, nha8i1y toound in air does not depend significantly on frequ o;tfa ,in1yh8ency?

The voice of a person who has inhaled helium sounds viq7 4ogl s ur9jjrlqv3d *9b(2ery high-pitched. Why?

How will the air temperature in a room affect the pitch of0 qf 9;:watzkfn p9bz+ organ pipes?

Explain how a tube might be used as a filter 4i:u 5fjnx z um7)2ig/ 7hhmmhto reduce the amplitude of sounds in various frequencz75m2ihi7 m4 hhx n mg:u/)jufy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced cl3lqk. ywtb 5f1oser together as you move up the fingerboard toward the 3w1fybk t.q5l bridge?

A noisy truck approaches you from behind a bu 6nm4.8lwfu mqilding. Initially you hear it but cannot s f.6l4 wu8qmmnee 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 diffraction.]

Standing waves can be said to be due to “interference in space, *+rb+uabin1h ” whereas beats can be*+h1irb+nb au said to be due to “interference in time.” Explain.

In Fig. 12–16, if the fdn1s26gjovrn8i 6y/ y.wsdp m0 ) *lntrequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart orjwm 8 / sts2ny)r o6ndgvl .y06*i1npd closer together?

Traditional methods of protecting the hearing of p eg.qgnt8e voqw5 :*1reople 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 tqn g5 e1t *:gvwre.q8ohe ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown i7opauz( 79d 4 hieixbk j++ 0mvc1;tepn Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explaini4ae0mc79b d(7pe j+;z hti+pox kv1 u.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer movec+c-y c/0 lt7 lsofi,u in the same direction, with the same velocitysoll+cc ,f 7/u-c0yt i? Explain.

If a wind is blowing, w f3ofg/ k6 qpn 1nc 5++mfcyvi(enx0e5ill this alter the frequency of the sound heard by a persoem +o+fi 0f6enqpy5/ v(c31gcfn xn5 kn at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions ofl)s 0/zl0xb( vqyk-pe l2m tav;28rmo 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 the msaxk;/b0lylp 8ov-em(z2)q02vt l r child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the lc,vswnav6zn yk 1 ,zm4bqe )4)ength of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s afte qnae16mk,4nz,ysv4wvzb) c )r shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the sad6i ozrn9+nc:5zn 8yw/du6j*j bej ,ide of his ship just below the waterline. He hears the echo of the sound reflected from the ocr ybeaz9/ 65ddnuoji*8:nn+j6 ,zwj cean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in airw8/ z 24uc.vw qhq. gkd9jdawvk/ak (1 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 abogl0(qa fq, /mn .yp-an -hmn6vve 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 hear-ahmm/nq,a l fp-0vn(g 6n y.qd (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes wsw fd66bxmtkr u1)c.g-q5k; khen striking the water below is heard 3.5 s later. How high is the cldf-mk r)qbxs1ktw ;.ck u5g6 6iff?    m

  A person, with his ear to the ground, sees a hug7 on53kfn8hovyi8+nse 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 concrete, and they are 1.1 s apart. How far away did the impact+hoo 5yn fkvs837i8nn occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one(f,d7 aa,yyzyva)pq:4m 6o f j mile of distance by the “5-second rule” for estimating the distance from a lightning strike if tj6v y 7(f qaya:a,oydmf, 4p)zhe temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sountxj9g lu04 ybf(a /3d0 7bexayjs;a: ed at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whof0o*7 lc pbiad9 1zd e70*fjzmse intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produrf cwkgl.*/znmgkj2h/,9.lz ce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hintczwm h2/nrg9 * gll,.jkf.zk/: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane zkuafp0cyy57.c;3 styg8 b9d 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? pd8bytac z3g; .c 9fysyk57u0 [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to hav8tx7. r9f/kqjk 7zobg e a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for eb8z ogk . kjr7x9tq7/fach device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output 5 xgw2xn7y w-pof sound from a person speaking in normal conversation. Us7xx 2pgw-w5n ye 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 strikest ka .yj/nk6f-(yrc9 o 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, while aez l83cf6wz1 e0h5:9fbitl athe more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m fr8fa05w:b c6a lt feehz9i l31zom 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 d:(7pvhzca2 4:pot qem B meter registered 130 dB when placed 2.8 m in front of a lo e:o4(2hczam t7p p:vqudspeaker 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 detechpba6 z5 o(uq7v zmq pc+3r6l7t a difference in sound level of 2.0 dB. What is the ratio of vqlm76zo rz( 5h +apc7b 36puqthe amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will thd hrluq6( 0gp;i ;zoo-z 7v(yfe intensity incfg0lvrdio(h -z oqu7py6;; z (rease? 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 has tr4gkk 6n x9:obwice the frequency of the other.6 nbkogk: x94r What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air thadc vfiwn)w/ i19t*r .st corresponds to/ wf9dv.s c 1ti*nir)w a displacement 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;m-f8,yb dqtcx -qc m9 as a 100-Hz tone that has a 50-dB sound8-cqq- dyfct m,m 9x;b level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ea f ok,0nk9.-bn+yl3w1 wgxtna r can detect when the sound kawb3xo9y +,w1-t.nfgnln0 klevel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate (opw)mg5,z+ uqh hgn)a huge range of sound levels. What is the ratio of highest to lowest im+ 5h)h(z)qgwu,pon gntensity 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 frequen6gv1o)l 5t6or2 pnp dscy of 440 Hz. The length of the vibrating portion is 32 norlvtdgop 1 6562s)p 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 ar / jbg 0tpzi.znmktk-s5pmlf5)0 r)hv3h 8 ;jye the fundamental and first three audible overtones if the pipe is r-m5 jz p)z. 0klnbpt/y0i3j; gtv5 fs mk)h8h
(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 8 omj dd1,f/urkol(2 pan empty soda bottle that is 18 cm deep, if yor p2ufk8/,ld(oodj1 mu 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 pipes spanning the range of hubl9y,n fui33d7auuk)man hearing (20 Hz to 20 kHz), k idu7,u9nbfuy) l a33what 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 tl 3v +s 5ywq/en:wfpn3hird harmonic. What will be its fundamee+y qvsnl3pw3/:5f nw ntal 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 i;ty0ri1 sdj **m ,68vjcfdlgys tuned to play E above middle C (330 Hz).jr*8y0; *c 1f,m 6ldtidsgyvj
(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 or 8 l8v:4dqsxregan pipe that emits middle C (262 Hz) when the temperature isx8:qvseld 8 r4 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 bw6az;j( 3g/f ynpp5lat 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–fp e92-xxj4f6td g: - ehs2xbl10 should the hole be that must be uncovered to play D above middle j t s29xle xfdg6h42--pe:fbxC 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 H,,rg edt0 9pedoh 2 ss8jxp9jtr9h8w 0z, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an op90e,s 2 hrrjg9tw odhs9 0,djex88ppt en 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 lon pxxa3-;2sbo ig is open at both ends. It resonates at two succ i;p2-3 xbsxaoessive 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 uc(wcgl*i ,r5$^{\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 97ib(xi pbtui ,tf:xyj/q)w;.p:qda a 2.14-m-long organ pipe atpaf7u(t. itp xib :w;qxj,/)y dqib9 : 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 jqkyk73l cqr.e:-;nlee vov+g8 kb )+ 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 informatio)ngy3.- ck8qk+kbl7v;: le+evjoq e rn 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,. 4r5 e0mshsqr one of which is sounding 440 Hz. How fas q0es.4m hr5rr off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and 4q-dchiuwkg331j b aa:ze( 3 d$C^＃$ (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 operq-i 7duxjndc,w0n :t ;ates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of-n,iqjwdtd x u :n0c7; frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string prod hni 0w4.;dlpwuces 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency o4wp;l 0wn.dhif the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same fref c t2v(-ydagp7(xgu we8 .)rdquency, 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 pltxpg d8 vy.)(r72 ge d(acw-fuayed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if geg;it * e2+dstwo identical flutes each try to play middle C (262 Hz), but one is ated;geg+ s*i2 t 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B hat:9s iik(7rb vs 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 v:skt9i(7r ibpossible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person staw318 p6n xdzhsobwz, 3nds 3.00 m from one speaker and 3.50 mzxzb3no 61s w3,hw8pd from 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 1:4mprdzjt)q) 32 Hz, but a piano tuner hears 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 the4) jmpdq )t:rz 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 xov m7l-/j*vsm hbt3kk-d:b+ beats per seco3-kbkjmsbxl m:h-7 vovt+ /* dnd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at ra 3x8pqiku0iq./ cs(lest. What frequeauqi 8 s0(/.ikpcqxl3 ncy 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 fr.0etp9.4w e n6ne8qvemdx d z/equency do you detect if a fire engine whose siren emits at 1550 Hz mv.89zmedqt .ennwp06 e /d4xeoves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if 6t 8 keho-8k/j +(noglovx ga)a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequenciak-okn(h/l6 vj8g)e8 og+ xtoes 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 tf y67 vhs y4zr rf,ju807ovp2dhe same single frequency horn. When one is at rest and the other is moving toward the firss fy06 r 7hod47fvp,8zvr2j uyt at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and recei r:i22teby7 deves them returned from an ob2r7d e 2byi:etject moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wa 4u-nc9apn,5(fqpoto* lwt )g ll at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear pnt9,wf uol5*oga c 4)-pt(nqin the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler expepw2v+a .)3 / dqolkb3b uz,iberiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the traiapz+bk .eibuovq 23 l,/d3bw)n car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasoundnca6/ xuc0is; waves to measure blood-flow speeds. Suppose the device emits sounc;i0u sac/xn6 d 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 frequenm cx 7qm9 *(2uvnhj1xmcy $2.25 \times10^{ 6}$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 a p pjz9(2q2m9ec-lpz 570 Hz. When the wind velocity is 12 m/s frozm( 9clqp92pjze2 a- pm the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on jat(+elfr :aj880mc jland 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 Mqlas o,bwgaup6,u/cb 6ti-: d +orr8(ach 2.3 where the speed of sound is 310 m/s (a) What is thdw ls6gra, /( ,-touu8ipbq:cr+a6 boe angle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where thb.1ij5d,n u tkkgcr.;e speed of sound is on,5rjdk bn gu..c;t1k ily about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/y*7 z.4tzoid (rjop 4*n ,awyfemo*z -s strikes the ocean. Determine the shock wave angle ,4yozpzi. z ja*d*ywtof*o(7e4r mn- 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 5h,o)ab afy5pm ocxc zu3,y42$/theta$ 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 1v,ewj rnl(o.g -43p -lbbsc z6.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See,gb w 4 pb(.cnze oj--vrls36l 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 pulsesp)uc37 g2usss tl6fy 2 downward from the bottom of the boat, and then deteu)u6 tcs3l2pfs27 ysg cts echoes. 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 octaves are there in the human audibl uj 5eivx5f bv6 yg-xk+-/n xv5y22:zaavfbb+ e range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of manyias-gl0 7 ;/w m7cby x9mwkt0t plastic pipes of vario7wgt0a/y mt9kl;b-mc 0siw7xus 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 n+ek7bq jnla4 a, tr/eo t3+llo (9e,zr3xb)a sound close to the threshold of human n4oq atta ,e+3eo)lkbjla3/7 ,z l+ 9rnxbe(rhearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound lev fgek+cw3.fe3 el when an 82-dB sound and an 87-dB sound are heard simultaneousl3 .cf3fge+ekw y?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 1o9)/ r6t,go.urkf o lq05 dB. What is the acoustic power output (W) of /rur6oq lo. ,)9kgoft the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 Wr473jds8 rz ycr srpc ona-4.ib7d,7u output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the powedb r47 3srrca8c.d7r4 spu,i7yzo-njr output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectivebpkt g2vz 2s;+/qv 4 k5; +7zxj4kjsqfpxn-cv 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 intercepted by an unprotected ear avgvzxs2tcx / k25 + pkjjfp4;nk 4sqv+7;q-bzt a distance of 30 m from a jet airplane engine?    W

  In audio and communicationscnvsyry *:j2, 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 v qqa:.sq4us 2frequency 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 fixed points with a fundamental tdi2bzi56;xw l3+za skesu3 : frequency of ilse63sx :widk2bzzut+ 3a5;440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical oa1wwt3y, /yi4 mr :bhgy*w2iepen tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and agai* bt:4wha irw,y/wyi2e3ym1 g n at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of myx6ru/ocq+u. 5s s/t )eoj+uk ass 2.10 g is near a tube that is open at one end and alsos.coys )xruq65+ /e/tku+ujo 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one mliu s) w7c9cx 7eq f-m0na++lfull 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. Tc:h m3 bmk2mh)+wg9pfhe sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the othefb m)2chw9hm 3p mk:+gr. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. Twp6q3 -l47tdbx6giok izkx2 3 he conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving traibo3 d-k6i x4w 6kpgzl37xt2iqn?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After dvgj0n 7txjq*d; f 22fit passes you, its frequency is measured as 486 Hz. How fast was the train moviq 07vn;f jfxg*d2td2jng (assume constant velocity)?    m/s

  At a race track, you can estimate the speedwiek/o b418 ek of 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 gok8w o b41iee/kes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, souh i6b5 i87dxu trgs/b:mj k0or2qdy13nding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long.2u603sqo: j 15yh mikd irb8g/b7rdxt How long is the other?    m

Two loudspeakers are at opposiw 7+:fzdsm 8t:f*q ixxte ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequencysi f x8fm:xz *w+:d7tq 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 i;w9fbqx7,8y s c ht0iln the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assufi q8bwcx;t,y 7hl09 sme 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 moth izc97(mur/,t0tw4bnmk gys4r s 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 off the moth? c(9t 4,umrk/0mr gsz4y n tbw7   kHz

  A bat emits a series of higt0- s lio :w8:vf7vlkth frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp 7:kf-iv ws8v0t:tol lreturns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals fjmo yg.n1030iigm 2rbx)mu b( rom 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 flat) horn. What is the fundamental frequency of this 02m3jbgb1nu)m xo(y0.i rmighorn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be d6wtyw 7yh8u * v:92jwhbd5m9pl ps4 ucompromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consijmp 9dvp4hw 69u * htw7:d ywu5ysbl82der 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,” involves a lf+ sokrerl l(r1zah t/0u7 8y+z7hwn5c,iam/ong, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound.zhw1 8 eak/unazl7r+ih7ytr(+frcl/ 0m o5 ,s 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 ear at a freqd m zc-og57qo7/* u clry(5dsfz+m6w cuency of about lg5zccrs57m o uzfw6c (*o mq /7ydd+-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 at Mach 2.0. An observer on the ground hears the sonenovv/6r(c 2vic boom 1.5 mi(n6vver / cv2on after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15oylj 2cw2/md/t93 ck d $^{\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