What is the evidence that sound travels asx md9g)0d y;oex56 ohclpsy6, a wave?

What is the evidence thahuj v,3y60 ghqt sound is a form of energy?

Children sometimes play with a hsc 62kg;bkmft 1 :f,:z 4s neahsolc0:omemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. g:msba;0tck lh s2z1::nkc4ff ,s eo612–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into waj w0/57jcux j td*c+jl;dmpz/,e3gq qter, do you expect the frequency or wavelength toz ujdc c+mgl 0*/,;7x qt5q/dpjwj 3ej change?

What evidence can you give that the speed of sound in air does ny nj+nz ch/-cq ucnf216cuc10 ot depend signif1 -ccujhf/n 2zc+q y10nuccn6 icantly on frequency?

The voice of a person who has inhaled heli1hwz: fq w;h 1iz2vg-ium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipes4j.p i ho/66igf x4sen?

Explain how a tube might be used as a filter to reduce the amplitude x3qlj1(r dt4pof sounds in various frequen3lrj (tqpdx 41cy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. b(/zsuv;cx 11) wyfuc5mr2q l 12–30) spaced closer together as you move up the fingerboardqc /m)uzbwl xv cu1 fy;s5(r12 toward the bridge?

A noisy truck approaches you vq(-0wna3dd tfrom behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section0v wqd3d-tn(a 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereaxg i,ny+wipxdf9 i67 5s beats can be said to be due to “intern yiigi+,d79 p6xfwx5 ference in time.” Explain.

In Fig. 12–16, if the frequen o-txzs+ft6 a7 .ciie4cy of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apar x7.oesi az ct6tfi4+-t or closer together?

Traditional methods of protecting thpig3icoh dhg07 o 7k-,e hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a 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 tho 0hd37 ghopi7-c,g kie 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 thougkh: c.g 2o*j;wurm jl8g-fg5;a;ubyfx -p(qm ht of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In wf;5x-j lbqp. fc;uga-h: grm 8oj muy;gk*w2(hich 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 dj i cs,2e8u.hkfb o:o2irection, wih:i8f2, juo.ck b eso2th the same velocity? Explain.

If a wind is blowing, will this,rk)98 e uawys alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity cy8srw 9u,eak)hanged?

Figure 12–32 shows various positions of a child in motion on a swing. A m15 ral y;hgu5xonitor is blowing a whistle in front of the chy1h 55rul;g axild on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of cm-hj4 .-bjlw6 4iaeq7oe0v*x s;kot 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 after shouting. Estimate the length oet- 0whlc ioeax- j;4*m7jo v bqs46.kf the lake. $\approx$    $\times {10}^2$m

  A sailor strikes the side of his ship just below the wate*y;yl 1j* f:yz8+/i ruy yoe9jwrm yc1rline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s laterl 8/; 1y fcij+*u m1yeror*yjyyz 9yw:. 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.    $\times {10}^3$m

  (a) Calculate the wavelengths in air at 20 7wiy0t2 jd)jy ${}^{\circ }$ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. ${\lambda }_{20Hz}$ =    m ${\lambda }_{20kHz}$ =    $\times {10}^{-2}$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $\times {10}^{-5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foj:vph8d)7 r kf fo78p tdi.co0ggy day. Withouk fof 0orph)v88dd:ptc7.j i7t 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 the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when striking th -, -l clmgqmn6;3w noi.3wgim/afq3x e water below is heard 3.5 s later. H;qwqfln-oami,3mcl m g. /-i6x 3ng3wow high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concret1ggzy kj,k -2je pavement. A momen 1j y,kjg2zg-kt 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? See Table 12–1.$\approx$    $\times {10}^2$m

  Calculate the percent error made over one mile of distance by the “5-second ruox 1qpu 6 cu+3an*t( xqnu3v9yle” for estimating the distance from a lightning strike xnoux+yu 3 (tvqn61p*3uqc9a if the temperature is (a) 30 ${}^{\circ }$ C, $\approx$    % (b) 10 ${}^{\circ }$ C$\approx$    %.

  What is the intensity of a sound at the 9;fv5+ glu-ax o(jnsypain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $\times {10}^{-10}$W/$m^2$

  What is the sound level of a sound whose intens9j*utbnj* r( iity is $2\times {10}^{-6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when firefhc (br5,l5kfp e+xf, d simultaneously at a certain place, what will be t f5c,xk, pl5(fh er+fbhe sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplanj:b753 cec behe with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add ihcceb3eb 5j7:ntensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, wher:o 7-jpx;uz mv4+g opdeas for a CD player it is 95 dB. Whpm+voo;zj 4pg-ud:7xat is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $\times {10}^5$ dB =    $\times {10}^9$

  (a) Estimate the power output of sound from a person ( 4 aqpikh.6yjspeaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere yaj(.ip6 k qh4centered on the mouth. $\approx$    $\times {10}^{-6}$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.]$\approx$    $\times {10}^7$people

  A 50-dB sound wave str*7;pisaf 5 0zkd 7wpumikes an eardrum whose area is $5\times {10}^{-5}{m}^2$ (a) How much energy is absorbed by the eardrum per second?    $\times {10}^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $\times {10}^3$yr

  Expensive amplifier A is rate.n fv ;gicso99d at 250 W, while the more modest amplifier B is rated at 40 W. (a) Esv9g; foc si9n.timate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 13tqs 8)a:)pj bv*7d 8;vzty2 pnzwd6d y0 dB when placed 2.8 m in front of a loudspeaker obnqz v;ts6dpz at)yyd7*2w)8 dj :p v8n the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $\times {10}^2$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $\times {10}^2$m

  Human beings can typically detect a difq0xe5aysj 8f9zp3z qs3czp+4 ference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amounpc a3pj+5x39ssz qfz4qy0ze 8t? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) byah r,1jvfd6m: b 7p/2cft9yymbh tz64 what factor will the intensity increase? Increase m9hfrma, t pt47d6jc1 :by6byv/zh2fby a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displ7qz n,wx57lipu uz)s:acement amplitudes, but one has twice the frequency of thz,pws7uzq7i)x n5ul :e other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a soundj dyro 12y*k;ke6;xftgk.ji - wave in air that corresponds to a displac;61rfk-jj kytg*.iox;y2ekd ement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 10)r wp v3dyrat56 gp))j0-Hz tone that has a 50-dB sountvy)jg w53) pp6d )arrd level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that aghexo2)ycvqc(p6p l8 ig 46 .cn ear can detect when the sound level is 3oppicc g6 gy).26ecxv8(4 qlh0 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound leule 61s*97 xqsb 5stbp5w jm:cvels. What is the ratio of highest to lowest i x5lwqss5p:7b*tj b ec1m6u 9sntensity at
(a) 100 Hz,$\times {10}^a$ a =   
(b) 5000 Hz? $\times {10}^a$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental fredp e)+ b4;spejquency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be plac)s4;jpdp +eebed?    N

  An organ pipe is 112 cm long. What aren4ck u +j2uv)2 d*,yh/xbdixf the fundamental and first three audible of22,u+cx /)d4ndx bhyu j*kiv vertones if the pipe is
(a) closed at one end, $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz $f_7$ =    Hz
(b) open at both ends?$f_1$ =    Hz $f_2$ =    Hz $f_3$ =    Hz $f_4$ =    Hz

  (a) What resonant frequency would you expecyz/q us64qja-kyu v.g s9u/6et from blowing across the top of an empty so u9 uy6vag j6s/e-sqz/.ku4yqda 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 4 1pvd ysa8dc2cbmj3p0*a ;qlopen-tube pipes spanning the range of human h*cv20jyacd3 8p s dpb1;mla4q earing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20Hz}$ =    m $L_{20kHz}$ =    $\times {10}^{-3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. What wil+ cqup8jm6mo0u mka+ 5l be its fundamental frequency if it is finp k5+mjm0+cuuma8 6 qogered at a length of only 60% of its original length?   Hz

  An unfingered guitar s4x1s2cj q6alxe ( oi8qtring is 0.73 m long and is tuned to play E above middle C (330xe8qxal 1 6s2oqi4(c j Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) whenem3wf5so- 3ra the temperature isra-5m3seow 3f 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 22a wwki37wzsmz34 u 3o0 ${}^{\circ }$ 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 should the hole be t6 8 6ad2eriljzjhge,*h v 4tjz6+e8twhat must be uncov,eje j4*t+zwg86e86zjtavhh l d26i rered 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 canl *6.cvf4cvil resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this icl*.lv6 fc4 vis 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 :s2eaihy)es 63vcudw 82/ k :vkj0yo fy4guc5 both ends. It resonates at two successivy e0dws::i u u2h acge4k8536kysvf)v 2j/yoce 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?$\approx$    $\times {10}^2$ m/s

  A pipe in air at 20 s 6nr bg+7 u,z3xkiys+${}^{\circ }$ 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 aud 5qv + 0f6h.*hbkghvuoible range for a 2.14-m-long organ pipe at 2fh+b gvq 0h.6khu*o5 v0 ${}^{\circ }$ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatel.x8 d f92tje.t. .shjvv y+pcdk,u bj-y 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Eje.+ pb-.8vj,dcts ku.xv9h2 dy.ft jstimate 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 2.0 s when trying to adjust two strings,/p ns y8ww.k hx v5o4d32d+wex one of which is sounding 4oes4+nyw w. /p2hdw 5d3xkxv840 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (:ed/ ah .7ok0a,z hd pdlf7nu3vyv0k+ 262 Hz) and $C^{＃}$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operajf8gk akm )yc7m1p/v c8xx 0fkl3 a,0ites at an unknown frequency. 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 oper,c/)80k fax j03gfi 1x klmkcpyv8a7mating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-14 edfxsla2*wr r l vn+r.,; j.(tmmqpHz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrati1r.qx .wj2 m tvm;+4pr*ndre ,ls (falonal frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 2n *7: v:xj xj 4h8e)+v*id mbymlxxoj/94 Hz. The tension in one string is then decreased by 2.0%. What will:x xlnjbvv 7yj io8)mdhm*/j: xe*4x + 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 middle C (3zc+g+yh0tkc ly*:p(bb ;.b 4ackq co/odv 9o 262 H/3c4hb b+o oz*o+;y yabcgdv.tpkcc :( l09kqz), but one is at 5.0°C and the other at 25.0 ${}^{\circ }$ C?    beats/sec

  You have three tuning forks, A, B, and k50dyx :qfyfjb1sd0gd3c.)y 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 arj 01.yqffygc dxd:5) k3dsby0e 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 per94v znem0 5+:ue/ju;r839ww5 yjs uvljtwbbvson stands 3.00 m from one speaker and 3.50 m f5/t v;9+nwv0z9j urs5 wjw y83 ujl4be:umveb rom 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 f9 3/q -4)k ppxioiukmpiano tuner hears three beats every 2.0 s when they are played togethmo p4ki -p/)fkq3 9uixer. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wa)e)(* x juogb, dvq o(52hebpvvelengths 2.64 m and 2.76 m in air. How many beats per second will be heard?oub)op ve(j2b5xv,*q (g hed) (Assume T = 20 ${}^{\circ }$C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fd.b4 to)tvdsm8g 3m5 vire engine’s siren is 1550 Hz when at rest. What frequency d mtd)5ov4v.ds t3gm b8o 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 t/ n*ewiu-sgh24 .ibw (77mwzvi bxv6 do you detect if a fire engine whose siren emitwug/i 4(.tn*2xbwv me76sz h -bv 7iiws at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hqd wf vb8qa*a k8rr-55z source is moving toward you at 15 m/s versus you moving toq5fr8a 5 wdrbv* k8-qaward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f_{sourcemovine}^{\prime }$    Hz
$f_{observemovine}^{\prime }$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f_{sourcemovine}^{\prime }$    $\times {10}^3$Hz
$f_{observermovine}^{\prime }$    $\times {10}^3$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f_{sourcemovine}^{\prime }$    $\times {10}^3$Hz
$f_{observermovine}^{\prime }$    $\times {10}^3$Hz

  Two automobiles are equipped with the s56kaif :gs/ce-icm ) game single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat fre-gm sa icgc56:i/)fke quency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 ${}^{\circ }$C    Hz

  A bat at rest sends out ultrasonic tr -oj-q4-bog w0o3q msound waves at 50.0 kHz and receives them returneb woj 3 q4-otm-qo-g0rd from an object moving directly away from it at 25 m/s What is the received sound frequency?    $\times {10}^4$ Hz

  A bat flies toward a wa265azmaxm z, n mosv:uee2 621a,ptep ll at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with f65aoa2zs v: e,eup2me np1tm6 z,axm2requency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $\times {10}^4$ Hz

  In one of the original Doppler experiments, a tuba wph+asdf )b/ :yas played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba playeds+p)f/: yhabd the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds fj(f2jmr.t/q . 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 frequency if blood (.qfjjtr/2 m fis flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usi8 9*tqznv7zh9pi t1 irng ultrasonic waves of frequency $2.25\times {10}^6$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 $1.54\times {10}^3$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind veloci.v d8b.vryiodtr3l7-ty is 12 vt 87y.or.rb3 i-ddvl m/s from 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 land ifgva g8deyia8d 2 87aw; 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 sound is 310 m/s (a) Whatpyi:j -ul a;4w4/.o rotdg*dc is the angle the shock wave makes with the direction of the airplane’s motion? jrt- oyl: .;a44wpo*uidg d/c   ${}^{\circ }$
(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 af z)dy)-)at ok planet where the speed of sound is only about 35))a )ydzo- ktf 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. Determine the smbf y 2t*,n t3 95zrufr3qje;uhock wave angle it pr3rb; *q,5y2 fn3jtum u 9zetrfoduces
(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 p jg3( g92ge2qbx;zsjqi9s3i $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead an uh5yo8dv2u0 7vjrwiz4t3u q(d see a 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. See Fig. 12–34. Ddvhj 8ui u3z t5q(0vw47u2oryetermine
(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 sok f/2qe -;nmcr o*t,punar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh -upc;n*etro/ ,k2 fmq water)?    s

  Approximately how many octaves are there in the human u 7s7dq3o44i2bv a +g ifovma(audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. k6fr2(b jbd4fIt consists of many plastic pipes of various lf 2b6j(frk4bdengths, 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 -zfotv5ez b2)pu bx9k9 zjz:7 makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquiz2bvb k:5z7u)e9jtx - fz z9optoes?    dB

  What is the resultant sound level when an 82-dB sound and an v;1f cgw; q8vg87-dB sound are heard simultaneouslv gf ;q;cv1wg8y?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dyhbbb53h ,nm*6az *u iB. What is the acoustic power output (W) of au*h536zb, *ibhb ny mthe speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The jj.k i)bxk2s-power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHzjikb x2sj.k-)?    dB

  Workers around jet aircraft typically wear protective devices over their /14 vkzxhm qvi y1e63years. 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 at a distance of 30 m fromxyv 163eih/4 1k vqzym a jet airplane engine?    W

  In audio and communications systems, thcw)vv6 s s0vf(e 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 tunem7qf qhun -ymuq+( 2my9ga,o3d to a 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 lo ;/aj7*vhq- m4mvz)gs ekg5b y4 (bgeung between fixed points with a fundamental frequency of 44 yhm7vmbe/as- ( 5b*vj4qgz;u k4gg)e0 Hz and a mass per unit length of $6.1\times {10}^{-4}$ kg/m
(a) What are the wave speed and tension in the string?    $\times {10}^2$ 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 vibratipk4a:2gbr .;l ccjwm v6q- 52j7xldgj on above a vertical open tube filled with water (Fig. 12–35). The wate2 dq k-:pg7 r425. lxajjjbwl;6gccmvr level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at on8q5qxi+dc4 x we end and also 75 cm long. How much tension should be in the string if it is to produce re4idqw8 + x5qcxsonance (in its fundamental mode) with the third harmonic in the tube?    $\times {10}^2$ N

A highway overpass was observed to res uu4d7fvuh0. su b)d.gonate 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 5z hvj,vywlxan d, 416on+4 0ym00–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequexzl,v4, jaw+1o nh 6 ndymv4y0ncy 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 t0j9/ 1nxwdrk qrain is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when therkxj910 /d nqw other train approaches. What is the speed of the moving train?   m/s

  The frequency of a stey0 -cl(mssh5 pam train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as l5mc-(s h 0pys486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars :z- qynwp2t+i 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 q-wztnp2 y:+ioctave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, prod72cq8riohq)) u l1bl guce a beat frequency of 11 Hz. The shorter one is 2.40 m loqi1r2c ) qlulg 7bh8o)ng. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pastqtgn1n gpmf,qw 7fc+y6* m:a5 a stationary observer at 1 1, a ywnf:+cm 5qqggtf*n7m6p0 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 speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in p+zq zp8/6rp*n3rksvthe aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultra qpsr kp6+z* z/8rv3pnsound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54\times {10}^3$ m/s   $\times {10}^3$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward eot,qc /:9dm8 r0jtwp the bat at speed 5 m/s The bat emitsw 9mq8tj/ r:edcpot0, a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses 0t2.abo:kelqp+p z 9bas it approaches a moth. The p 0k9l 2zpqpbeob+:.at ulses 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 returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was on: rtq,f iw7d9lce used to 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 Gqfd tl r:i7,w9 flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereol4*3qq m sb+fy listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consis4yb 3 *ml+qqfder 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 demonstratibz90-bu0chup on, called “singing 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,” or9 c b0uuh-z0pb emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $\times {10}^3$ 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 humft6 xn)b5;jj dan ear at a frequency of about 1000;dnfj56 j b)xt Hz is $I_0$ = $1\times {10}^{12}W/m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1W/m^2$ corresponding to an increase of intensity by a factor of ${10}^{12}$ By what factor does the displacement amplitude, A, vary? 10${}^a$ a =