What is the evidence that sound trave. ji;ab ;+f+vryz0o tuls as a wave?

What is the evidence that sound is a form o 3o39zjgujf: bfxl6 .tf energy?

Children sometimes play with a homemade “ten m/onjs4r:3 wlephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Expla 3jsron4/ nwm:in 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 or wa +p hr62lntccb 0uzs7to*bo+0vecl*utbzposoh r6t70+ 2 0bn c+length to change?

What evidence can you give that the speed of sound in air does not depend signv zp*);mh:ry70noo/ 4cch 6cl joss:wifico0zohl:cpn m7;v*sywhrc:6 4o/)c sjantly on frequency?

The voice of a person who has inhaleds 60wdsdq -i;d helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of orgvy.kxm;5bw4j 96 6)r kgfj yzcan pipes?

Explain how a tube might be used as a filter to reduce the amplitude of z ymju s/2e-9bc fng6:sounds in various frequency range /gn:2ucf bmjzsy -9e6s. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spac q a7ftva h+y9v7jp78ced closer together as you move up the fingerboard toward the j7t987pvyvca +q 7afhbridge?

A noisy truck approaches you from behind a building. Initially you hear it but gam/9fx ak11cqm. 9hz-0 yhq kcannot see it. When it emerges and you do see it, its sound is suddenly “brighter09h. q/mqxga9c1-kzfykm1 ah ” — 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 “irgn +1q:)m giaq,a/tsnterference in space,” whereas beats can be said to be due to “interfere)rs:q, n1qg /am+gaitnce in time.” Explain.

In Fig. 12–16, if thexx3) 7+gkajbkl6ph g. frequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) movekxgx3k .blg6 7 +)pahj farther apart or closer together?

Traditional methods of protecting the hearing of people whovm.k 5klj)4s 8xb qo.o 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, .sq bl4k 8jox)v o.mk5inverts 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/l5o 8fmifgl8 shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18.58iol fm/ gl8f 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 sourc,.pl.utv99b8kmb.pl .x qiab e and observer move in the same direction, with thb..t9p.8 vp9lklbiu, amq .x be same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sjv7hr454hti) 20e*zwkzgs v g ound heard by a person at rest with respect to the source? Is the wavh gi5v z20e sth)rgzkjv 7w44*elength or velocity changed?

Figure 12–32 shows various po:db9alifa 24( z8-deobs jwt jr2l98 usitions of a child in motion on a swing. A monitor iiadauz2f 4wl: 2bd 98(l-9 teorj8sbjs 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 sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lakejs )3m s7u1nsw,x y1nk by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the jwym , nss1ku7s x31)nlake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterlig w-t)a /:6 mbm0kv8q gznh7obne. 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 12–1) and does not vary significantly with/q8hgbak mwbt0gn z-v 6 :7mo) depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in airh,+y exnj: paob s 4:.h/q1ic3jlhv2x 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 of tuna on a foggy dxnw,*trv- ;o tay. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How muc *-,xtnr;vw oth 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 makt .6si 3l.niacjo.h)w es when striking the water below is heard 3.5 s later. How high isc3hsijint. o) .6a. lw the cliff?    m

  A person, with his ear to the ground, sees da65efkq (rt y 0azn(v;x6x c)7fr8tza huge stone strike 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 away did thec( 5yzk6dqn vf(ta )az6t r7;x rex8f0 impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second9i8suwb 95xhunilgt39a d2 5s rule” for estimating the dists idxhuwi992at58 nb5 3lus g9ance 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 120 dB?guv bdm66l a h.o)/grn1o-w+w g9sev 1    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of io:v6;t a f9aba sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level9/b b xj2jekh iq9kg.5 i*sv)a of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hin e9)kxqgjsj.h* av59ik 2bib /t: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplan1 p hna mxa,1,uo6,kq zu(hq6ue with four equally noisy jet engines is experiencing a sound level,h uh uqankx,61(q,amzo 6up1 bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to hq68:w hv:xoz rk3zi+lave a signal-to-noise ratio of 58 dB, whereas for a 38+vwil:rkh x:qo6 z zCD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a persoh vd/5ccrari0b- , m5an speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sph 5cbmrah,vr 0d i/5a-cere 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 )l 7ogf 78737je j +k;yvwjxldz,ntah 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 Auj- f(*qnl;: ymba a0mly2x: ;wr 2cpi is rated at 250 W, while 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 connected in turn to ea0;wpm*c iyly x:2(n f; :jmqab2 u-rlach 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 r 3(s7bkgsdg5cb hf+w3egistered 130 dB when placed 2.8 m in front of a lb7sg3 c+ds 5fkghw b(3oudspeaker 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 of 2.0 dB. W75xtm v+q2 noep x0ij2 t9y,qkhat is the ratio of the amplitudesitxpt9,q57 qx2 mv0 y+k oje2n of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the i* zq0 dh0zvv1rqc,7y jfng1p8ntensity incq1*r0v8 nzf qj1zv phc ygd,07rease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equareilht: 4xyqh7/j)x5:x)kay4vp 8 ge6 tet e;l displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their :ek xxe; j:8qye)6v 4gth/pyilhx 74ert ta5)intensities?   

  What would be the sound level (in dB) of a sound wave in air that cy - 1x9coixfb,orresponds to a displacement amp1fcx9byxo - i,litude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone t42iyxl* jxg/ e,alm: hhat iea l/yxmx * l:24h,gjhas a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highes jicn (m;i9aq9dgrk7 -t frequencies that an ear can detect when the sound level is 30 dB? (S(g;qcmnia7 kd i9 9rj-ee Fig. 12–6.)

  Your auditory systemf6nxoki4( mej)hy cnmqk 6+t18(o indyp:q :) can accommodate a huge range of sound levels. What is the ratio of highest to lowest i6yj)) mdityk qnoe mo41khn(::(+xipnc 8qf6ntensity 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 frequency of 44x1 i-ee otgvay)oq8x(k:f0+r0 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the strin+ox - rto1e(i)vg :xyaq efk08g be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audibevhoi-;. ncv 2le overtoneve no;c h-i2.vs 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 from blowinnrfep9qblkm 45m:4 +wg across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a 45fmqlm9 : ebwn+p kr4closed 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 yxcyy( wt(i 5u+,of1 pdm48hk open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lop(,kdt yh 4(f5xymicw18 +y uengths 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 t1hivem.8q8w l(m 0 znkhird harmonic. What will be its fundamental freq eh. 8vmk8mzqi l10w(nuency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73);cqf noyi. g3 m long and is tuned to play E above middle C (330 Hz) n3.i)yfg;c oq.
(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 middlcol6bn,b ;3:;t ka bqcot3jou* /una5e C (262 Hz) when a ;o5l bb,; 3unbnocuq*3a/tjk:c6t othe 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 2vh g932pshs q1r*swc10 $^{\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 sh7xcv7cekc k-o i f6a/ 9-qdi1tould the hole be that must be uncovered to play D above middle t1qko7vck-/fxci9da7e 6c- iC at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 26uvp9 7k)lv;.ann rst- 4 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is -)v9ln nkts7prvu.a;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 issxmyih 13 w6lmooh6 )+bg v45l open at both ends. It resonates at two successive harmonics of frequencies 275 bmgov 6o+xlhy6hl3s1)w 4mi5 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 zljx-x hw/g au/5 q.n1$^{\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 (h t*f:o9,v bn h4f(k *gmw5g9xw aiwwa 2.14-m-long organ pipe atmwkh**w 9:5av bo f 9hwg(,(4x wgfitn 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 c/o3g v-/q8yyxldczhp4 lnf4 8m long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the auy8/-y fnvc l /g44xoh3qzlp8ddible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strgwv1 xfh-84 hkings, one of which is souhvw1x4f 8hg- knding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if miud qe8uk 2qb59ul .i6lddle 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) operates ahdh9i/ep/+7d) n jvns *pb k,nf8l(ant an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occbhnh7knf )/, pa8/ned9j i+vnpl(* sd urs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with 63jhiy6(c6 bptn;;jlqswg :a *7y vedme,;bya 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequen e;;6sqgh ap:6byy7wvcmebjd3j , *6ytin;l(cy of the string? Explain your reasoning.    Hz

  Two violin strings are tml)mm(2s*h4c dje sx .uned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequdcl(s)jxmm.4m s 2e h*ency 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 tryc:zof ak a,wk41 1ib+s to play middle C (262 Hz), but one z1+b,a c 1k4osaif kw:is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, aqs :wpmno78fee a* ,3qnd 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 freqqs7of3 eqn8 mea*w, :puencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person standsa5 * 8awc(fxmh2-spfn 3.00 m from one speaker and 3.50 m from the otherhw-m(5a2*ffp c8nsx a.
(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 pbbkc2d7;y ;nv iano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, whbc2;;ynb v7 dkat must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m aniv-z (bza :nrb-p)pm*d 2.76 m in air. How many beats per seconv a: zpn)bb -rpm-(z*id will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certai0br40fq i 5nadn fire engine’s siren is 1550 Hz when at rest. What frequency do you detect 0a f0r5b4nidq 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 cn v ,z3 wjg*by*/til8ua1s,k detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/*n, v38 lcgu*tyb,1aw/ zkjsis
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you atvu3jjze(q;j47t0 qhff8x,q;ld 0 d.q x/zr mo 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactd70jrq m uld.f(xz ;;h /fqvzx,t0qj8qj 4 e3oly 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 equ r uw,ucecyb,d ;4u+/yipped with the same single frequency horn. When one is atu, +/;edyrcywucb, 4 u 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 frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound (65cx-s :jxwxi bo-adwaves at 50.0 kHz and receives them returned from an object movjo xxwia6 5c -d-sx:b(ing directly away from it 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 b0p 0akeh s; xgk,t(e 7r7d)wa25qilanat emits an ultra7, w2r)gi(ntxks;qdh0aa7e50 kp el asonic sound wave with frequency 30.0 kHz. What frequency 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 flat qx 3r13oyy;k,kos/4dx b i+kvtrain 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 xro+, 3oikbx4 3kky s1v/;yqdif 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 speed9 vyque;*pfd r.+m r9m6jt l*es. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissuel+ dujt 9prqm* .6;9vfey mr*e 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 uluja,.g4-xax 5 (ckue.ks4rwh trasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity is -e w : s*i:5-pcgme;kwhp ja0-h)dxbp12 m/s from the north, what frequency will observers hear who are located, at rest, - ec gs:e*:w hjbx;haw5pmdi pk-0-)p
(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 7-(resz;r3 ;pq zlnkbjre/i ni5w 1m- 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 Mach 2.3 wm +cbq/e)m41ih43 naa ,4hnj i+ pndiyhere the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the directioneic4i/p)h jhqam+ ,dy4i1 bn+ 4m a3nn 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 tfurrl q nhh4 1u84 *d3x:dez-bhin atmosphere of a planet where the speed of sound is :fu n1 ur4xd 8hb3*hqlrd-4zeonly about 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:8fwwi6, dl st 8500 m/s strikes the ocean. Determine the shock wave angle it tdsw ,i8lf6w: 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 w9)lqykr :q2u$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhid6eid2sy( j5poj t) :ead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the planee52 si6do jyd :j(pit) 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,o b.su9zf1bg1x 6ss, r000-Hz sound pulses downward from the bottom of the bfxz1, bs.sgu 6b 9sor1oat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many oz37g j8zrbu ;ectaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe syqb2n 9rm ,(ykw lb. o(vl(v7x67zcrvwbu3sg 0mphony. It consists of many plastic pipes of various lengths, which are open onbr vq(3 ,6 m(r bvs07clwxoblu.n(k7y2 v9wz g 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 cxkp sr0 34tnqwg6/owc2c r9 j-*jl2t vlose to the threshold of human hearing (0 dB)o3 xv4lt nrc290gwwtp-/jsr2 kc * qj6. What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound44 uud) lq7odnc7bxkc j1uv+dmt( b22 are heard simultaneo q ovluj)41 m7n cb+ckd7ddu42u(xt2busly?    dB

  The sound level 12.0 m from a louy1e/ypo m2b )tdspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates 2toe)bmp y/ y1equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dcv)9ryc:zppx2)m y(ax5qf r2 rops by 10 dB at 15 fmr9 y 2p2):)zyrvpa xq c5xc(kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typiv0kx( / yurw5g--fj*m afr3nvcally 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 ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distx0/5-wv uvagrfn(rmj yf-k *3 ance of 30 m from a jet airplane engine?    W

  In audio and communications s jwi,+5 l b0zkx-i6fdy: ho/ncystems, 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 tu*c c+ spfqkjfqv2/7ww0 ft 6:yned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between f8soaam er /7;aixed points with a fundamental frequency of 440 Hz a e /7or8aamas;nd 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+2q1wk hnubo*uds6 j5ld5 +id into vibration above a vertical open 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 whdwn+ iudjo1qs2 5lbd5hk*+6uen the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 gvm- xt3h73r jqzhk -(a is near a tube that is open at one end and also 75 cm long. How much tension should be in -(3-mqjth r3 k7xhz avthe string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to 3gzrb .bp08 e d/i(yjlresonate 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 500–1007wo0md b2 2/gjctesb *0-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 fiodtg70m bwc/e bj*2s 2nds 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 conductor onz s 4( whq/:ciej5eqe: the stationary train hears a 3.0-Hz beat freeq5 ic zs4q( we/he::jquency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as 7z,ti4 4dn6. i-(whepivx m)btn5iqv it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was thexvmw4b) vpt6n 75.(i4eq h-,it niidz train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the dzuv-.d e(w,1 xv5x2arh8 pv vjd.g m3wifference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops bv.draxwwmx52 jv.eh, z pd 3 v(18g-vuy 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, produce /lgdx5cisx.6a beat frequency of 11 Hz. The shorter one is 2.40 m long. How /x5cld. i6 gxslong is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pbbllc. jr3x27mync;.ast 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 the car, (b) he is between the speakers, at B, and (c) he hears the speakers clcr j;m7nb l.2b3yx. after they have passed him, at C?

  If the velocity of blood flow in the aorta isaw gy+woa1*zi dj* 1y, normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along aw,g*zjy1a* oywd i +1the 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 toward the b*: whi87dj0w6 zrn xwdat at speed 5 m/s The bat emits a sound wavez:rw6ww dxd87*nih 0j 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 ox+ 2x*i02/mhtdyd tie5 z1xktf high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apa+yx 0ei1 itmhzdx 52xtk/ 2t*drt, 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 used to send signals from o0x*3 5mr (svu kxgki7jne 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 frequencymux(73 ksv0gjr i*5kx of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of s5bjv*l n . wea tmmr036tf2ph.tanding waves, which can cause acoustic “de 36 5t pf v2bjtnrmm.h0.ea*lwad 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 a long, slender ahbi7a8.fw (o kluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, lou .wo(f7hkb 8aid, 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 hutpg wx ;,;ie-.lrmd,po e +/gkman ear at a frequency of about 10 w/ o;tg,e +m-;prgxip .,keld00 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic b*)k,zdck5 c4f i4wvhg m,g 1xyoom 1.5 min after the plane passes directly overhead. What isc ) 5v,m4ckhkd4 wi*fz1g g,yx the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboafp s tb)y+t.bg8q0fo7t 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