What is the evidence that sound travels as a+ e9w , y,mwmoqwz9)od wave?

What is the evidence that sound is a 0lpsvkk 6ni,1form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to g-1fgk:echwnr3) y/wthe 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 travenfk:cy 3/1eg)h g-rwwls from one cup to the other.

When a sound wave passes from air into wateb cjor.;)q8 ijw5ke0v;p s9ycr, do you expect the frequency or wavelength tor)v yjsibkc0q .o;c;pj5 w89 e change?

What evidence can you give thabdq )w *,jktk;t the speed of sound in air does not depend significaw;)jk b,t* dkqntly on frequency?

The voice of a person who has inhaled helium sounds very high-pitcn r8h8+g-kr b,lkjb p.hed. Why?

How will the air temperature in a room affect the .;m mje;u q9mtpitch of organ pipes?

Explain how a tube might be used as a filter 1 -0qd6vdfga vumg ( +r0xxa8uto reduce the amplitude of sounds in various frequency ranges. (An example is a car mufflv+8v mg-d (ag1rqaxdu6 0xuf0er.)

Why are the frets on /fk dt7g:m9:y5prmiu a guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward t:r/9ifp udy: m57 tgkmhe bridge?

A noisy truck approaches you from behind a building.k ab 25r+ode5 b;let;m Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — youaoeb5m;+ tedb l;kr52 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 xj s1( 6a+iypsx dc;z,beats can be said to be due to “interference in tspxsd6 yxz,1i;+ cj (aime.” Explain.

In Fig. 12–16, if the frequency of the 2pyp f6w1s b/mugxl m4s+)8nanmt53t speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart o/y5gf8b+3n)6tlm 4su w nxtm1mp2 apsr closer together?

Traditional methods of protecting the hearing oi i42pyk4b ;cqf people who work in areas with very high noise levels have consisted mainly of efforts to block or reducip;qk2 4y4b ice noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can bvr:(gamm;5 sww u v*w*e thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farga w:vvr; *smmw(*u 5wther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer malix0r, +qx:c)s6 q djove in the same direction, with the same xc)qsrj+a :q 0l ,ix6dvelocity? Explain.

If a wind is blowing, will this alter the frequency of the-hd zn.fh4 zd;y;tub2,0r+3aeymnz f sound heard by a person at rest with respect to the sourzd 2;y .tdmaz4znuh r f0ehb+,f-;y 3nce? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a chxfn/q2/8u goxild 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 frequency for t /q2 8nox/ufxghe sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listab1g.(h-bbx p xa- mi8ening for the echo of her shout reflected by a cliff at the far end of the lake. She hears thbh--amgbxab .x i81 (pe echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of nm9 c 5qhyhc+3ahn 13c, idxt0his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in se3n0th c i5,nd ycca+hhx qm319awater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20 fo+/rx1mr:mf $^{\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 driftin sh alxh)efe5.p5g 6:hg just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.)eh:ah5hlgpf5 es . x60 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when c3n/s9g,+dza nwe;lc striking the water below is heard 3.5 s later. How high /wldgnez ,c 3a;ns c+9is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pe c5;pfte09v cvc),z/n,wfi uavement. A moment later two sounds are heard from the impact: one travels in the air and the other in 0 unv f5,w), 9c pet/;czveficthe concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distanc j5,x5g ysb8q .vcdlou *cso5mnc2b-;e by the “5-second rule” for estimating the distance frq55 2 lcyuo.5gosv -c,jd8n* sbc;mxbom a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity ofd,;ysgcm f+uc;u w 9xo2a1q2g a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whoh:b, gha9dt (po rw8k3/otw0xse intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when v +luwg1f(je4ng12dc fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB v(n1jfl1d u+w2 gce4g’s.]    dB

  A person standing a certain dib.8+ouww e3ykk fxh12sen:k 7 stance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level wou ke7o 2.8 nh3y:uk+1bewsxkwf ld 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 have a signal-to-noise ratio of 58 9a. wrwcz5( 6wsefk;91k8gu2q lrt redB, whereas for a CD player it is 95 dB. What is the ratio of intensitieskwrs2cu(gre1a8z9. 9 r e;kfw 6qwlt5 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 person spxd2p5fh p*( pzeaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centeredpzphf2 x(p 5*d 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 eardrum whose arer68q ;ewhyindh+b0w2 y.t 4mma 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 modest amplifier B is r1/8n1nbvfbx z(ev 0hbgf(u7bhgnh h u6959of ated n b6b9u71eugvh v nbg 85fxfhh( 0obz(f/ h9n1at 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 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 reg 7xi 4dmsslja2tos r70m( go0;istered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. gl7x0ij 27o to am4s0;sd(mrs
(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. What ig)y iwgh6i --c;cze/ns the ratio of the amplitudes of two sounds whose levels/--hig6ei ;zw) cgncy differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what f,5imvua 17evm r.y u6,dnpltrrl *s4 3actor will the intensity increase? Increase by a f 5ru6a.du *rl,rmile yptv msv4,73n1actor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displpedmn8rejv0 (m49- l jacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensities? j9l ejve4d80mn(- rpm  

  What would be the sound level (in dBv/j 1t5chk/zeify6sf, g6 er2) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.ijzc1 h tk f,/v5re6e2sfy6g/13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what soa4prk kk/7-wa und level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Figa/7ka4w-k rpk . 12–6.)    dB

What are the lowest and highest frequencies that awi3x:c mw1l):v -yjkan ear can detect when the sound level is 30 dB? l ix:1v yw)jw3m-:c ka(See Fig. 12–6.)

  Your auditory system can accommodate a huge ra(nq -ggt e2hd5nge of sound levels. What is the ratio of highest to lowest intensi(q2eth-5d gg nty 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 440 Hz. The length o n8-v9uvru )14lut1rojqsmfi02gh 0 iate)o8f the vibrating portion is 32 r8mo0 ie2)-tg8l9u )vqu0s1 f uiroj4vh1atn cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cmnb;ub fykwd2jgl .q14);vpe / long. What are the fundamental and first three audible overtones if the piv 4yqp e.b 2l)/ufb;wdg nj;1kpe 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 yel 34bc o,ixq oag5gf+ y1g8pk9(axf;ou expect from blowing across the top of an empty soda bx ;91egko4 lx giqofaf(b+85pacy g ,3ottle 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 i 17igdkn8v b,organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of ndibi7k, v8 g1pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic i:2 lx*(tp :z k-ecfw:bj*bnh. What will be its fundamental frequency if it is fingered at a length of oninf(t :chb*eb:x:wz*jk p 2l-ly 60% of its original length?   Hz

  An unfingered guitar str(dw 0*knnugg03 x ltpl56: xcling is 0.73 m long and is tuned to play E above middle C (33(lu wk : gnllx0n*p30xc6d5tg0 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 8ydf/ y;ynddwv x1(.k an open organ pipe that emits middle C (262 Hz) when the temperature is 21 yfn.d kw/(; ydy81vdx $^{\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 fj0k9 oz0utp2 8 ohe3m20 $^{\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 should the hole b+dvt 8o2(r i*voy:gwle that must be uncovered to pvoo(yr wigl8t+2*: v dlay D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but no-f98qc3kwpr 26dm a s(ec3dev t at any other frequencies in between. (a) Show whycv3kr6qmd a-pefd (8 eswc932 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 hj;k;bly+e1r io /h*rboth ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz.hbeh*+or ;/yjkl ir;1 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 3lgl +20nrlul.pnq 0; ;nugit$^{\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 the0r4 ,bcm--j pm w9tesn audible range for a 2.14-m-long organ pipe - wmbr,tcj0s-9pm 4neat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal ikj3.je *l iub3s approximately 2.5 cm long. It is open to the outside and is clb jjuki*3.3elosed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat cgaz19mydysgm ,z:iz9,;r78 kvw4xj every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far offgai k94 dj71yzm 8 vrsz cgw,;myz,9:x in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) andmg4p3ehvg 2-nr)2 gk o $C^＃$ (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 Xs ivagteyj *-5fi.2/o) operates at an unknown frequency. If neither whistle can be heard by humans when played i.jo2 gifvste5y*/a - 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;p. +vgp0 pcdu/s when sounded with a 350-Hz tuning fork and 9 beats/s when sou up.p;+c0d vgpnded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same fic8 qqv++hyymzp. qu( ecbnu+z2 2x+4q9w/ rorequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat freqrbv++wmq/ 4yzhiq2 .x(9y n+c2uu8cpzeq o + quency 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 play m 35u k 0ezeqh;er5dc;aiddle C (262 Hz), but one is at 5.0°C and the otherq35 de e;uc;a 50zerkh at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequen/pftuul3 y)4h f9:xfk cy 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 b:fpu 3ly kfh94t)x/f ueat 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 are0icx)wdluo0s ss396a4y6 a fv 1.80 m apart. A person stands 3.00 m from one speaker and 3.50 m fr0y3i)66cufxo a s0lsvs4 dw9aom the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piab*n n1mvxi-jdh67e. lm( 3clxno tuner hears three beats every 2.0 s when they are played togdm6v(7x*. c- ilbehn ln1xjm3 ether. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. m ;cp*;kv+ ll jn6bgt1How many beats per second will be heard? (A1l c;p+vn*k ml6gjt b;ssume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren 5 fiwy,m1wemh0aw., 7vqc c 8xis 1550 Hz when at rest. What frequency do you de5. ,a 7wm ,1hfyicc0xew qvwm8tect 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 dhr .i4c , mc6fz) 8n6dm(edkl j*d4ujif a fire engine whose siren emits at 1dcdfj6 ( i*z4u)6mecdk,jmrld8n h 4. 550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sourr ds*,bw5+s tl7 u6tylce is moving toward you at 15 m/s versus you moving5,rdlb+l s7yu s*tw6t toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequ pqwc(hnuz1( jlllqhrb+fi1 2 hk36 7(ency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency p c(lrhk(hw(q12bn6 zfh317lqj uli + 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 f85,qq f b,myx96q qkgat 50.0 kHz and receives them returned from an object moving direct,6gb 5x8q,qk qq9 ymffly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wal k96edgw( sdm;;znp gxhl*c4 -l at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 3dmhc9-ed x ;npzgk(g w*6sl 4;0.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler ex ni83yhym7n,operiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequem7 i hny8yon,3ncy was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wq4mekjo( o56javes to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue(oqej6k jm4 5o 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 ultr, pqco)+2 wbfrasonic 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 y+; k5t;x x2zvhvd+my Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are lozmd v 2kxt+;+;hy 5yxvcated, 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 so): zi.b09nu :dino tfpeed 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 +sb yat d(yn4dlq8r4+g11yv6qo9 qiilj/p4s sound is 310 m/s (a) What is the angle the shock wave makes with the direction 96ba4di lv+/g1sq iynj (t +yqyld o8s44qpr1of 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 k.b0ihd z c7enutn+ 9;0a-wn8 dmrz 4zthe speed of sound isebzk.dzud;ca hwn98m0ir n 70 +z 4t-n only 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 8500 m/s gvj/4f+ksg 3g;nyzy(sy ,d :jstrikes the ocean. Determine the shock wave angle it pro3k sz:fy+svjjyg g, dyg;n(4/duces
(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 2e./jl:tteg*-yht8luw s : bu$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the ground n y7 o*bgaffwxlon+ 71; p9v-kflying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 kmwa *n7vp-xf1l7b9g oy f;on +k. 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 e (e/xumt- yqc,1x7ai sonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, 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 watec/a(1i ex7u- yxt q,mer)?    s

  Approximately how many octau hfr3j.zh lsyo)9*x/ ves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of m,mxok pg -ox 47ba-xa6h)4jx uany plastic pipesh-,6a4u)7xgom p k4o xxxaj b- 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 soun /hs4wsl m;w*( eimve10(jkend close to the threshold of hum*;w(i(ws v hm/kne41 eejlsm0 an hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dwrrfsm4a m*nc k97 xf:bw 01f6B sound and an 87-dB sound are heard simulta: 9fx6 70rnw 1rm km*ffcb4wsaneously?    dB

  The sound level 12.0 m from a loudspegh .1m, )yn+-dgx*wmt 4c evdwaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in alm w,+w4emvdhcn dgx-)tg1* .yl directions?    W

  A stereo amplifier is rated a4wtu4(hz1.l m ( nszaat 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in wattsmh1z zualw a((44 ts.n at 15 kHz?    dB

  Workers around jet aircraft typicayofem/ap9 ,+g :fy m e./ :admgnq6)gf-oxvx9lly wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distanc/9 :x:ge/ff) gmy 6 ,fyg m9oop+xqnamda.v-ee of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the ga ( aiboj6v cq4a(.va/oin, $\beta$ 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 frequh4;e vya5- qcwfg;io*ency 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 violi291pw3,w.szh*rdhgtdz lr s2uky4u cz+2 z u1n is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass pel,z.*3wd dy 1tpgz2 u4hh1zcz + 29urrswu2skr unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with watea- v.6mrq de khfe4gwc.z k9lz2 (.l/fq j6)rrr (Fig. 12–35). Th cf)ldqk z r 2.f rl6j4z/-mk.6(weq9ravegh.e water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again 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 ao// 2vy ldzjv myu14h3 tube that is open at one end and als 4v z1/2yh m3ovylu/jdo 75 cm long. How much tension should be in the 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 resonate as one full l+penyr.8qd+xfmz;u8d8 m/gzz6 *a e s oop ($\frac{1}{2}\lambda$) 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 tqyw5b5 9wznx6x re:* fhe 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 a y5wzrb*e:n w6 fq9xx5bout and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductofmhb;i/yj*j;s 7qs, b x(uej(r on the stationary train hears a 3.0-Hz beat frequency when thxyqf ;m*,e( i(;sb7bs/jjhjue other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it apprt*50yg 2;uv+ n wlj8p/kdnro.hsxnd :oaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How *ouy 8lrn;t0+gwdpnk2 xh5d/n:js .v fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate enoo 8ql*,dqrivg; * 5the 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 by a full octave (frequency halved) as it goes by on the straightaway. Hi**,oqe nvl g5oq;rd8ow fast is it going?    m/s

  Two open organ pipes, sounding together, produce59bwd 2 **jvhhttkc+u9 ku)dx a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the otwtd9k) 9kvh+5hbu2*xj ct *duher?    m

Two loudspeakers are at opposite ends of a railroad cx 2:cadgv,m( 7jhicdne*.q;v ar as it moves past 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 freque(ddcq:hg ,;v 72vm n*j.i xcaency 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 no9zeq xh 3+ )hhq2 oj(y9lky2irrmally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrje r+)9qy(lh 9z2yo 2xiqk h3hasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at gpv x3(fd5 vl:ojkr;(speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The rvg fd(3p5oxlj:v k(;bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pyu.8 e zkeaw+; m+tzbepy :/4nulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be dete/8k+ben4yu :wz+y zpame;t.ected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) wav3 x1zpym yj88o 5o/xps once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fuzo 1ox3v px8y mjp/5y8ndamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of s0 0c , kud24gfgbxhecmmkz*df(a+ 4 3gtanding waves, which can cause acoustic “dead spots” at the locations of the pressure node b04hg zc xmfckdkgd*u (24+a0f,m eg3s. 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, call pbxz22gmz7cf8ckkh *+ qb h-/ed “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, thezh-/k2p 7b82+qc hbfm x*zc kg 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 hut,6+hp3p lgmw man ear at a frequency of about 1000 Hzhwl6t+p3gp, m 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 Ma5 w so:;lst:os +e7yl )zz5aovch 2.0. An observer on the ground hears the sonic boom 1.5 min aw za o;+es5ool )z :v:st5sy7lfter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1ux-m xc-l voqo ,.d0r1v-zbk0 5 $^{\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