What is the evidence that sound travels as awgp-4/6rw)56a.kf yuibar nx wave?

What is the evidence that sound is a fo56nr+xgru y ej4xh(+z rm of energy?

Children sometimes plxjn138 -w; 9i w3;v ratnkynkxay with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is streat1 w y-k n;kx33nvnx;wi8r j9tched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into wb iw+x/ b-*;q sflf(dmvz2mj3ater, do you expect the frequency or wavelength to change?mq-w mfi l+v jd zf;/3b2*(bxs

What evidence can you give that 8bn 2rqcuw ;p7the speed of sound in air does not depend signifbunw;c7p 8qr2 icantly on frequency?

The voice of a person who has inhaled helium sounds very high-pitwew ;gqx2q (mja- 9z5qyq1x3gched. Why?

How will the air temperature in a room affect the pitch x3rr he*t;afqig17, s of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sj o1q5kv qr5q1ounds in various frequency ranges. (An example is a r ko5v5q11qjqcar muffler.)

Why are the frets on a gq4nd4 x yon7-xb+sprua(i*y+ uitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward thens pd4y4b*(ir+-x + yo7uxnqa bridge?

A noisy truck approaches you from behind a building. Initogv wss2ovsrdx+k2pstp+4( +6 eu )1ji0ot +qially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on sq + ox)rki2ts+2soetd64g o wsj pvup(v+10+diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beatsge l;..mflqu: can be said to be due to “interference in time..emfl ;gl: qu.” Explain.

In Fig. 12–16, if the frequency of the speaker,z;xxf hmofpx+2,rm5 s were lowered, would the points D and C (where destructive an, oxmr5xp f ,mzx;h+f2d constructive interference occur) move farther apart or closer together?

Traditional methods ofk g0b,ai0p(l r protecting the hearing of people who work in areas with very high nbig( p, lar00koise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it 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 wavexrh w,s hw0(b(s shown in Fig. 12–31. Each wave can be thought of as a superpositionb,xr (( 0hswhw of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the sa2m17 yie7w (:s ngm; ix3bouqeme direction, with the same velocity? Explain.eb :1w i3;(o7qms ie 7u2nxgym

If a wind is blowing, will this alter the frequency of t:1hepdo,qg.xj ifbpr2. x9m3q ): ciwhe sound heard by a person at rest with respect to the source? Is the w xepwj op:1)bq3qdi.cgi.2r:xf9h, mavelength or velocity changed?

Figure 12–32 shows vw*xcjm;v+q k+arious positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At wh;j+c m*wqvx+ kich 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 lg ell;25cv;dxipk 9b1 ake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the ech9cvpd25lb; gi lekx ;1o 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below t1hth u ,,; zj/upls+zshe 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 p1lhsu,z;/ptz+hju s ,oint? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in a86 zhmfdl ba3h sg.a0e*q jc*2ir 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 asziw0h na+4 4sbove a school of tuna on a foggy day. Without warning, anhia+n4s4ws z0 engine backfire occurs on another boat 1.0 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 of4,q2d 6pgt4po gpv wyttw *m3oj ,u(0j a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the cli,4gy 0 3 *t(uoq j4p6 jotvdgpwp2,twmff?    m

  A person, with his ear to the ground, sees a huge stone strike the cob zu(4cx8o,yq ncrete 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. Hoxqcu4b(8,y z ow far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over ol6b12luvv no1 ne mile of distance by the “5-second rule” for estimating the distance from a lightning strike if thnlvl6bou12 1ve temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound ati ue,07m05mft bts,to 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 intensity is 7:qvvnmmx0 n( $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneo fef(ca1gd:e8 usly at a certain place, what will be the sound level if only one is exploded? [Hint: Add fg81 e:ecfa d(intensities, not dB’s.]    dB

  A person standing a certain distance from an 2 6 06zz9p wggmidmipz h,9sg7airplane with four equally noisy jet engines is experiencing a soz m,igzhm72 6gz6pigs0wd99 pund level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have ade7 ws2of3jx2t 2k 1kb signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal kf22t1es27bxkw od 3jand the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outp h +d7txn(v.jdut of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound .+ vxd7dnth (jspreads 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 isusmz g .k;)v.s $5 \times10^{ -5} m^2$ (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 3o iio1 0bx-n4ltpw p+e:p6n2tnl),z2 zxymomodest amplifier B is rated at 40 W. (+o:e,o-i2x3iy0lxl mzon w2 4 tppn)1 tb 6nzpa) 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 130 dB when placed 2.8 m in frontu;b q/axvkdn86 k 4h8i of a loudahi x8uknb 46v;d8/kqspeaker 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 diil.v-;q r kg*x gh36rpfference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose lev6rgq-3viphlk*rx ; g.els differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what f0n(cca mf nxkqqnqmzey 8; 9 n:k+*b;5actor will the intensity incrqm;e c0:nkza9k; +nfn ( c*8xmq 5yqbnease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplqh0*ut 0d2rf l 0oe 7 r9wp4vrcp,w(ueitudes, but one has twice the frequency of the other. What is the ratio of their inceo7 *r4d02p r(eht , qpfu 0vl9w0ruwtensities?   

  What would be the sound level (in dB) of a sound wave in air that correspondsot )e2pkt-wf +.bx /5wulf6ys to a displacement amplitudkf+bpw/ w .x5oy2els-f)tu6 te of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to lxs;(oa;yz6h seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Figx; yl;ao(h6 sz. 12–6.)    dB

What are the lowest and highv;5rh *mn,8baz y, qocest frequencies that an ear can detect when the sound level iv orm,ah5qyn*b ; cz8,s 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate av/5a jpw)cti(f 7*vp9 qq2khb huge range of sound levels. What is the ratio of highest to a2 j7(vpi5k9*) /f wq qvtbchplowest intensity 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. Th,u2dhnz yuu c3 4mx8b2e length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placxy2d4h zm,nuu3 c b2u8ed?    N

  An organ pipe is 112f7q+dtkh/x8 j cm long. What are the fundamental and first three audible overtones if the pipe is +d qkt jx/78hf
(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 fr)go5 rx fo( o:5zd2lrtequency would you expect from blowing across the top of an empty sodzoxrdr5(to):l2 5 fog a bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-: etgr+p6z14 9frvc*o;i ipc ptube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of 4iecz+1 ;*p:it6rf gc vor9pppipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string nxw/8*g /7rb1dz,vloo 5n sdg has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fi z5o*do,xr w7nglds ngv//b81 ngered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middl+i ovzn./5 )wm u v1crc-itw2we C (330 Hz). /+r zwtc2wi- c.on15iuv)wmv
(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 ovk*5rt g a:m)cpen organ pipe that emits middle C (262 Hz) when the:v* kt)gm ca5r 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 28 cw o2;br (wg9hs0seb0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiecel4kq p(bs0f:jqwx)(.1j u,bg ywt6kj of the flute in Example 12–10 should the hole be that must be uncovered to play Dytf:pb0u,kqjklsw jb( qj (61.x) 4 gw 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 /*em-h stt; wa264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show mwh-tea/s*;t 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 i 1np;yf:g*sm two successive hariy:ms* g1pf; nmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 tz qt7p(q fhw9vt 9;p8$^{\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 a 2.14-m-lokei *:)q o*ekj(:il6e/f fh(hs fg4h,o x8osy ng organ pipe at 2((he li6hoie o xgh4y :j,/ffek*) q*8kf:oss0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outsiagyv ) 9f(12phoqtk e3de 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 your answer to the info1t9kg2apf( hv3qe) yormation 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 0gdjre 5 .+opdbgw m1-adjust two strings, one of which is sounding 440 Hz. How far off in frequenegw.db5 0o-j dmgrp1+cy is the other string? ±    Hz

  What is the beat frequency if mid8 wa5xjmbfr 49dle 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 232pkomj7.z/e,bai qc p +p-pd2.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz /pickjzp2p. d-bp+ q ae2,m7ooccurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 bea+qtk+ux ,scrwb4o., +s4e m kyts/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrat .+c bmuqryste4 +o,k, k+xsw4ional frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The b ke +jt5ru0e t2(0gastension in one string is then decreased by 2.0%. What will be the beat frequency heard w0b5 0ujt2r(kts g+eaehen 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 middl3iwp*j ajqr;hkl9 21we C (262 Hz), but one is at 5.0°C and th p i;q ah*wrjw3l29kj1e other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. 1+mdvamtc9gm. hzq ;)Fork B has a frequency of 441 Hz; when A and B are sounded together, qv1z hgtc . a+;d)9mmma beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What 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 onl8k s n9rmy-*je speaker and 3.50 m from the otherjk-n8 my 9*srl.
(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 t v36)ttszgp+ oq//ixu o be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (z/s/+pt iu3gq6vxot )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. How many beat p2*g7t: ej 1glhwr-vts per second will be heard1g gl7jp -:w thetr*v2? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz whei 2nwr) hxuo x,2b-0:1h ejznzn at rej,0ze2)u xnx:i2hrn oh zw -b1st. What frequency do 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 fbx.cs(4lsh rd67 9zkok)x/fu ire engine whose siren emits at 1550 Hz movedhuc7s4 k(rz6so.xl )f9kx/bs 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 source is moving toward you*5b2j52ek zc4a: qrr ,ovfg *ts,w ozu at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Aoa,srquw 2gj c z5 24 foeb:**z,kt5vrre 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 singles)zl5s7dspk /ihlb/,zh/l m(xei( /i frequency horn. When one is at rest and the other is moving toward the first at 15 m/s tk/7xs/ d/e ,izili5lb z((m s/hpl s)hhe driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at)2kov( titab 0rh(o4 g 50.0 kHz and receives them returned from oho)0i 2(rtt 4gv b(kaan 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 speed of 5 j; 2mw1r+acim m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequewr2 m;m+ja1 icncy 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 flatdn*y:yy n;m,k train car at a frequency of 75 Hz, and a second identical tuba played the say;n k:my*y,nd me tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blxxhp)ktr 1z)a/zy()1x ,lhpr ood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the shr),phx(xx1k)ta ) 1zl zrpy/ound source?   Hz

  The Doppler effect using ultrasonic waves oxzp44 dr o9 b.ou. uc.eq(pses/2mj/e f 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 570xdwu30:u 7 xzz Hz. When the wind velocity is 12 m/s3dz:0wuxu 7x z from the 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 movingmzqgg 5k.b(t) 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 2.3t3s mgq,yxew;2w vk+ 1 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes w wq,;k+sx3g2v ywme1tith the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of sound ise b/hu d)w-u0vnlmv2+u bti 0 (;du9tt ontuui(d9 ;wv 0n+)bml tteubv 2d0- /uhly 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 strikes the ocean. Determine to;h( ;oa dl(tahe shock wave angle it pro; ;d(alh(ao toduces
(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 g2c4sz6sg n 97cmt4eg+w)k sbk8 n:g i$/theta$ 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 go2pdc 4y9c *e fd*3sqthe ground flying faster than the speed of sound.o qys9c2p *d3gec4*d f By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downwak) afhu /t1em;rd from the bottom of the boat, and then detects echoes. If the maximum depth;m)ku h/e1fat 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 human audible range zr,vf84:vaho7flp5q ? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of manytl4/swjl8i-o 9f6n*y cb p/tk plastic pipes of various lengths, which are open on both/kb-ojt4s n8wlitp96 yl f*/c ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close tbm*ztrho 8r9ol/4 bu3 9(ktpco the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosqu/m ru9lpc t49b8(z o3to *krhbitoes?    dB

  What is the resultant sound level w -bs3zsajk(s) ag9l42 2n eryshen an 82-dB sound and an 87-dB sound are hears3s2yn 9s abjk2 s)gzlr-ae4( d simultaneously?    dB

  The sound level 12.0 m from a loudspey89uwehg n-1miz.al 5h7 xbp4 aker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all y417p9 -ub5halmzgw8nhx.iedirections?    W

  A stereo amplifier is rated at 15fnb l. hoxd;8+0 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the powxhln.o;f8d b +er output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devi6 2std 8m;uty)+anvnoces 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 distance of 30 m from a jet dn8ua 6nsvo2 my)t+;t airplane engine?    W

  In audio and communicatil;iaz*ojgn .udrj1 nn :0ph *y/ual;8,jgbx ;ons systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin ianxbwbl,vy g6 a3:n cfg,q(s)e -pi 992ryq0qs tuned 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 fixedf7ujjxv+h -hqo8.zt 9 points with a fundamental frequency of 440 Hz and a mass per unit length -uhh8to+ fj9zvqx .j7of $6.1 \times10^{-4 }$ 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 w zw(5igz*jo; h6vgyk+ ith water (Fig. 12–35). The water level is allowed to drop slowly. As it does k *6ivg(oz+ g5whj zy;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 g6a 9hrznud5dt z:p *j8 is near a tube that is open at one end and also 75 cm long. How much tensiou5z*6adth9:rp jzn8 dn 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 o b5reebg3*bm 8xolz6x qz ayf k3/n,7*xz)l1vne 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 coming frommei.nq :d8;phwk.: w y 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 p:ey:8 kpdnh. wmqwi.; oint 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 tvi f94a1:z 1faezludabui0+mf1m.(is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is zm4a aftuai1f (1.fe0b :ild1um+v z9the speed of the moving train?   m/s

  The frequency of a steam train whistle as ityooh;r h)navb)+4qp-ub6o c( approaches you is 538 Hz. After it passes you, its frequency is mqyo6v cph)n(4;bou)hr+ ob- aeasured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you canb/emqk: fw.-; l: uaye estimate the 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 certw:u: b;-q e/fyklm.aeain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding toge:w 0ex gn,d0rm* fpz+ up)cq1vther, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How xnewcq)vfd0zg+pu0m r,p 1 *:long is the other?    m

Two loudspeakers are at opposite ends of a railrssdxo4s2 (5troad car 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 frequency heard by the observer when (a) he listens from thetrox42sss d(5 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 innf1q ccnp9 dqev1 q//sy2tn4c7vgd32 the aorta is normally about 0.32 m/s what beat frequency would you expect i411 edcqs n/nvt9 v p/dnq2gfc37yq2cf 5.50-MHz ultrasound 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 speed 6.5 m/s while the moth is flying towarv .d7 *aeszyj9d the bat at speed 5 m/s The baj *s9v .ayde7zt 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 fi*c9 tpxm9a83big xc2(jpze 9requency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 m2e9az(b3i 99xxp ccti 8pmgj*s 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 signa+3-y,8ar kdavggd +a7bxn d-g*h u+3i ;qbhqjls from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sg+ng*hbua+3 y qq dh+ ,jg-v;r8a i7k3axd-bdounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromise ug8e;l:4 livwd by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for e 8uvl ilw4:;gthe standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” in-yxn *n rii.w0volves a long, slender aluminum rod held in the hand near the ni w.ryi*-0xn 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, 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 humau;;wlys mmqa3 mhvm9;w2 o8m;n ear at a frequency of about 1000hmmo8 32 l;uqy9 ;;;am vwmwms 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 kql.j 16,dl +n kk;2wahgul0j at Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’skl ,wj1gaujdl 6h2kn k+l0. q; altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is ixo b0)vvkv 1515 $^{\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