What is the evidence9 .bv-wk q.xz*z4c chd that sound travels as a wave?

What is the evidence that sound is a form oai9 .q;qsafl :3isk8l y*do)of energy?

Children sometimes play with a homemade “telephone” by attaching a string to thejg07uowr fg v:i 1w v2(qbgh+/ bottoms of two paper cups. When the strwggi+bf q2 ojhv1uvr: 0w/7(g ing is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from 8q7muyzslumm9. qc(k 7)iw7 oair into water, do you expect the frequency or wavele7mm yw98muiuz 7 (.skc ql)7oqngth to change?

What evidence can you give that the speed of sound in air does not depen mus5a/2j8evn dj)p+sd significanjasmj s2/+d )enpv 5u8tly on frequency?

The voice of a person who has inhaled helium sounds very high-pimw*,jy0g q9sf tched. Why?

How will the air temperature in a room affect the pitch of organ pipesylp;q 1 ngi1v6v 3tie.?

Explain how a tube might be used as a filter to reduce the amplitude of sounds vs.) yr*hnh u.in.)*. hvhruyns various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–3bq9szt; ri4u5i06 +x9faoq sc 0) spaced closer together as you move up the fingerbobq rf;tcs x+ 5z0uq i9o9sa46iard toward the bridge?

A noisy truck approaches you from behind a buildinvqxxedha6 (z :ev eae+5/d 0g8g. Initially you hear it but cannot see it. When it emerges and you do see it, itsvexeqg+ hddezx e(/8v65a0 :a sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beadc4/wxnv *h: gts can be said to be due to “interference in/v w4d:*hncgx time.” Explain.

In Fig. 12–16, if the frequency ofvjh70z-jnr(1:k g: tuo,y boy the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move fartherb:tr-j1( v:0ju okzyno ,7gyh apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with d z5umm,8dk1em f)y,7cl dea4very 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 dev d,eua)dmdz57 c1 mleyk 8,fm4ice is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31) ;2r;iij9h d- pn0az k:klsuoyx io.1. Each wave can be thought of as a superpp)d9s- 1n;:i xa.hoz0i;u ykjlr2 oi kosition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in vc h)rj)5z9pj the same direction, with the same velocity? Expvjrp 9zhcj) 5)lain.

If a wind is blowing, will this alter the frequency of the sound heardilkf8l50+xt t by a person at rest with respect to the source? Is the wavelength or velocity chantfi +0l5 x8tlkged?

Figure 12–32 shows various positions of a child in motion on a swing. A mon2mrhps+ a/erw ,*f:zfitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sou+awpzf s m*r,:er/h f2nd of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the ei+ 2 q(8bxcw bzjprz3w4h-/lpcho of her shout reflected by a cliff at the fawp zbhbrwc-l2q3pi z/4 xj8+(r 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 y 3t1dl2y7v 1bag6 /n:oqlcjdjust below the waterline. He hears the echo of the sound reflected vyy1dn1jb2a:37 gl /6l q tdcofrom the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveleng1z a(pj8i-a)3mvaz* lssx6gz2e,5o z upaih1ths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school kwdv -lf69 4)y maan :h;q)lrtof 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) qrh6ma l wat; :4)lv)9 fyn-dkby the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff,vk8g i0pqvh3mc1 ol0. The splash it makes when striking the water below is heardi,col hg 318pk00mvv q 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strikz7ds(cu//e mte the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far /ecst( /zudm7 away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distaw.wm;/33)rxnu a1tiy5 ye h y3ck gtw6nce by the “5-second rule” for estimating the distance from a lightning strike if the tempk6xc /aumw wh3tr e3g3.i);1nywt5y yerature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sout j u ea9oagmy6-ug.4zk.69mdnd 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 whose 4crfs 1l ,r8 9ecwkrt4intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level ofa+ - vwu9vhlc 92j g6ny5b2gxg 95 dB when fired simultaneously at a certain place, what will be the sound level if only one isg- 2nva9l cbgg65h2xjvu9y w+ exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisjv. /j (vd0nt9vp3sqyy 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 intensities, n9jv.jdnpt /(s 0vq3vyot dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, g,efy si:e8bz 5x - xfv+5:2dmga r:sxwhereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the g8fxdie: m,::5-e f xrsvb2ysagz+ x5background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking ix e bj/v -vesley60*h5exw5l5 n normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered onw56j 5*e5ey0xl-xe lesvv b /h 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 st 0gjvu n4(wto8rikes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modes9nh w8bjuns8(t amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m fromu 9nbw8sh j8n( 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 1jy br; 4oz2gei7a8w t430 dB when placed 2.8 m in front of a loudspeaker on t8y7abti; jge2ow44 r zhe 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 of 2.0 o(mildi, (-p fdB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hinolif (( ,-midpt: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tri.wf8f)3kl nau;wmpj q tb.-*lpled, (a) by what factor will the intensity increase? lfq*-l wmnkb83wa).; t.p jufIncrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but oop;9)jr0g 8wybyhm2one has twice the frequency of the other. What is thw2ymj bg09);oo8hy rpe ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corru(v4t*)p++4p rv q5 vglmczkoesponds to a displacement ampl(5m +g+ v tokrvlppuqv*c44) zitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have(fs*0zh eajxj(ri2 x-r 9fzc5 what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–(rc-z*h a09fs er(j xi2xf5zj6.)    dB

What are the lowest and highest frequeeq.ts x .k;mbhaef/4a ;7y9ikncies that an ear can detect when the sound level is 30 dB? hy4;; b/sax.a9et.k mi feq7 k(See Fig. 12–6.)

  Your auditory system can accommodate a huge range ;k 0nar76a m ndu01yddof sound levels. What is the ratio of highest to lowest in 0naak17d06y du;drnmtensity 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 fr/zw 7deye. ub*equency of 440 Hz. The length of the.wdy bz*/7e ue vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112h5kedzh9o vb8*pk17a cm long. What are the fundamental and first three audible overtones if tpe 97v1hdoh5b* azkk 8he 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 yp 0es9ha+ s(biu6dt22motsuw:co +uk216d azou expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tu2t 2tuddeu 0 +b 92cuki(aoshsa 6+6zop1m:w sbe?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of hu*uptkf zl,/ +wl8wbq -man hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requkzqf/,+w bw 8t* plu-lired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. *1 t.lmwtc*bio5 5mysWhat will be its fundal .t*5cm1ymiw t5*osb mental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m lvy+m ,k+rv qge;jh4/nong and is tuned to play E above middle C (330 Hz)qvg y;jkhn,+4v/e+mr .
(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 pi:l l*:3v qz9c l2uc1bx3qcc pcpe that emits middle C (262 Hz) when tq 9vlpcz clu:1qc2cc:l3*b3x he 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 at 28y)o5.- td ybjsh9m,yi drqc30 $^{\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 shoul k6dqdfce6j7/d the hole be that must be uncovered to play D above middle C at 294 k7q djedfc6/6Hz?    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 Hitl u9hp e(/l.z, but not at any other frequencies in between. (a) Show why this is an open or a tu9(hpei.l/l 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 yx+iqmt*: xmd6*(wda open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is **xw+ d6t(qm d:xymai
(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 xt57e:*tyega5ak:5-kew a xu$^{\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 range4anrd. 1dwfu4el ao76.1d/ l 1v5a3hazcid p y for a 2.14-m-long organ pipe at dd u.wc hp4yalfrd4o5za1i.a6v1 /7e3 aldn 1 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 opena9ngfnl2: p+ y to the outside and is closed at the other end by the ear ag9n2:y+nl fpdrum. 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. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tryingam2s u.t++rz b to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is thmtz+b .2+a sure other string? ±    Hz

  What is the beat frequency if middle Cx+q+gx2hg6yqmqi c;;y(x 2zulzu a * ( (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 ea:k6gmf , 6uianother (brand X) operates 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, estimma6fe k:iu ,g6ate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded (imb l *z,yk2wwith a 350-Hz tuning fork and 9 beats/s when sound,m(2b ylzw *iked 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 sa*zjpbhofhy. +la9+d2 me frequency, 294 Hz. The tension in one string is then decreased by ho2hy b+ .dzl*pj fa+92.0%. 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 5v-,payd f xri+r3eyi/8oc(h +d u1xgplay middle C (262 Hz), but one is 8 i ufxr-+yxrgvi5h1 e/+yodd3 a(,p cat 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C*4 ydx-+gew mzj7i t,f, lulh,. 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 b4z7w,elf+ gy dtj*, xuh ml-i,eat 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 apa -n,:r9(wcs2jrofrkcd. t z3zrt. A person stands 3.00 m from one speaker and 3.50 m from the oth wdfz,c.onr jtr29s: r3ck-(zer.
(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 suppo ;:hwy opt(ig-b6c5d rsed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the othe-y gro ihc;:bwt5d p6(r ?   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 owrz-(yoa8b-if 2sf: trk)b bjz9(w0 t f wavelengths 2.64 m and 2.76 m in air. How many beats per second willyr )f( 0az92ft(bbsi-8wt-r ojwb z :k be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1yg1(0i7 wxupm 6og1 eb550 Hz when at rest. What frequency do you detect if you move with a1i0w(x1om geb p76yu g speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire ej opt(-w 2*orsngine whose siren emits at 1550 Hz moves at a speed orts2o(o w* jp-f 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you c)o(s in )1edlhwca)j:i( f4g at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? A 4:ih cwie(sodnl)1cgj( ))fare 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 0,;ch 8cjfto by. *q( csu8hxpsingle frequency horn. When one is at rest and(8u xbcyp.hfcq8 ;, st0c*hoj 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 frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends qveb7ej-v04 ,unow -wout ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What i7wj0vq-v -we4 b ,noeus the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it fli n8 s.avdg+/bkes, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What +v8b.s/nd kgafrequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving fldvpsr2 vh;p/d o,noca 3:g9i 0at 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 thn/op ;r vgs02ih3da d,cv9 :poe train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter7qi9azx*m(y khgto2o. uh,o;e 4+g f e uses ultrasound waves to measure blood-flow speeds. 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 is fyhoio9e(zg2.x k4mq gh;a *+o ,7efutlowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequenihu ggs1/l 29tt-ot :vudz(3v cy $2.25 \times10^{ 6}$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 emitjg(-+ ioja waj9yun,ql(* lj; s sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observeaq+a*lj(wj9;niyljo( , -u gj rs 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 +s;hbf9 4ser/7sjrumet +6fcmoving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Macgvfbz+3h q+(o h 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes o3 bqfz h(v+g+with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where qpr jzlx ,w92 evh*bw6 x:7oy(the speed of sound is only about 37z lbj9(x ww ,ypo2:heq* r6xv5 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 sho2w9)qoh z1c)s 0 tolxlck wave angle it produces)1hw l2o0q x)s9 zclto
(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 h rx3nqd0vj6 clty0gj41 c:8n $/theta$ 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 ec( yi 0lo,ighl1/8s othe ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has 8i l yiceo,gs1lho(0 /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 n4e)+m7yaz* eek9 tr 8fc1 pzosends 20,000-Hz sound pulses downward from the bottom of the boat, and then dkfc7o1ey 9 eznp)*rz+4 ma8e tetects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how manyfroo1 21c+ t)ex vvb,9x t6viiqax00m octaves 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. Ithymnuz0dnp(+n *d, n* consists of many plasnpd*m,hz+n 0ny*d u n(tic pipes of various 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 the thres t8)l sjund 9k6 pmua3/y3*tsmifnd (+hold of human hearing()df9sk/ty3 t3i ma8n+u umplj6sn *d (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound lccnvs8 8 l*inc aa/s o(+8- fitn8l3afevel when an 82-dB sound and an 87-dB sound are heard simultaneousllvla n*n -8i 8 co+fci/aft38ac (n8ssy?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whbftqc n+r3 6.6r8zn yrz,ks +eat is the ac.8 r6re f+ b 3syznq,cntrz6+koustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Thzzp1q .hx-/dde power output drops by 10 dB at 15 kz dh/.p 1qxd-zHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft ty7b82 )cx0nnvmq- regr pically wear 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 enceq r)7gv8nbm rx2 -0ar has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems,sy9 wg.f0a*xg.j2 zs e 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 :/qv4o ua+;vxsvl d+ zto 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 vi;/4wdyu1d 6zll3*.wysl fb ysqaqj3 ; olin is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit ld3. w1q z6l y43 /y*s;alulbdf wsy;qjength 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 opjsnhy ; fv/0gu)a0lw)en tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and a00/fs;gvlw)n hyau )jgain 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 agjfg3 :).ccc7nj( vyb 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 modvjj()y cnb.cc7 : gfg3e) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed r*sfv(4g5 oaz to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 56;x(;(iz m 2.xwzb oxi8nslvzw+2gfbhilz- /00–1000-Hz range coming from two sources. The souwzl(8 l22h-zi(x s6in i;xf+w ;xb vz gz/obm.nd 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 of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationarefs r)qo.d5wd,os2 a q0 +yvj)y. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train ay) ,5 fs ea.+wqdoroqj0vd2)spproaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Afterth*1 drr6,o etr,h*s5behx(5rhiq l: it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume conrr5d*(6,he : tlh* rot,rxhqeh si 51bstant velocity)?    m/s

  At a race track, you can estimate the speed of cars justbx3zmlfd9s in874i(x;u q r7w 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 straighta dw4xuz3lnmi(r f7 i;sbx 97q8way. How fast is it going?    m/s

  Two open organ pipes, sounding together, prod6(/ti qx )dvosuce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the /i )d(q xotvs6other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a6: zo6u nb0, pqege7qh stationary observer at 10 m/s egqq u07n zhpo6b6: ,eas 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/s what bea3scp7i y4o x-yt frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the rx-sp i 4ycy3o7ed 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 whih2dw15sub-z b le the moth is flying toward the bat at speed 5 m/s The bat emits a sound wavsbz 1d5ub-w h2e 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 as it approaches a3h+,zj0bst-ui0 e fly dsm)l- moth. The pulses are approximately 70.0 ms apart, and eh d0-, y-szule lsj)+bm0 t3ifach 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) wasxlqaxb9l(e*qj*k3z5 t:l.c rgl 20 i u once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns we:j093iqz be**al r g (ckl.u 5lltxqx2re used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listeni n;:lk-ig: sdt e*smdouc:k42ng can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m4g tdk;o :2ui c*m-:dl:nkss e 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 7be8jevb1a6t09/bsad7 )uojjw5 kov (nq8j ja long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked b798k 7du b6bv0w8va1 oj5saq joejenj(jt)/with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the huzh1x240pu bi pman ear at a frequency of about 1000 Hz is 1upzh40 bx2pi $I_0$ = $1 \times10^{12 } W / m^2$ 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 ; rjc6f 7g:- vlqqv6zlzo0gd3hears the sonic boom 1.5 min after the plane passes direv:l jl7f-gzodq;zc r6360gqv ctly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1) r.efxt-: hqe5 $^{\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