What is the evidence that sound traveur; lhu lqwbe5a :6mgg:658jjn3dg 3f ls as a wave?

What is the evidence that sound is a form11gqi (epsa/6 t9psz7ilw f,j of energy?

Children sometimes play with a homemade “telephon/81y san+sdyh 5 q1dvhe” 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 thes yhnsdy/+vhda 5q118 other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from a;e.hgj t(r5 t +yr:y-tqwt6yair into water, do you expect the frequency or wavelength .g r:-+e(y5qy wa;hrtj t6tty to change?

What evidence can you give that tdwv kq0 u+ k1j;s. suv*3hw9nehe speed of sound in air does not depend significantly on fudk1;ej+ h.u 0ss3 vwkqvn9*wrequency?

The voice of a person who has inhaled helium sounvw (b cp;,**usw jeik7ds very high-pitched. Why?

How will the air tempcsbgegeu). t6ijs-: f11c: bn erature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a fil * hjqjyls04ov973pe ;z ro(dlter to reduce the amplitude of sounds in various frequency ranges. (An example i9d ply ;v0hj szr(3o74oel j*qs a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you moveh;i7s 5);o1kmg -8 8fdccc osl6jnoq e up the fingerboard toward the booq -li m6;csh fg5 )kcon1sc8jed;87ridge?

A noisy truck approaches you from bnl9pm u2ox1 -cehind a building. Initially you hear it but cannot see it. When it emerges and you do lop x92cmu-1n 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 space,” where cidml/7pm 05bas beats can be said t/0cd7b5pm milo be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were9yex *t bkjp k45yxl(: lowered, would the points D and C (where destructive and constructive interfe *e pyl5btyk9jx (x4:krence occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work vi+8n+/ h),nz xqsunvin areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a r/n+vnsi+un,vx 8zh )qelatively 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. E6kv/d 1 do,mpvach wave can be thought of as a superposition of two sound waves with slig v kvd1/mop6,dhtly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same 4i y;q2-r drok i;+,l6g peqledirection, wit-rd6q i+e r2;g;qy4p,o lke ilh the same velocity? Explain.

If a wind is blowing, will this alter the frequency of thril o926n(fzv ml;m5he sound heard by a person at rest with respect to the source? I z6ofilmm295 r ;n(lhvs the wavelength or velocity changed?

Figure 12–32 shows various positions o 3enuv w :*m2jck9m-(a(ynbh af a child 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 cy ca :nmwuvn*32(k9- eha mj(bhild hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the epu 6.+l fvi*ihcho 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 lake. 6+i*fuli . vph$\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his sh( uzb*25jpq 15m/rvfdrq ztb8ip just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with deptzp mu2bqrt 8vrdbf z*51j(5q /h.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air ct:81nznh ,uqh1fak wmh549 bat 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 drifticx fjz6ggm(er -mn0 99ng just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1rm9g 9xe m 0nfc(gj6-z.0 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 spla c7nyb 8b0 l)dde2el,kqj-, mtsh it makes when striking the water below is heard 3.5 s later. How high is the cliff 0llq)d, ,j- d ecm8b2btyk7en?    m

  A person, with his ear to the ground, sees a huge stone st/bfnw* ;*: ee1 mbdflhrike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the otherf*b1e:ew/; lhnbdm*f 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 over one mile of distance by the “5-pn-cew)c+ldu0q: s4 gsecond rule” for estimating the distance from a lightning strike if the temperature is (a) 3c:s- +0n c 4wgqeup)dl0 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a s9ri pa2 bw2d/c9kx4a:chg pm2ound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose inten7grl(zty7q,h xa 7ob:sity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when firedmx:- 3wp epj0dy5f9y q simultaneously at a certain place, what will be the sound level if only one is ex9d50 x3 qyye:j-pwp mfploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airpl4tn/9v, e26fgb(b2hxsp u e8amoq: ix ukqg:.ane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one mu:.,qsbe2pg4v at 6xbun8o egf hx k92iq/(:engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a )7qr7vob:h ersignal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background nheq 7br or):7voise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power o;l25i acp (ksts0i6nx utput of sound from a person speaking in normal conversation. Use Table 1(tsk 60;5sxc l iianp22–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area isobdox)kz . jc4+. 7gnl $5 \times10^{ -5} m^2$ (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 cj2 9l-7;-dp aqzpw8hh4)wmxh+jslo , while the more modest amplifier B is rated at 4aq-c sh j9w42hpx d w)olp7z8ml+;j-h0 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 registered 13tzu ,7ajf ..nz0 dB when placed 2.8 m in front of a l f,zjanz..u7t oudspeaker 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 o oss fp9/ x2/qvdhumx.e(l (i4f 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See m2sv(hi.p /ul9 x(fe o q/x4dsSection 11–9.]$\approx$   

  If the amplitude of a sound wa i;ziuv:z;gqsy8 w ;0tve is tripled, (a) by what factor will the intensity increase? Increase by a facu; :yiz0;gq ;vizwst8tor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the freqnar/e7jg: po2 1ea5*no exe5k8i5gkduency of the other. What is the ratio of their intensitikgoeeda 7j12*55n/anx:po r 5gi8eke es?   

  What would be the sound level (in dB) of a sound wave in a/a /(-+1g es)pxy5 ugk p1effp( 4ylhp)zsmc air that corresponds to a displacement amplitude of vibrating air molecules of 0.13/ sf4 ey(axzs lkg/1phf)p)5 -ameu +pgp c(1y mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound;ko;8u m6r xk8tnnnq4 level to seem as loud as a 100-Hz tone that has a 50-dB soundou 84m8kn6 ntr xqn;;k level? (See Fig. 12–6.)    dB

What are the lowest and hiz * iy pqh,1jg(m0d6vighest frequencies that an ear can detect when the sound levi6(*impd gz01y,qj vh el is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Whatv/qv8 7;qi kqi d*qd; l90-f2hl mdoie is the ratio of highest to lowem8-2dl0*o7vqhl dk i/e qv;iqif d q9;st intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin hat 9fjec 8/bk n;e(owy9qqmjd1:r78s vs a fundamental 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 the stri: jv9wq9 s8neb k 1e7o(tcfrmj 8d/yq;ng be placed?    N

  An organ pipe is 112 cm long. What are the whpix1kd +;1apo: 7zafundamental and first three audible ov;kw7aa1i1 :xdhzp o +pertones 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 wj;9z2 od4ubudz0y. mwould you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a cl .dumw 4;9uzdyboj02zosed 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 spxcobuxelvo3 3.p-e *v*-f as(2chu9vanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? 3(vh xovl. o9pbse-uce 2-axv *u*3cf$L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic.5hpvmof cyp 82::w7kta gdj) + What will be its fundamental frequency if it is fi+k7 y:fh: 8capgv)52d jomtpw ngered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0wa (46mvhddmx84qx 0c.73 m long and is tuned to play E above middle C (330 Hh0xd8a(44xm 6w dvcmqz).
(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 3a4gq8 ; 8gp8ut/.-k -btzna zro inwmof an open organ pipe that emits middle C (262 Hz) when the tempgwt k qb8m-8;rg3 a8n.4tu-z/oapn zierature 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 200f xvq 4jvcs1qpgdg +6 p.rovl :k.+,q p0l-ds $^{\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-q( uod uqnwk th*iwd2xfi-3h d/ *q02 should the hole be that must be uncovered to play D above middle C *q0dkfwi iho2/dw( u n dqhu- q3-xt*2at 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, 440k x0 k05jlfv:p6wy7 ky Hz, and 616 Hz, but not at ak6pklf0j : 7vyx 0yw5kny other frequencies in between. (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. It resonates at two h 9qh.: wao mbi:7.e*k2 mk7whb bd7gr5,qorzsuccessive harmonics of frequencies 275 Hz and 330 Hz. What is w*7qghkdo9k2imhbha7 bwrr. bq7oez.5,: m:
(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 g2vr,do,ob afz, g53b$^{\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 thel*z,hugp j1(h 01yttk audible range for a 2.14-m-long organ piph tt*1glzy,p0u 1jkh( e at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It i fvb9onjp6/pyxi5 cuj2h7; t7s open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of youc; pvj /h7oubj59i ptny26x7fr 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 strin4bsdgr hi2z;- gs, one of which is sounding 440 Hz. How f42- h;irgdsz bar off in frequency is the other string? ±    Hz

  What is the beat fre/ gich 5ng4uwj c5xk7(quency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operates afo9jfl+ 96qqvt an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when96j+fqlv 9 fqo they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 betz y t.tdm7(4vats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibry z dmtv.t(7t4ational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned :fu yh)hq 92ulsmq38 jto the same frequency, 294 Hz. The tension in one string i3l)hfmhsujuyq q2:98 s 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 he 84 jl r/a77ysc0dzscaard if two identical flutes each try to play middle C (262 Hz), but one i0r l/7yj4s8as 7c acdzs at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and c2ptfc85*yxx 0a8:a)k exvxj 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 soundeat)85:j xvaxex 0xf2c8p* cykd together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C 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 stands 3.00 m from one spe:g n h) dq0 mq,riw8xpz;.jys9aker and 3.50 m from thed 0hwiqs 8rzxq:9;ngj,m p .y) 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 :y36 6vd.lqytxlvctc 7a ;mg+coe(7yvibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ? :t;7ycvyl (y lx.d76etcqga+m63ovc   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 q*j0g :7z77sfk t sxt,ftxqi3and 2.76 m in air. How many beats per s 7: 7*,xktgfqtjiftx7qz3s0 second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is x, (d:y/by3 kc .farhu1550 Hz when at rest. What frequency :,3 .r(k/ayfduxhb cydo you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fizce5guo-o .7k u8/qw bw,1 g(7n wu:0bsgtxc gre engine whose siren emits at 1550 Hz moves at a speed of 32 8(tesbx o -01u:gg5gwcwgz7 bno,7.k q /cuuwm/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a h;l;vxk id/z*2000-Hz source is moving toward you at 15 m/s versus you movin;il h*k dz/x;vg 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 frequency horn. Whe k orjdnv.917yn one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is1o nkdr7v9y j. the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasoniru g4nx)gd;kz (rp 0t2c sound waves at 50.0 kHz and receives them returned ()t02r4gx ;k d ugznprfrom an object moving 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 spee g ,yfc ttchs68c3cq5d p+ lf*gv2t+m82sq2 qwd of 5 m/s As it flies, the bat emits an ultrasonic sound wave with p2vs8w*qm tqgy8+cd +2cf sq5 6lcth ,g2tcf3frequency 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 fln0k/tjb n;x: ouqa 58b1ucsl0at 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 be/ ;onblkxb5:nc 0 qat1j8u0usat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wavesqzn 1ngi (4ugx(yyv76 to measure blood-flow speeds. Suppose the de yv16 4iqy(nunz xg7(gvice emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of fr1))3s-xl* u phjc+g k*tglfxbequency $2.25 \times10^{ 6}$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 emitsopc.., sv*dl/0v vkwa sound of frequency 570 Hz. When the wind velocity is 12 m/s from the0kd.lc pvvoav/.w, s* north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if itslfedt33jj /04*.bs xnmd8saj m(ya8 h 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 where the speed of . pjl0 4kxiuo; bz0m,hsound is 310 m/s (a) What is the angle the shock wave makes with the o 040lbzum hxkpij,. ;direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmo9zb,n -ja gxf)i3i +xxsphere of a planet where the speed of sound is only ajnzx+ -a ixgi39,bfx)bout 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wa)ke) gcflw2hwwo/ y5 0ve angle it prod2 5k/gchww0 lwfy)eo)uces
(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 4rl cmd jt/(alj386+ r:adykp$/theta$ 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.:6gg8b socx ( 60csxcr5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, thxg:08ccrcxs 6ogs 6(b e 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 downward nl2, +gw xq1ws0sw6dnz;zau 1fros2 wq1uw1dnng+6wz l 0 zxas,;m 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 water)?    s

  Approximately how many octaves are there in the huma0(f48ht ht2:agu7pz3 f/7 pp grherctn audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displayn ypo,ca ;*pyg iea-5a p6q5,v called a sewer pipe symphony. It consists of many plasticopn55acaye -6aygpq,; p*,vi pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a o0bhl-ixx ,a( vie 5-aperson makes a sound close to the threshold of human hearing (0 dB)0heao i livx5(-xb,a -. What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sounax11,if,dy, ir2d6cj56c 2 ij n w0 vujm+lqtrd level when an 82-dB sound and an 87-dB sound are heard simultaneously? 1q2m ui +2n,icc,6iyr 1v, tdfr l06jj ajxw5d   dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is3uqjmqwce.r5h6l , :w 105 dB. What is the acoustw:e3 .mlw r65qh,jqcuic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drop1b 7wufwqo(0gdfl 6k: fi2x; ps by 10 dB at 15 kHz. What is the power output in x l0(gu1 p:f7i2dqfwfo;bk 6wwatts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears. x m;pl 6f6oz2gAssume that the sound level of a jet aig omlz6 6pf2;xrplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sys,h;b uh3)1 3 ftsomfistems, 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 tue.sw2;nyb j4xned 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 fixed points i;ww *5uv f309q 5svzgg g:ruiwith a fundamental frequency of 440 Hz anr ;gsf5:uwi wiq*v5g zvg30u 9d a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertr k.a.q.0x l:pg6 to gbwb,ry(ical 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 when the distance from tw.b.x :ryb .k lqp ,(grag60tohe 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 nea4;gu;kg z b ;)e;nhazfr a tube that is open at one end and also 75 cm long. How much tension shfgazg;) bun4; z ;;ehkould 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-pv )c1zrb gvy2.0gez observed to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range l xe.-ni31 oyscoming 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 farthe -yl3snxoi 1.er from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz g6e.fw ggl+(,tka:czwhistles. One train is stationary. The conductor on the stationwlka z+(c:g f.te,g6 gary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approache/5fqcagw k t:5yc6m4ls you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. Howl 5ck 6cq4m5:yft wg/a fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars jusm b5 s3if/osy75 k.sbdt 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 straightaw s5 5ks/bb.mds 7f3oyiay. How fast is it going?    m/s

  Two open organ pipes, sojl2o0.k 4 jnzae+0 qqbunding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the z0ejq0l2on .jk+ qb4a other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves paot7 .,xjv/(h igkk (fqst a stationary observer at 10 m, (v ( k7i/fkjt.ogxqh/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 after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally abmxt93:l(x,t vif a r)oout 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves t9a )3,i tvoxtfmxr :(lravel 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 v v vay4s 47q:zsiogdh-y4,f. bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. Wi44.7o:- af 4hsygy svzvdqv, hat is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approach*w9k 0hww/qohes a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the mwhqwh*w 0k/o 9oth 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 one Al6fj w 4.ynwrlz4i ; :)r q2nbm/knum(qpine 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 mus(nu;nn4ilq4j q.)/wk2b 6 r:wmmzr fyt be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presencef *f xbsx4z9ml53ikc0*swr2o4m ,ho n of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.2ih cs04 xb,mnw5r 9fk3xfm* lszoo4*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, ) vr6 jco9fmflh-c7 /6mmz7awcalled “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other mhm ccmr)7 vla-w66 j/zffo79 hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequendbp/dp) 8wmf2 fqc 3c1cy of about 1000 Hz isc2/pp dw38)dfmbcf1q $I_0$ = $1 \times10^{12 } W / m^2$ 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 si)j6n5* tu4k96r4z m-x f+f albilajuonic boom 1.5 min after the plane passes directly 5mf t 4lx)4a9n+rj ai lz6uj-ufik6*boverhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ise1:aa*1mihmu .f 0ts n 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