What is the evidence that sound travels as a wave?hw ny8qyfyqe-;p k1n 0hv 0z7*

What is the evidence that sou3ar*djz67-/ xr1jx d*u 6nqoxlwyz0 tnd is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to thhzwz 39rk7y dh+c2;b ktwp52k0mk; nfe bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave tra2zktf5kpwdb9kc 02m ;knrwz; hh 37y+vels from one cup to the other.

When a sound wave passes from air into water, do you efj(.tx12 yfsgxpect the frequency or wavelength to chaff1(.2 ygsxjtnge?

What evidence can you give that the speed of sound in air does not de9/6pv3vp o nrhpend significapr o/n96vv 3phntly on frequency?

The voice of a person whor.pbjyg)pv72f o;mzj1n3bj. has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of orgaqu3c i8jdfc mrob0(4+j3 /kuen pipes?

Explain how a tube might be used as a filter n , yc1y.es q6k3gx5epto reduce the amplitude of sounds in various frequency rangcky65 nx1,3qyg ese.pes. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12/h qlw/o, - r;yp t+ 4dlagg*hd7dycy8–30) spaced closer together as you move up the fingerboard toward thw g/rl-,*lo;ygcyph da4 7y8qhd /td+e bridge?

A noisy truck approaches you from behind a building. Initially you hear it but c brg2)jt fdec9 aufzo(vc7,3 .annot see it. When it emergez2 ,o b3.c)dtcjff9a7 (vegrus and you do 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 to be due to “interference in spac zjb(m0a8tt5ie,” whereas beats can be said to be d(ait8b 5jm zt0ue to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakezuo8y7w ,p /+jut cqm)rs were lowered, would the points D and C (where destructive and constructive interference owm/ op87cuyj t) quz+,ccur) move farther apart or closer together?

Traditional methods of protecting the hearing of peope/ /rix 2*lmnule who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electro2r/*/ ime uxnlnically, 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 iczk.x) lj lhs: /ab:f:n Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (l:hkl:)sbx .z/f:j c aa) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if 5z+wqm stat99o (3e/q xpzp 1ithe source and observer move in the same direction, with the same velocity? Es+ztoq tei99 x5qzp( 1w/ apm3xplain.

If a wind is blowing, will this alter th03in: nb+ipp8 alal8 me frequency of the sound heard by a person at rlpni8m0ai8+p:na3b l est with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a c j9t h))hbbb7.kqu/wmhild in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequenmqwh 9bkb.7))/ju tbh cy for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo0a*m-6l p rdg qh4mr8m4yo p62 ls/tln of her shout reflecmqlypmhn/rl8g*m-2 alr6s0 64 po 4tdted 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 jucdmv . aw+2xi+xm7 h*ust 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/s (Table dca x+u2mwi+7v. hx* m12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengthsc ;79e)l1rjyxc o,tdc.t5zko 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.n1hz86zd::gdfts pp school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km aw :zppnd6 h8s1td.: zgfay (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 strikyn.hl) q2 pau/ing the water below is heard 3.5 s lateqa2l)/ .yuhn pr. How high is the cliff?    m

  A person, with his ea.j*kg18 c7eaui:aorx1,b+x lodrl vkv0 4u8 zr to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are hex ad1r +7rgcz uk8x14.,0j lo*v bvlu:ioke8aard 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 ov1e+naeo3i-v b er one mile of distance by the “5-second rule” for estimating the distance from a lightning stria31novib +ee-ke 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 1m7 j +g;a-p)b qmpwg(w20 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 inten eu9nw ,nt5 frb83oi;pgpn: +jsity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of d ltll:,er q;48 xeoh;mcw7-z95 dB when fired simultaneously at a certain pl ;dreh8ezmcllow :-qtx,7 l4;ace, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four ese jm*xf.;q k8hlsj7gh, + v+hqually noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain sh8qsgj;je7x+*,.skm+ lh f hhvut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise rati.h+spf3 jtdvkfo 5.n6 o of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device?o .65vj+nffdk t.3s hp 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in notv.; r-pkt0t 4pxpz5imj: o.brmal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on tpx :tzp-;vomt 4tpjk0r5b. . ihe mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose arepa r:mizj+9e7)8ej oza 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 modestbz3p)a :s..xo5 wjzw t amplifier B is rated at 40 W. (a) Estimate the sound level in decibels js.)az. xw:ow5p z bt3you 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 130 dB whe+ nfittkf4v o4 z8ye62n placed 2.8 m in front of a loudspeaker on the stae ti4k+f v fn26t84zoyge.
(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 le0 d:sqi90 btsdvel of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? 0 d i9qsb0std:[Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) b2n35gd3b ,b kkhm m0uwy what factor will the intensity increase? Increase by a3kbmnkbd ,mgu50h3w2 factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amxo -5fk 2vi(p/nvo 9l/wj7 ueeplitudes, but one has twice the frequency of wokeuin/ l(p2 x7e/ v-of95jvthe other. What is the ratio of their intensities?   

  What would be the sound leve7rp: 7jyu+yu/m y1xt al (in dB) of a sound wave in air that corresponds to a displacement amplitude o/yypj7+ma:xu y1 7t urf vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loudf*i41x+ gj73dlqix zi as a 100-Hz tone that has a 50-dB sz7j4xq i *ig3fd+il1xound level? (See Fig. 12–6.)    dB

What are the lowest and highes wij7yco:a l/ v*hr02st frequencies that an ear can detect when the sound level is 30 dB? (See :7w/icaj2 ohl r0*vysFig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels.- t59wui b,alb What is the ratio of highest to lowest intensity atiw b9a5 ,bt-ul
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamentale+. r c .4lcdg i93oicluy)dn0 frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must then0g3l d4o c ..de)c9iulry+ci string be placed?    N

  An organ pipe is 112 cm long. What are the fundamenqjx ; ad)kc6z-,v1lxp tal and first three audible overtonesc6x1kv x)d,p -qjl;a z 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 fro1myo-rsteisw;/k3 0 gm blowing across the top of an empty srwistsgkym/3;- o0 1eoda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes s2-bs qn ;uad+vpanning the range of human hearing (20 Hz to 20 kHz), what would be the raud+qv ;n2s b-ange of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its thir bm-3cw68ys+c 6j6 m*x dezpdkd harmonic. What will be itsd*w 63-8xp6mzd c6bks cme+jy fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long an jnn,y -ifz5uk7a u6+sab6a1k,r /bmtd is tuned to play E above middle C (330aknytnm7-ku5 jari /6b6, fa bz1s,u+ Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle Ckdsc*2q,z-0lvjee/ ydkk1: vj*eoe0 (262 Hz) when the temperature i2 *eq*1 e:j0sde-kkc l0de, zk/yvvojs 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 agbh4(brpo3 .3n; xbmxt 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flut im6dnu 1ow1 l4(2bvc8iw-vcae in Example 12–10 should the hole be that must be uncovered to play D above middle C at 2wc1u ial-v6 cnd b wm84o21vi(94 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 pixu8g 0mo y41eipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in gxu i48y0ome1between. (a) Show 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. zct x8dvu3/ubi.w-0dz/ mn -zIt resonates at two successive harmonics of n0i/wc x3/8 z- buuddm-z.t zvfrequencies 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 xh1( ,nkl8nkrt3 qzf3$^{\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 audiu dbrph4 vtjxee7e7:6s4 k1 o;ble range for a 2.14-m-long organ pipe46tosbevj; khu4 rxde: 77ep1 at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is anoq -w0 0 h7d7smgduo;pproximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencinoqs7d 700wudh- ;gmoes (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 8r h0+oz,k ox gy)fy1uwhen trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other strfy) yxh1k,ozou r 80g+ing? ±    Hz

  What is the beat frequency xt04gg2rwk /e/ri5js77qbx e 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, whifs :y z7c(dkkq/ 2puq5le another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when playefp7 :/2dq z5s kku(yqcd separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when som;1i )qjdp)x of ,t )fdl3)wdbkn8dr8unded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz nfdj1d3fm) )dodi;ltr,)x 8k) 8qb wp tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in+ tpdmfsag8 is*5st ijnzo;+*01 y8tf one string isz5m psty +ot;a8fni 08 j*f+is*t1gsd then decreased 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 i8 h 5lvc8perxfym,5.two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the ,f8iphm.xlcr y8v5 e 5other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A7hxhb :v0v df5y 96sbv, 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 beat6vsxh 90 :bbd5y hv7vf frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person st,eyi+2chao x 8jl s8x+ands 3.00 m from one speaker and 3.50 m from ,ixac o+hejx y sl828+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 vibra 7wgj*wdpsi71y0gs; w ting 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 i 7p;10dw jg7*sw gwsyfrequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How :m/0 jq zstszku +f)3thbtp-4many beats per second will b-tsp)j/htb :z+zq4tufs m k03e heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hzz scdl9 s (pe4j0)3axw)wil7q , wi0iq when at rest. What frequency do youx9iqls(iwd,ww izp3s)a e) ql0c74j0 detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fisop3,jr 7pv tdy 9jp:*iur 1e4ca /xt4re engine whose siren emits at 1550 Hz moves at au ,s 1/7prxp r 4jceojai4*v:93p tdyt speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift 9ln k:)e ili+qx3rnmu(+24 iqseyp;h in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 4)sqqhn(uer+ly9nlpi32 m i x; e: ik+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 frequency hornm(rq;/z dx+pi60bg, knl3k f n. When one is at rest and the other is moving toward the firstdx;nfrgpl n(zi3bq/0k ,m 6k+ at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHo jwxz psb488v:uyi36z and receives them returned from an object moving directly away from i8ws4vu8y x:3obzipj6 t at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a ((b z5bbkk/jscc,zj2jf /r3 mspeed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does t,c(j5cms 2zrfbb(/k /j k3bzjhe bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiy 9mp0 p7t1 ak 88,ceqv.jxdqfments, a tuba was played on a moving flat train car at a frequency of 75 H xq,e980qp7ck.jv a1dt8ym pfz, 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/s ?   Hz

  A Doppler flow meter usmo;uf 1gkog xgp7q:,s ,iv1 n1es 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 expecko:,pgx,qmfgnu i1gs;17 1ov ted 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 wav8(awowk) h5jowm 8* wges 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 souz2 *v wcn))r/0ra0:sjj5bqiiyd 0 bgynd of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will obsi wby)j dj0rzv/byinca* qsr02: 05) gervers 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 speeo,p jh f 4zpm/9:z7vuid at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) Whl8 d ncz:,wbq,at is the angle the shock wave makes with the direction of the airn: d w,,c8zqblplane’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 atmosph5txezj9y mu5sw6j : 6pez 0qg)ere of a planet where the speed of sound is only abo65zm eep:qw6zj)095 yt gsxuj ut 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 strik a*n /rc)k2 klmnvaa*j-:q)pkes the ocean. Determine the shock wave angle it producesaj-/k *2navq ) lkk)r:pan cm*
(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 r49s518ed*qo k 37kjga qgka,f ne ez5$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead andlrb85if8/)p azg x1i s see a plane exactly 1.5 km above the ground flying faster than the speedil1s/8zf 8 )piga5 brx of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses down ))qycowfbh82m egr3 *ward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m,mg yb eoc2whrf))q8 *3 what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the 2nan)1m 7 slp+qizv z2f fvy(2human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called c:t*2dut.y 2e sotbk* a sewer pipe symphony. It consists of many plastic pipes of various lengths du:2 y*bec.tk*2 sott, 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 tw8 r:ap9 rz7ivqqi: m8hreshold of human hearing (qa7rpwv: iz:8i89qmr 0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sou 0tu9a xk):hsend level when an 82-dB sound and an 87-dB sound are heard simultaneously?:kh) t0ue9a sx    dB

  The sound level 12.0 m :nf.(pj9ewomoy0 3edfrom a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all de 3p0yd:.oe(mjf9wn oirections?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dropv evsk97clyujq,7t 1n07 igi5s by 10 dB at 15 kHz. What is the power output in watts at 15vn5 07 ikis77 qul9jyvt,1 ceg kHz?    dB

  Workers around jet aircraft typically wear protective devices over t0dve;o- fhe.mh9 vfm;heir 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 unprotected ear at a distance of 30 m from a jet .v 9-dhm0e; ;eof mfvhairplane engine?    W

  In audio and communicatin( 9r-af+t,clsuxq3 mons 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 frequencq2if mr7v:zddj.8c if++cn8z y 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 kf2ql+*(q 4g f,bz sye,* lfzgfixed points with a fundamental frequency of 440 Hz and a mass per unit len,k,zylqb*4f +(f2 legqg*zsf gth 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 l6 gt.n)no,fp, pj6pcopen 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 openit nfpgc ),j p.op6,l6nng 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/7nm)2yxxi70x 9g u :yvlsdjm 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 yj9 x ni /vdxu7mxmy02s 7g:l)the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to res0lyjvprsdj0n2 1uz :-onate 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 ton41npp *o9nqbts5up9 ze in the 500–1000-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. 45utq*1 s zpn99bpnopWhat is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The cox,wj oz1 ye-g* ;6tn9tugdmk8 nductor on the stationary train hears a 3.0-Hz beat frequency when the other train appro,t9 ngkeujx*d o y16g-m;wt8zaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approache2 y3r5hhwazww2d j :5gb/7lmy s you is 538 Hz. After it passes you, its freqr 7ywldj3:hwwm5/hy g22baz5uency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate ther6:til0 jtwmf7q,st 6 speed 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 byil6: rtqts,w76 jtfm 0 a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, pu5ch8f6*b, nbkrf7/ (ag ih6r z og*frroduce a beat frequency of 11 Hz. The shorter oner(/7z hn okfhfbr6ib*g8c,g fru*a5 6 is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite l 3* tr)egtmv2ends of a railroad car as it moves past a stationary observer at 10 m/sle vtm2)gr3t* 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 h ja pk7eg9m:/normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves wekh:g p7 9/eamjre 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 mot9wumw+( u :q8gtxc f3wh is flying toward the bat at speed 5 m/s The bat emit3 g8+umq(t :w9fcwuwx s 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 sounrw1i:d4 c /hqn:. usfqd pulses as it approaches a moth. The pulses ar4 1.qiw rh:dcfn /s:que approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once usedvp dthyhyfw((e :6axm9 o)b5) 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 (y eaybd95th (mpx)6) woh:(fv 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 by7 u2em nszyxqrjj)d5h j: 3p8./zu-qu the presence 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.sjpj:u8j3rxzu 52dnz-)mquqe 7 y/h .8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender d-vtzve, 7t b8d1;*ylkqj 5j maluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little pracv1b jtldqe5*tj; m,v k d87zy-tice, 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 threshm1kwi za4 x2:w*ryg +pold of hearing for the human ear at a frequency of about 1000 Hz is 4rg:aww2zy x1k+mpi*$I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic b yl).1wd yko 62jmr(juoom 1.5 min after the plane passes directly overhead. What is to jm.u 6 kw(2rydj)1lyhe plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatd6+: w9pdemsp u s5,ub 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