What is the evidence that sound travemil.emx15 vkw7d: d 7sls as a wave?

What is the evidence that sound is,) 5yraq gv+pe a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string toc :atd.ysrk 6/djl(y 78uas u2ej62 lm the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the (2 y6ame jysrdtl6/cu:jls7kud2 8.a sound wave travels from one cup to the other.

When a sound wave passes from air into wat6d igfksy- x5 *4tced4er, do you expect the frequency or wavelength to change yiteck54x* gd6 fd-4s?

What evidence can you give that the sp0wo*1hws*23uay4vq hlt+9gi.hr van eed of sound in air does not depend significantly on +1v*qhy 9a4ring203 hhul tavwwo.s *frequency?

The voice of a person who has inhaled helium sounds very high-pitches/u2+ gjtmn7( vpkn v+d. Why?

How will the air temperature in a room affect the p qwiq *f.lym 7bc1w8r5itch of organ pipes?

Explain how a tube might be used as a fil*g3ri pe/j gog3gzm irkr2uo7o9( f6;ter to reduce the amplitude of sounds ioreomg (go 3j7kr; /*g3 u9iiz2rfgp6n various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as yo2k6hfjp g*z .tu move up the fingerboard towarpg6k.h2 jftz* d the bridge?

A noisy truck approaches you from behind a building. Initia8n4jq4h9h f;iufs k s-lly 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: 4sf4;hj9u qsnf-i8hk See Section 11–15 on diffraction.]

Standing waves can bebktzhk:l77cq*t ( d h, said to be due to “interference in space,” whereas beats ckb7kdz(,hq:th l*7t can be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of9(v5l g-n mvs k-hqc+/ry0i 8u vep:rv the speakers were lowered, would the points D and C (where destructive and conqgm0y- vv+-9(h uvner iscplvrk5 : 8/structive interference occur) move farther apart or closer together?

Traditional methods of 7zde t q, ,g-lfe0byj f+6(opgprotecting the hearing of people who work in areas with very high noise levelbg 0j7qo,ee,l(ff gpdt +z-y6s have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as m-f yqhrj( -m7ao(p+.nm 3u qsa superposition of two sound waves aoumfhn7(m j-3yqq+rps - .m(with slightly different frequencies, 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 sc: y(fi 9okno+ k7apk g)mk9xr57ug ,wource and observer move in the same direction, with the sai7kcym7: )k( ouwg pk5o,knf+rg 9a9xme velocity? Explain.

If a wind is blowingkt 35p-0 dkwlre u(0vo, will this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavt0( k5dvluw pe3-0korelength or velocity changed?

Figure 12–32 shows various positions of a child iz rx 3p0 ) 6almf5hnjee-1gca7n 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 frequenx 3jracgnf- 5eamplh1)07z e6cy for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a la 86x gq+fsk7ws9 5obekke by listening for the echo of her shout reflected by a cliff at the far endgkbx+7q5oes 6 w89skf of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterlivawrdt6i/m.be0 o u87ne. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) andoa0rdu/b7wvit. m86e does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wave2 ht2ng1q 42lp, qc:shqtxm2s lengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just abovevdso( tx5nk (b.hgnyw(zj 51 ) a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12y )5txj(odhz5(sbgnnw. 1vk (–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when sbimz4mv3l4sn kocde7bmk ;-+s* m--etriking the water be+s4ek b*--z ncesmm m-bvo;k7i34l mdlow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the grouq)k +bc-kop9 y(ujavs+:m1vfnd, sees a huge 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 occur?pojf+ v)qsa9-+: kvcy m1bk(u See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of dista0 apovd,a7 nvs 3)qkm1nce by the “5-second rule” for estimating the distance from a lightningvasq n)omk310vda p7, strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of4wr j6vf x6g f5kp t(94.irgqw3o/rrl a sound 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 s l03u2 xz(e, (fah tqby)xlwp4ound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simdzr17l1ixxn,ey1 y n 9ultaneously at a certain place, what will be the sound level if only one is exploded? [Hintz,in119 yxx 17rndy el: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy rk0l3g 1 yt -x:hx2rhncy0j* sjet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not d1h2-rx00nsc:jgklyt3ry * hx B’s.]    dB

  A cassette player is said to have a signal-to-noise rami9e5,x;ahg .1fz dee tio of 58 dB, whereas for a CD pladix5,emf9 .zg h ;aee1yer it is 95 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 fro c6xc/)aylia gk i::d-m a person speaking in normal conversation. Use Table a:d g:6iy)icxal -/ck 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 isc ;3foqpgci//ppn e1: $5 \times10^{ -5} m^2$ (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 lvb2 tu 0 7gx(8)5:uifm.modgm/ bxdd rated at 250 W, while the 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 from a loudf)g mto( 8:dl u20vbxgmx i.d7m5ub/ dspeaker 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 metgfvj0 j a6l(x .a3g1jgee58pker registered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. a01v 3 (.le8jg6ggfek 5 jajxp
(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 dete )n9fw9+ivh qnct a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by th) vifn+wnh9 q9is amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave dw ,ldfsi.0: usww;2wis tripled, (a) by what factor will the intensity increase? Increase by i. wl:wsf;wd,0sd wu 2a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has ty k,2ifut+hw. wice the frequency of the other. What is the rati hy,t2ui .wkf+o of their intensities?   

  What would be the sound level (iqtp*f9 r 4r74pdgbg:p :5xol73qu vs in dB) of a sound wave in air that corresponds to a displacement amplitude old4gr x:poiq9u ftv*4 7 b:s7p53 rpgqf vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what soanyd3n p(4a5rj.q ke 9und level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6 k495a3nypna.q( j red.)    dB

What are the lowest and highest frequencies that an ear can detecti 0tca5g s(zf8 when the sound level is 30 dB? (See Fig. 1tgi0sf5 za (8c2–6.)

  Your auditory system can accommodate a huge :+o9jq4rbuz9(l rtr.p msy9 gavzlo1m *,0bm range of sound levels. What is the ratio of highest to lowest intensity b0,l9.ojmm4zsgbyt9urzrp*9r v+1malq ( :oat
(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.n1ozup)+l1qg The length of the vibrating portion is 32 cm, and it has g1 oqu1z pln)+a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three5na 0jt5wdkzz;cv i ,) audible overtones if thez cnw0jka5idz;)t 5v, 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 blo+ noj2azr/g 6iwing across the top of an empty soda bottle that is 18 cm deep, if youjizogr 2+a 6/n 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 p5j1c0 oyp1wt m7kgsn8ipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), 1n 7kgo0tm1wpjs yc58what 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 H,x. py d,krphv; jl2a.z as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 6vp kp,h . .lyrd;j,2xa0% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle1: .,s(tx gpiok /lken+om5o wmls, -y+kyfa6 C (330 Hz). - mgwk oao6.+xk+1me(yf yonstlp,s:5i / kl,
(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 o8i g485wt 5 -d om5qfdnh7qcgfrgan pipe that emits middle C (262 Hz) when the tempeng cmfiohd7qfw8 4-g55tqd85rature 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 at 20-lws+/u)h bj en,hze- $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in z9+i9 tse37mugr v0ga Example 12–10 should the hole be thati eusvtgmz3+ r g790a9 must be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at se nkc7:n4az1 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an opee4zsn:n1ka c7n or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1k1by0g7(6 ehbgw v( zg.80 m long is open at both ends. It resonates at two successive (v 0z bywggbhg(e176kharmonics 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 w2y7q5g( ,-8od r u5xp levkwq$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-long orgatm6* 6j rj6a x,/9d wcnarb,ken pipe / nrjr *6,k,dc6j 9axbetwam 6at 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 anvw z a.zsv8w -gwo ))se3ldutx43xd(:z+fry4d is closed at the other end by the eardrum. Estimateyrd: 8 xglaoe wz(.xz)+ v4z-wd) wv4suf 3s3t the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2w99wn+2tpbsz c7o 3uoi+b,tr .0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far of+ z7+,9 3ruwnw9cobptbso 2t if in frequency is the other string? ±    Hz

  What is the beat frequency if middle C k - kw4j g4+q/*wj:szs5cyvdi (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 ajk1 -lcfjizf,nhyx2bfs14: .t 23.5 kHz, while another (brand X) operates at an unknown frequency. ,:xi1 fyj2cnsf1bj-f4hlkz.If neither whistle can be heard by humans when played 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 a0gk3f:n osi z 4dlxf67d 1khx8 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuningd6h: 7xs8kl0 3x4fifdkgo1 zn fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the sak gjt1+pvg3c/me 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: Rec+tvgg1 pjk /3call Eq. 11–13.]    Hz

  How many beats will b1.uw 2 b /z) qp)/l /u187harzz lsl9nrkklkcae heard if two identical flutes each try to play middle C (262 Hz), but one b)k.8 pn l2qc)zasrl1/u w 9l hzkzul1rk//a7is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning fog5b1d9 hujz,v rks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B arg5 uzh1v,bj d9e 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 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 stands 3.00 m from one speaker ar dl(pb8(1i(jfb :js hnd 3.50 j8jbb lri :f (d(ph1(sm 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 132 Hz, but a piano tuner hear1-o;ly )c.03zydg- yvx wfwdgs three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be thx ; f1c g.dvl-0zwyo dwy-)y3ge 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 bea1mz .3pkxjn.ebz y:d5ts per sz1z.bkj3mneyxd 5 .: pecond 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 whe4vn-fixi 9tc .n at rest. What frequency df-xn9i .4 tivco 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 a fdr+)nj 1qg );eiu zwl4ire engine whose siren emits at 1550 Hz moves at a speed4dw1iqu r) nlje +g)z; of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequr)t qshw* .al2h t;bp3ency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? 2salptqht 3);r.w* bh 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 wzizz33 0 1hgo;*nrs0 )uj teprith the same single frequency horn. When one is at rest and the other irez 3 uhr 0tz 01)gs3*j;ozpnis moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound wav3a9dzcjhxqsh9 0 g.6um h9o u/es at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is theojsd99xumh0u6a9 gh .qhc3/ z received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat z cv m07. wuq/ok;knb*emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does thekv*/w.z7bn muoq c;0 k bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on nb56p6+u gc5ocfpwyec41 p5ma moving flat train car at a frequency of 75 Hz, and a second identical tuba p o45yc66 bpnec1wcf5mp+g up5layed 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 thc a93s1 fvq/b 7b(seqo measure blood-flow speeds. Suppose q9e chq 7(v3ssf ba1b/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 frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usdl4arh(9+jg w ing ultrasonic 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 of frequency 570 Hz. When the win aw;t,-wda )ru s/y:y+kv7ixi d velocity is 12 m/s from the north, what frequ+xr;d k :vy7u i)w,watai/y-sency 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 )j fwsmz-4 edop:obq0ak)n 54 moving 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 Macl jfv rs*l7:u(ka2p z.h 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction fs2l(:jpv7l*az. urk 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 t8g 4 qyhzd;t.zhe speed of sound is onlz;zqd8y4g.h ty 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/s strikes the ocean. Determurqh2 q1j7 l7iine the shock wave angle i277 rlh 1qqjuit 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 2/448r/ ( qm. lgn3pyeftjcslrz7d zs fls8z,$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a fw-hei x0.mc6,. ypqjgpy8z )plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km.z gjywqp -6h,8ifx)c. .pmey0 See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downwar 8bunc)+ dj*gbc wd-j4d from the bottom of the boat, and then detects echoes. If the ma*cbdb gw+-n ) cj4jud8ximum 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 audibv. 0z921yibe/n, j(ux hdbdswle range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It4+9ka62j pmfa ezk zk9 consists of many plastic pipes of various lengths, which are open on both enk+ae 9z4jz6f29kkapm ds.
(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 close to the threshold of 1(yd(a2enxkt fxu.m - human hearing (0 dB)..(x kyuf(m1adxne- 2t What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87.lo9;r9 h gvqqy6kse9du: bv0-dB sound are heard simu vkhr u6q;e: gs b9q9.0lvyod9ltaneously?    dB

  The sound level 12.0 mja5mdt0dysqi ,ycxn 8:pv u 7;z6 5(iz from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speake6n mv0(5ptxu; d7zy q,85ydzc iiajs:r, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W q4cxz9;nyc*foutput at 1000 Hz. The power output drops by 10 dB at 15 ky; xc*zq94 fncHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectij/u3f(aoblz: j9*o, p1 45otfiuhkajve devices over their ears. Assume that the sound level of a jet airplane engine, at a d(flpb :uoj ja 4hka oi*jz 5/,3ft9uo1istance 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, thqt00s b8.f veej) p-sie 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 a0+z wxduenv09k 7l7o- wp ;tio frequency 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 betsk fcq+a2a;z d(3e:ht ween fixed points with a fundamental frequency of 440 Hz and a mass per h z;a qf2(c+a3d:etskunit 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 abo)c -kl +lq5g h.eh+prcve a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with thel-5hl )c+rq.gphkc e+ 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 ogi2fe:zvll / ,ic4 3s w3amea.ne end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) wi/.s eilzw ca,:24 vf3g ail3meth the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obserolr d)4r. rcyz:g,) 5gcn2gz oved 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 sourcesaf*e*50ad tqfd:2o yc. The 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 t*oqdcay : fe0*d52 tafhan the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistss+z w+5*k ysbles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other ty* 5 skz+s+sbwrain approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is fjhy(.8/o8ql9 jlvj * 1p r.tivwvyp(538 Hz. After it passes you, its frequency is measured j* vl.voyr (j/ (qpyl8vwi 1ft98h.jpas 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the d(-b)m nm kv*hng(v9 ztifference in pitch of the engine noise between approaching and receding cars. Suppose*-gzn( knhbv(tmm) 9v 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 tog.y dzfsw8r+f 8. ol+lbether, produce a beat frequency of 11 Hz. The +fl + rs.bwzd88y.lofshorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves)b 779hfsgwv fga ,o,w 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 frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speh)aw7 v,7,o fggfwbs 9akers, 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 nor (. 5vfgyqga2rmally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ul.gyrv2 (q5g fatrasound 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 moth is flyc/1p dci. 7et- etpzo-ing 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 detetepcit -p-o1/cd7. ezcted by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sou20weorg j0 1.ya) snuv qb m ,y,8di5cx-caoo1nd pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, anjxuciy,g0sowacn0. m a) 5qoo 2v-1ry,8 de b1d each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals+ mgi0dh g p,j;l4w-rn 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 flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Mod0;h gd-m + gi4pwljnr,el as an open tube.

  Room acoustics for stereo listening can be compr;b-gigkn*+ac omised by the presence of standing waves, which can cause acoustic “dead spots” at the locations o ; ikcg*+n-gabf the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, sc (y4p9i6o7ma 2d olpvlender aluminum rod ho9vdpolp6ay4 7mc (2 ield 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 hg ooz9 +vi.f1 4s27qc zr xmikzn0d,d:uman ear at a frequency of about 1000 Hzvmq,zifd:o sgd zc+1iorx 7.z2n4k 09 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 soniyy(3-v hprw3 vuf(0yf c boom 1.5 min after the plane passes directly overhead. What is yyrhwv((u0 3pfy3-fv the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15s2d0hk p7 /lsz5;okq b $^{\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