What is the evidence thang f:16tg.4 kgyovc8v t sound travels as a wave?

What is the evidence tha3krf , s0n t-sv*l:,mc ikc6gyt sound is a form of energy?

Children sometimes play ;+f15o qknbthwith a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks intobqof 5h+1nk; t one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency s(, -oc03fqtb0xragg cc9/ uhor wavelexq/9a hcb 3o f stgu0c-rc,(g0ngth to change?

What evidence can you give that the speed of sound in air doekvq ,yl7l0yncg* r+bkr75 0jzs not depend significantby +n*,l0j0cvl7qgk7r kry5z ly on frequency?

The voice of a person who has inp5 lt 0/qt iw4+lj1xkin6:uhshaled helium sounds very high-pitched. Why?

How will the air tempe,hi 963isvpsk lh a:,if)cv2rrature in a room affect the pitch of organ pipes?

Explain how a tube might be used as)yb;9r zoatmvc1 yq+( a filter to reduce the amplitude of sounds inz)o9qy;y1ca vmr+( tb various frequency ranges. (An example is a car muffler.)

Why are the frets on a gui6 e/.vm5ts-b j8 jrwxntar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the brnrjej 6/5w mv-sb8x.tidge?

A noisy truck approaches you from behind a buildingxy5rb6vll-dr mi25 1g. 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-frequlg6dlb r1m 55-ir2x vyency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats c)b zm8c j0lwi0 8rc4tpan be sal0cwzbm)4j8 8ti cp 0rid to be due to “interference in time.” Explain.

In Fig. 12–16, if the frj (f-a5qvap7j3z k/kz equency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther jaa7 q - p5/zvj3kf(kzapart or closer together?

Traditional methods of protecting the hearing of people who work in areas viq b m5xubog686j) n3q6up2p with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound legi bj6o2 pp xm6q58n)bqv3u 6uvels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can .ysxk5+s 9oyu wr 33o1rx*ksxr d,1 kcbe thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two compo s1wy. 3kksory+rux1do5 ,*9 cxsxr k3nent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same eamrh8edx4dg7 cz( g1 6r.2q ndirection, wia z67e.m cd(2g4d8 egx1 hrnrqth the same velocity? Explain.

If a wind is blowing, will this9e1t6 ok +6q91c mu cy (s6asxja,vret alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity change61xyo(k9cs61tc69esjr,u+v aq tm a ed?

Figure 12–32 shows various positions of a child in motion on a swinkx x awq9o(r7r4h81p;x nz b+e;0jg6tanw /vug. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the chilxb(j4n u vpnxekah6wx+9o8rwg/1t ;07za rq; d hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lakzxdf4c(d2f 3v e by listening for the echo of her shout reflected bvdzcffx34 2(dy 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 sides3j-ewo 8 stqh jo.)f( of his ship just below the waterline. 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/q83jo s-(js t o)f.ewhs (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wacfu5 m3xpz/ y.9 b4h9j lc5icdxv(.dovelengths 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 drif3yn fkv-2)bod ting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fisho byfvkdn3-2) ,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when striking /qd6ndi6x)bcthe water belqd /cx6nb) d6iow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to thwqzygnfa 5oc6k q/g 4wi:5.6ae ground, sees a huge stone strike the concrete paveme6/ yacf5qoq :gw wng4a6 k.i5znt. 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? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error mad/kswo 2z0 vgj6ko9*w9 u upz+ue over one mile of distance by the “5-second rule” for esto+ oju*k2ws v k9uu6/pzzgw09imating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 12.tj w,8eoclz 18ifsx /0 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 so1elmq(g)bhx oh9m -wfnk-;k: und whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simul6 j, lplci q,nn8:ntxf94 b8bntaneously at a certain place, what will be the sound level if only 96jx8t,c:4,8 n nqfnnibbpl lone is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an aix pc/0n8anq e,rplane 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 x8peq,ac n/0n intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, wherdumayty:w 2ia2o 63,k eas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the backgroundwuky2toa, ya63 mi2d: noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normak7j hik(gn 7*f38spnml conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a8kmp k h7 fi7n3n(sjg* 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 eargq q9,qzwd a9,drum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, p c18fmg-no)j 1s6q nf6lj9;h6fw fbywhile 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 loudspeaker connecte6 f1m96 nn fbh6c)qjfs8gwpf-j;y1l od 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 130 dB when placed 23teybai2 ;t4g .8 m in front of a loudspeaker igb;y2 ttae34 on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level ofzgow5,iu w;i+ k(uwh/z u,ppr:sa x)3 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amoun ,piz zks /p3u5;awx r,(uu)h:w+wgiot? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factorixi0. f odl+*l will the intensity increase? Increase by a factor of lfii*0 o+ld x.   (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but o b1*i+qagrb i4ne has twice the frequency of t i rb1q*ai+gb4he other. What is the ratio of their intensities?   

  What would be the sound level (in dB) ofu 8o. v)4n8zndu)klkm a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules ofu)m )du k8.84voz nnlk 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have 9r)g a fq -dhk2riw6)kwhat sound level to seem as loud as a 100-Hz tone that has a 50-dB so 2d9qfkr)kwi r6h)a-gund level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when*uhou/r+5mg wph 4bz7 the sound levelo 5rhbp+g4/zm uwh7 *u is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is the ,ab8vxmedt5w755h73l- aohk/h pq d cratio of highest to lowest intensity atphm7ad b35we5 oh5 t/8a ,7ck-vxqlhd
(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. The len,-:6 munj5esu7vfmqv gth of the vibrating portion is 32 cm, vv7n5smu- j,fue6: mqand it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. Wh(5gw,hafs*.k s e/odw at are the fundamental and first three audible overtones if the .ke /s a5*(wghfd,ws opipe 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 frbg m,nqly2p-knprwc 7 9+ b;d4equency would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it r,2pbmqp;n9ywb-l +kg 7cn4dwas a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipxok8:cjaa:/i bg8 7 r gk6nt,des spanning the range of human hearing (20 Hz to 20 kHz), what would /kbax,r n:k8oi6g8:d tgcja 7be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a freqf flwgbi8-4pdi e9;7uuency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered a idip7glwfb8- 4fu e9;t a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to playh yk hf di ;45:oq+dqeq3-+d zbs*k3ee E above middle C (330 Hz).dkf4*ieo z +eqk3; h:+ sqy 3qeh-bd5d
(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 em/nob.w22 rp tme -u*wuits middle C (262 Hz) when the t2w* o bm netuwr/-.u2pemperature 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 aa5si483xq 0 1zk a tz- w0s;6nmqsebs20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute inhy(n qxmzu96 + Example 12–10 should the hole be that must be (+ym 9u6xqn hzuncovered 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 pi h62g. cxbi-7avzkzi:5 :qshxpe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) S qg:xxa7izch2 svz. ikb- :h65how why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at twoyybu0 k3pnvo10zvb-; successive harmonics of frequencies 275 Hz anpz 0 kn -;v1b3oyvbyu0d 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 -e(+rn-wn z0vuqnx+x $^{\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 og,4)t f)w2a zoiec7iuo)gul 5rgan pipe at 20 7lt)cze iagfgo4i 5 ,uu ))wo2$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2a/*8 rtyvaly c1na 5 t8;bnva5.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig.n8a/8y ylv t;ar c1a 5bav5*nt 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when try4r4 nu8/ nxdhming to adjust two strings, one of whicx4 /rnnh um4d8h is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequencak(a .y.wbs-+azw et1y if middle 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 operates at 23.5 kHz, while another (brand X) oe*vsgxb)bziw+x14 (0 qkk r- xperates at an unknown frequency. If neither whistle can be heard by humans when played separ sq)+-ix0 ke(1 grzk4xb*vwxbately, 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 a 350-Hz t ,n3bm/59;9nw6c pbrig tplft uning fork and 9 beats/s wh,pnct igtm9p3nl;b95wf 6/bren sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequen- :lsx.yr; coocy, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard wo;x: olrc.y s-hen the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be he) xtk uq5m.0/vj cz7lnard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C akx. /lvn0) z7ctqmju5 nd the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C+lm8oe7 cco3jnau1(wo *-f b 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 when A and C are7 o(e n*o c1o8uf+ba3-wcjlmc 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 fromeq2 ms nda+*7(hbzz4c+ ave 8d one speaker and 3 aze+bh+(s2aqd mn ev8zd 7*c4.50 m 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 z.a.hbti 7 i*wpiano tuner hears three beats every 2.0 s when they are ..athz 7iw i*bplayed 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 soundsi5(ql /5u yky of wavelengths 2.64 m and 2.76 m in air. How many beats per second will be hy5lqusy5/i( keard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequenln(0 ay k:i-gxcy of a certain fire engine’s siren is 1550 Hz when at rest. Whai0:(ylgnax- k t frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What fr9b)5h r9 cdjaoequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/s 9bcdj ha o95)r
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 200a7ok+8 v4mn.tdlv, ga0-Hz source is moving toward you at 15 m/s versus you moving toward it v4 mn7t8a.l va +ogk,dat 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single zb 4h1g4,d bjnfrequency 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 frequency of 5.5 Hz. What is the frequenb, z4 h14djngbcy the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz2c2nv xv )u)zmxp2 ke55a9ezl and receives them returned from an object moving directly away from i)mxlkc zx e2zeap)v n559u 2v2t at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an ult8kj 9 c.fwbg5arasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wg9 8bcfaj .5wkave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flat t,s s)uavqz(zr o/4+jg rain car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. Whatq zs4 za u,vs)/gj(r+o 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. Suppose m0olvwg )ko21 the device emits sound at 3.5 MHz, and the speed of soundw ko0om)21 vlg in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wavesm4kio2+gkpe0 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 6(h4;dak k qpjdr--ghHz. When the wind velocity is 12 m/s from the ;-g6 4jqpdkhrd(h-aknorth, 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 if its spe2 oxww4)e d7nes3j i8.eoii -ced 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 whe ii p.mppc,f:3re the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’p3.fip:ip ,cm 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 atmospj o1h6tpu *l+/m +3pqfda7u;f en+f tdhere of a planet where the speed of sound is only a nhu /al +d6+p;pu73tot+f1f* jqefmdbout 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. Determine the shock waaipuo (f );/mq z9h8qyve angle it izfpu9qo8;m/( q yah)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 oky9ps: kh bf1o7;y)9p3ljbt $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the ground flyibl2;nj rl:vh*b +o+q9f s *sding faster than the speed of sound. By the time you hear the sonbns:j 2+bof*ll;+ ds *iqh r9vic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20i-pp;w4gmwi/h s-3 lv ,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If wp4ml -i;v ghw-sip/3the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible rqr)h;smzu .y4 t me vl(47cq2yange? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe shg5ie5 +hh cb88rxg-4 git,keymphony. It consists of many plastic pipes of various lengths, which are open on bo+,88 gti- 45 rhecigghhxek 5bth 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 the threshold4sabvxpy bs 1-*fcfx;pe;51p1emx0j of human hearing (0 dB). What will be the sound level of 1000 such mosquitoes?;-sx5bys c; p1 4japfem*011vex xfbp    dB

  What is the resultant h mljvoi65nf9 fe q2e)+ p/oy4ydgr:+ sound level when an 82-dB sound and an 87-dB sound are heardf) r+ vdny:ph65+m o/le g 42eq9yjofi simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What i1gr m;jqr6k+cs the acoustic power output (W) of the speaker, assuming it radiates equ krmjrq+6g1;c ally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power qkuwpg v7y v/0c:2p y*output drops by 10 dBypwp2*quv g:vy7c0/k at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear prote h3m2oulvgt:9pu) ) oohrs3v *ctive devices over their ears. Assume that the sound level of a jet airpla oh h)vuv 3op9lug*)2rt3 m:sone 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 from a jet airplane engine?    W

  In audio and communicatwxhn ds6 kt+.)k1nr.qz3li l2if +9 jhions systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequen2a4 /2gc in-com leih9cy 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fkyl* ia ij1,k2undamental frequency oyiiaj1 l, *kk2f 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube fillc0q:lu e):m1pho+zc87rcojz ed with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again a 0cpo)7 +rc8h ::oueq1mcj zlzt 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string oa57wfr.45tn2 k7bzxt; nv tjg f mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmotbanft jg7n5k2 v.z;5t7w x4r nic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fullw x-4/ezhlsf+ 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 thes7tvuefomz4rr:ke9j; x qc98rid.* ( 500–1000-Hz range coming from two sources. The sound is loudest at pcd;t7m(r9rfxo*s erj: 8vezq4k 9 i.uoints 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 of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductob6hhoa su8 fw-v/fs9 8r on the stationary train hears a 3.0-Hz b86bf ss 9huawhv/o8- feat 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 is 538 Hz. n8 jl*4 (gvtunAfter it passes you, its lvgn4tu8(nj* frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of 1 kyega;7evr1cars just by listening to the difference in pitch of the ek 7e1ayergv1 ;ngine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding togeth/ (4w(qmtci txer, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long imt /xwq(4( icts the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past jhh jp:8x8z zxyxi33: 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 t:xh8pjxj yzh:z3 x 3i8he car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what beat nw6 hl7wxw.zgknu3 h) 4: 5dwycy3lp/frequency would you expect if 5.50-MHz ultrasoundwh:ln6pu3hw5w)ngcd 3l /4.7xkw yzy 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 flying tuzpl )cv 59bs0oward the bat at speed 5sl0)v 5 zp9buc m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pueed0qbv ogu;1a:e6u4azg. . klses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long61a qb:vdze 0aeeo.k;u 4u. gg. 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 ammnpr1o gv6t;8m .7n. 12–38) was once 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 G flat) horn. What is the fundamental frequency oant.m;1 mvg8onr7pm6f 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 comprolg/:6pxm xjv/mised by the presence of standing waves, which can cause acogmj v: 6/p/lxxustic “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 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 s393 yu utt (vel13obka long, slender aluminum rod held in the hand near the rod’s midpoint3teybuv3 1s9(uklot 3. 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 h ljbe- aj7t5k6;+kpcd earing for the human ear at a frequency of about 1000 Hz dp5 ;6bj7+-ka tckle jis $I_0$ = $1 \times10^{12 } W / m^2$ 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 obr .mp i:kvrs96server on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. v: sr. ipr6mk9What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbv :ij3ada2 pg7u .ipfe-d9. sdoat 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