What is the evidence thi ram1 oc3b,t/,vkj.yat sound travels as a wave?

What is the evidence that sound is a form obes m9t:3+hn ef energy?

Children sometimes play with a homemfhob7u5rir /(z 8 y5pwade “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. 12–29). Explain cle 58 5iu(/o7 wzrfhrypbarly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you ee:vxr 47o.nr15-r q6 gnn walaxpect the frequency or wave. nrqrrl-e5nnxwo4 g1va6 7a:length to change?

What evidence can you give that the speed of sound in air doexi */k ft6nr*v9 wti;zs not depend significantly onf6z9 i/ rt;w*kit x*nv frequency?

The voice of a person who has inhaled helium sounds very highnjo79l6/5ipw7i iw em -pitched. Why?

How will the air temperature in a room affect the pitchas3 gq7qe 3ovz7tq0e* of organ pipes?

Explain how a tube might be used as a filtewi; 1bt-gk5 3otdd-itr to reduce the amplitude of sounds in varioo -d3;-gd ti bk1ttw5ius frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 1z0hk qai4 br5-zj +beuz )(5ry2–30) spaced closer together as you move up the fingerboard toward the bridaz(zbhb-q4e5i0zur+j5 k y )rge?

A noisy truck approaches you )0 5de09ix.:ml9 c ,afape 8ytirkmjafrom behind a building. Initially you hear it but cannot see it. When it emerges and you d 9,y8 kjlidaxa5im te.ma re)pc0f09:o 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 c 5o9tg 0 ej0c)cuko)nto be due to “interference in space,” whereas beats can be said to be due to “interference in time.” cgk)0nuce95c o)t jo 0Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pn5d5(h 1bllu/ wn dvgema4(- yoints D and C (w ldlw5u5(-avhne by( g1 n4md/here destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people wh upz -qe 8/mr 0tfs+ctvdy44x7o 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 additiondq+u rp8z v4t7emy/t csx-f40 to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waveniu 01de:/ 6jruse (fus shown in Fig. 12–31. Each wave can be thought of as a superposition of two sos e(/ eu0:rnj1f6uiu dund 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? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obsemql(rt l4 hs6,39iuuwi5yt b*rver move in the same direction, with the same velocity? Explain3ys65miuhtuqt ,*9bll(w 4i r.

If a wind is blowing, will this alter the frequency of the sound heard by :sscjnr/-5rz(nzlg q 9,tlw u4 1)tlda person at rest with respect to the source? Is t4jlsnl s5run )-9rw z,t :d1(gczqt l/he wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion ee, wjmsg/ u/73/pf.kuwxn +p on a swing. A monitor is blowing a whistle in fre/pf /,gs3uujpm xwk+/ we.n7ont of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening7ms + v(tp)qg/secjfv;kjz ;8 for the echo of her shout rev ;zepj cv/7s +jg)qmk t;f8s(flected by a cliff at the far end 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 waterline. He heavnvp1 e5cm t*9 /,bmshrs the echo of the sound reflected from the ocean floor directly below 2.5 s later. pvst9cb hv5,1 e*n/m mHow deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20 jwg6z8vxi0c r2 4*d np0dzmy /b l8t.o$^{\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 above a school o s0u cha/:dpou7p8.qif tuna on a foggy day. Without warning, an engine backfire occurs on anotheua/ up8dio7 q:p h.0csr 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 strikin / akgvuqj9g75r- nnv*g the water below is heard 3.5 s later. How high is n7/rqavk*ugv 5-g 9jnthe cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concret ujujc k7db1f435z -6 dkwifl4e pavement. A moment laterkk-wuf i7dfj6zul 454 1djcb3 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.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile om6(j(, nnpt npf distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) mtn,p ((6nnpj 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of ahr.u v;x,4zva x)c7ema 4 vj2p 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 sound who,y*hnaq5gm 4cse intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when hd g2.pdcx l8 /sl9mq;fired simultaneously at a certain place, what will be the sound level if only one is expq 2hpcsmgdl;/l89dx. loded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy jedho4p8gg i()k9eb3djm ;ut*fb6b 3 lg t 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 integj 8f d9;lbubok3tei(gmh6b 4d g*)3 pnsities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, wh r/ f-x54epcp3;apewnereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device?34x nr 5fae /;ppc-ewp 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking .0k0s gce2xc vin normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mvc2xe .g0 c0skouth. $\approx$    $ \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 ox3shrp4ov 21an 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 a067 w xf/-jzd dj.oovit 250 W, while the more modest amplifier B is rated at 40 W. j0 6vw dz/oo.jidx7f -(a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered m1bj hbjyhn/g8v, k 3*130 dB when placed 2.8 m in front of a loudspeaker 8, 3bymhnj 1jbhkv /*gon 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 detect a diffea tz +.dz d- h3s d1p:xdmc.1xff8do:zrence in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amountdx3. 8o1 d pzf:fcdd1 xhms-zza:+d.t? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by kya ki alog -(2gq;yx3orji90pgh +(2 what factor will the intensity 92ayo( 3 gaygr;(0lkkq pxg ji2h o+-iincrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplg a++t0cafina88 vn4j itudes, but one has twice the frequency of the other. What isn0a a8agcfti+vn+j 48 the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corres-e ;k/k 1;p -i5gemna:fksh dqponds to a displacement amplitude of vibrating air molecules of 0.:aqm- hekdfn /sgikke- 15 p;;13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sout8j ylp 6onffu7//09pnwr+ah nd level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (Seetwpnuya+lfp8rnhj 0 67/9/ fo Fig. 12–6.)    dB

What are the lowest an4 u7 rbf7u07vyk6ufmtd highest frequencies that an ear can detect when the sound level is 30 dB? (Se0y67kuumbvtf74 rfu7 e Fig. 12–6.)

  Your auditory system c tmqo0b3xu w r3oocv; nf.9(2yq ycl+;an accommodate a huge range of sound levels. What is the ratio of hm.ccbx ;nf09 3o( 2vq yul+oqy3t;wor ighest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental freq/;t)sxl g 6wgdm-dnhftv4 9 r,uency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. U6 gdft) s,vgn 9dtm4xw-r lh;/nder what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first thiq5c+(gan4 ma o ijj;0ree audible overt g0cj5i(na;i 4om+ jqaones 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 expect fromu.4pzq 1jg2 otnasr0)t6xi p 6 blowing across the top of an empty soda bottle that is 18 cm deep, ifo6u4)sr .inqt2g jpp1 6txz0a 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 wi4gqw*fj6 i,u:tj(pgwshp , ;pth open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes re,jps :,upghji6g* ;pw4fw q(tquired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequ +/x31ibymjc -xvc 1hsency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its origb1- 3m x c+xhsvc1ij/yinal length?   Hz

  An unfingered guitar strin+ 3mzx(hlw s e+w8wbo/ 6cyg4lg is 0.73 m long and is tuned to play E above middle C ((8c m lw+/+lhsbe ow y6w34xzg330 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 th rjngmg k8r /3c6:3gooat emits middle C (262 Hz) when thek6r/:m3gg8oo3 ngc j r temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune /xlk)8a t.av z9b(d ezat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flu3) ehc1a) b1b)9zit rtl -oqpjte in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 Hzct i)93 le) p1q r-b)1tojzbah?    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 Hz, and 616 Hzq5u tlrdu8n;* , but not at any other frequencies in between. (a) r n utlu8;dq*5Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long i kf28/y8achtubtujrr8 : jr 7+s open at both ends. It resonates at two successive harmoni+auy t:8 8t7/kb rcf2h8jrujrcs 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 8j+rczk /f nv,j k.on i0u ;njm pie;z,,84wct$^{\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 organ s6t c0hq8u q7ppipe pst068hu 7qqc at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to twgwn4 / aaq6:che outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in q4 awgc:a6/w nthe 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 adjua/*8i bv/ffjb wx; f 9ver5g2lst two strings, one of which is sounding 440 Hz. f bi/ /f lf8re*wajgv;59xb2vHow far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle h9 1yzv 4q uqnk1jpcyyjie+-,luxd4-(l l2z 7 C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operi/.;pz)arfr ne 9b6n(/j kppnates 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 sh/n(f r.npz e )abrpk/;j9i p6nrill 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 r27shy 0 rbsrkmvatjjcya2ztzp.v- 889e*7+a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is7kbt+8ra 9czjjeh y t2spm0vsyr rz8v2 -.a*7 the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same freongno57 yn1mn7+ )botquency, 294 Hz. The tension in one string is then decreasednog7tmo1)o +nnby7n 5 by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to .c +1 9bwlyj wujqhquto8,-n7play middle C (262 Hz)cuw ,tljhw7jy81qb 9o-qn u+ ., but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning fork2s)(sktg2,+vbih /5x cddq jas, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible s2dkxs,th)bv5 +dgc q(/a ji2when 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 stansk3t m84 gzc33 )ucrknds 3.00 m from one speaker and 3.50 m from the um4nct ) r c3zk83gks3other.
(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 c(ub 8n(y2 japvmp4 f 4- 1aydkk5eaa+vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they ar2fmeb1duy 4ynp8+j(ck p4-ava k a5(ae played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m 6 emz g(5:p8r vyou:yunu /h2yvmci.5tb+:usand 2.76 m in air. How many beats per second will be heard? (Assuu6o8uhts+ev5::m r mn/by2v 5ycu(.ugpi z :yme T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is yz)9gib* kvz1 y ph 6lsdv*77v1550 Hz when at rest. What frequency do you depilgyv*6k* 9 sz17y) dvzvh7b tect 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 det c .3uu5pp/fvoect if a fire engine whose siren emits at 1550 Hz moves at a . fc5po3vp uu/speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sours1-s115ma y9 il4od olmg -xckce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are mli9k5-cg1-s1ol o4yd1x asm they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequen/9uuhj4 at35h ut:ayr cy 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 frequu5 tyhr:at /9 ha4uju3ency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound6bi zb:v-stj8 waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25bz- :tj8svib6 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speeuhm 1beo9xvm05k gk*9 d of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What9m0v5h eu9gk1 *xbmko frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler 5slo2eeqv9qbp 4rn *k z :4ylz/2vjz4experiments, 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 train car approached the station at a speed of 10 m: z442y*5evqlz zelsn/kvpojb4 2 qr9/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure343 +pbqxo bzl5 fh r01,gqjtx blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of so3h +01fg3q 5zr4lob jbqt x,pxund 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 ultrasfl i:7u4v sg*te w.4msonic 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:71fn 1cuxh1a)o;a:;c9bsa o bh uuwi 570 Hz. When the wind velocity is 12 x)7uub :u;s9i wf1 a c a:cho1hona;1bm/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 i oj13pj6 q*ty.3mdklre6ets6 f 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 Mac ; w07okf;k60zqa )z2anwpevph 2.3 where the speed of sound is 310 m/s (a) What is the angle the shocf7;pew;qzw2k0z pv0 6aakn)ok 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 whmmmt-g0x 5) oux9acf6phu (-bere the speed of sound is only abougm --cmxaxf9u 5 bo up(0htm6)t 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 +xy,naitr8 u o6(arp s0-ze (xstrikes the ocean. Determine the shock wave angle it produce( tx6 n,(e0+sprya- r8ux izaos
(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 zfl r.c y8y5j yb+ig.-$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and s*h7+fxs ;lz zhee 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 hlz;s* 7h+hx zforizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-ps0tnr0mj4j ynh.r i/ 1 yyj-6Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for whichtyhsip y. m4rj0-ynn6 0 jrj/1 it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many oct-39v *10elenuab bstnaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of mi4cb -,9i36nhv zrsas/k6peaany plastic pipes of var,rzb9ia -3civ6/ nash4pse k6 ious lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to th;k))b3dflb gye threshold of human hearing (0 dB). What will be the sound level of 1000 sub;kgd f3l yb))ch mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sounde n,5 vj- 6+acmtlndb- are heard simultaneousln+b5 naj, v --eml6cdty?    dB

  The sound level 12.0 ms2klexb x20xj7 mbnx 21gs3r0 from a loudspeaker, placed in the open, is 105 dB. What is the acoustic powx skxg0 xnrbl21es 7b0x22m3jer output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at21 8pg, ccumaa 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 28mcg acu,ap1kHz?    dB

  Workers around jet aircraft typically wecxa4r 4rkz2wij3d6u5 ar protective 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 u62r xjk a ridc4z543wunprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems,eli.8 hhhr1n d.3g c,,mrivf, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequency px+5tre8ud2 a1$\frac{1}{2}$ 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 bd pwbn;p;kx nc)r 50ne9mzgt3qx2 9t9 etween fixed points with a fundamental frequency of 440 Hz and a mass per unit len r;px9)2tgme0n ndtk pnzqx;b3w 9 5c9gth of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tubvxud/ tp 662e, lqkb.pe filled with water (Fig. 12–35). The water le d6,/.vexkpptq6l2 u bvel 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;x ovq8jv0+je .10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string 08v+v ejjo;qx 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 onxrgv/j) kxuiv 6217wm4xgvq )e 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 503-: chrh04kb o xjztb30–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves 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 3tbhxb cj o:kh0r4z- 3of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. Tvqj zzv/0zph . 7wb+d1he conductor on the stationary train hears a 3.pwq 0z./d7hz1zjvb+v 0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you isbr6gp.r7gbai y4 38x vg u(6uv 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train movinr 3g47b .p8gxvrb(u vygi66u ag (assume constant velocity)?    m/s

  At a race track, you can estimate the s,yqhi o*yq9 of7i yu);peed 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 goes by on the straightawayy,*)u q7ioqyh;9 yfio . How fast is it going?    m/s

  Two open organ pipes, sounding9tu:i c0r0j-8y uk*zkdazim / together, produce a beat frequency of 11 Hz. The shorter one iskiizd-8 0:zr/ a*u0my 9kcutj 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves p s.dkdt7q4)cuh/ (nmxast a stationary observer at 10 m ncd7mtq/s.khu(4) x d/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 the aorta is normally about 0.32 m/p(ssspxl -zu(7a1 k,es what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travelkxpa sp( sesu(,z7- 1l 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 fly8aak *j:xn,ds ing toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of j,nx:ak8 *das the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as iy-t8 i3u yhg8 ,1t6cl; mvfucjt 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 b1lfth 8g-mty3;ujc8,u6 cvi yat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine sp9 y.gf;v3mdw7y fk1village 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 tv 3g79d1wf ;k.ysmy fphe 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.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presen1d95(9svevp0l im(wngry lr h2:y *p qce of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamenv*q59(d y w1lhersnr p( ig09:lm2pvytal frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration,;w +raqqvb 7*uy c hsi6o*mj,im+h1g ( 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 ua bv+gii1+jcrw,(7;6qy*mo s*hm hqmade to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear ad3t ul0jchi9 b(:o i*so 7ym)tt a frequency of aboml yjco )ht(9*is 7:t03udb iout 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 hearmmcv2f85cc ) n1xo7rks the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s alfcoc1rm 25n7x)mv8 kc titude?    $ \times10^{4 }$ m

  The wake of a speedboat2m mp9+g x9kp3xp:z iu is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h