What is the evidence le8a3wsnw88tvq9b8s2w; t q1kt k qz...tz sethat sound travels as a wave?

What is the evidence that sound is a form of energy. lep2uinrb10?

Children sometimes play with a homemade “telephone” by ath l,om3bx b4tz4t(ye:g x 1fj(taching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the othxh1:gb tz3o,tbl4 ym j 4(f(xeer 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 water, do you expect the frequency q3-3rma mnp* /)encesor wavelength to change /mrce3)meqsnan-3 p* ?

What evidence can you give that the speed of sound in air does not xf qf1 w.v+e-xxd/h 8hdepend significantly on frequen-xf8+w1. hqfxd hex/vcy?

The voice of a person who has inhaled heliuq2/mtswg: n- km sounds very high-pitched. Why?

How will the air temperature in a ua:6wdja7rce1um fjz dy)2+ 1ef fk82room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of so ibz*ua1-ahu0 unds in various frequency ranges. (Anu01 ua*z i-ahb example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you movh;fh .uz7lp )gtk5.rc e up tgh kzp5rht .)7f;u.clhe fingerboard toward the bridge?

A noisy truck approaches you from behind ofgz- qsc;d, qoja: bo)59ijze7lk53 a building. Initially 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. g5-c,9sk fq 7; eablzjq 3ojz:odi)o5[Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats cw,tw :fw i;am0an be said to be due to “inte;fa w0mi:, wtwrference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were loweredw , df,4 we5ewmql*l)q, would the points D and C (where destructive alldw*we5wm 4q q,f), end constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with .7dnyz/; sfa1m naq+uy go* 9bmuwy,5 very high noise le ufzwy s*mq.d ay19o anmu/;5n gby,+7vels 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 waves shown in Fig. a1g( ep.es) bzjz,qp912–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two componenzg p9,z.)p (s1 jeeqabt frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if thepipzob *r (*oemd09o( source and observer move in the same direction, with the same velocity? Exp*io pe9*b((0rzood mplain.

If a wind is blowing, will this alter the frequency of crrrn2e y6utg+*s fv.6, o do,the sound heard by a person at resr,.u n2rd etv+6o,gys* o6cfrt with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on0 f3xisg-p:kg a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A tgps0 -igk xf:3hrough E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listenin+ .z*delpj jy3jch 6-99kyznrg for the echo of her shout reflected by a cliff at the far c+69dz*zrj9ljhk y e.3pjn-yend of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the sid--cper* 6dcije 8ys ,j,+druse of his 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 seawater is 1560 m/s (Table 12–1) and do p+,ijs6-u -er,es drc*d8ycjes not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelee0gvj ee2-bxs:g/ vn.ngths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is driftinl, j wu5u+gjr5g just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is hj5g,lwu5ruj +eard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from 1i7ik w-grjk* the top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the cliji1rkgw7k i-* ff?    m

  A person, with his ear to the ground, sees a huge stone strike the concje 85z 599hitw8ytf vloe8.gm rete pavement. A moment later two sounds are heard from the impact: one travels in the air and timt tgvj5. fl8eoze9 8w985y hhe other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distanahi9/dtvqz/ 9n:eco4ce by the “5-second rule”4 ne9/oad/qz c:i 9thv for estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound a zsr,mnx.ct+ l.7 4eyst 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 of1w/7k+(rtau h-f/e( kygezf v a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound le6n*5 rvz(fr v 2qees9ufi .o*dvel of 95 dB when fired simultaneously at a certain 5sqnru (e 9 vf*.zifd2orv*6eplace, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an2;k7,3eo sv jqjx,nkbb2 k e6k airplane with four equally noisy jet engines2ne;qkx sev6ok3bk, 72,bkj j 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 engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, wh/:n;pf- sndj zereas for a CD player it is 95 dB. What is the ratio of intensdz ;nf-:np/jsities 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 perso3t)/d8j qsjz s0 - mhsauke19yn speaking in normal conversation. Use Tablk/9tsah z 1sm)y 83e-uqj0sdje 12–2. 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 strikesa;xduoq,ot2 6 an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 25l(j/u vh/m+l f0 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connem(vl +lj fh/u/cted 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 frontn5dd 5(*re-shw dm ;ax*vd5f r of a loudspeakesw5nxdr-;5 d**vd5ar( fmdher 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 levt *-8e)p-j8h pd ; duguk2iulfel of 2.0 dB. What is thh2iludt;*8fd -e )kg-pu u8pj e ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled iz. -n dwldu 7)u:ju3 t.,:bz4efr63g uhorcl, (a) by what factor will the intensity increase? Inczel6u3dnfuc:h:bdr3tujz) li 4gou w..r7,-rease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal dish 6ne4lprya, r*3 cqhxy+*5 sqplacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensitxn3eql*+hq hy,*psr yar64 c5ies?   

  What would be the sound o njc6e6*/ k izm*d)qokk/4g xmni-5vlevel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating airn)c5 6qi*jok/vz mg -e*n4okxdm6k/i molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to sec goocrp-mtq 7t3*j+. : q9seeem as loud as a 100-Hz tone that ha.j+e3mp7qg o c*tstoq r9c: e-s a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when t; c . e+cjuhmh.7 h1udfe/sb;khe sound level is 30 dB? ( m;+bk/cchu 7sfej1e;h.d.h u See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is thej)cj8qrqcohg14su8t 9 83so r ratio of or1scg8rocuhq9 t8 )43 sq8jj highest to lowest 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 fundamenlw2 v2j*,kgxko uskf6sbc ; ;4tal frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under gkfu2 jw kolk 42*xbc;s,6 sv;what tension must the string be placed?    N

  An organ pipe is 112 cm long. Whj7n *9on1c5b8j v lfcnat are the fundamental and first three audible over 71 j5n cbcfvnljo*8n9tones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing, b5umii;y:zsay a 7fa,r8i7e across the top of an emyiy5ze f a8uii,;a b :7r7msa,pty soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the rane5tzzz.g(w -j, *br; gvvoka- ge of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requi,.(5v -vbtgz- r* ;ewzko ajgzred? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. Wk.b3ffr +jo 2*bh0wzohat will be its fundamental frequency if it is fingered at a length of only 60% of its o32ro. b ok+bw*0ff zhjriginal length?   Hz

  An unfingered guitar string ise5q1 xrpu r.4z 0.73 m long and is tuned to play E above middle Cx zeuprqr14 5. (330 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 ofsk8lxb3/ ik i2,*ld6* clteui an open organ pipe that emits middle C (262 Hz) when the temperatureb*3d/6i8c*slkxie ltklui ,2 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 ak trci1)/l y2m pv;*zc :jovz7t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece osiez u qzd-oy .q-.6k1f the flute in Example 12–10 should the hole be that uo-zk1-.zyise q. q6 dmust be uncovered to play 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, 5g4jx-h5iwvgbut not at any other frequencies in between. (a) Show why this is an op wgj-g554xvhien 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 rejmb1 cg n.gu0. m :t5;nh/bonbsonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What 5. ojm.n1g ; 0bb/bg nctmunh: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 u 9zkc)maeri/64or4d $^{\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 a*f9 :l:l1m t5: dlywm5floq jare present within the audible range for a 2.14-m-long organ pipe at 2o my:5a::1dqm5lw9fl ftl *l j0 $^{\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 outs-8cvfshz (tmu+9 -z.ixv//o pvgz gw3r,3vbiide 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//z x 3vh+vz(gw9-vb.rptgvi-8 fizm,3u c so. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strin7jgxeie3d 2, wv1rg*ags, one of which is sounding 440 Hz. How fe2 aj*g3w7, 1d girevxar off in frequency is the other string? ±    Hz

  What is the beat frequency if middle Ckj7 xd 9pw-(vr (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 2( isj*p8ql.dihxin. s3* i4ge3.5 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 occurs when they are played simultaneously,(hii.e inx*4s8 ij3lq sd*g.p estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fo1em9k0 u*)b anxi- aupuw7at-rk and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reab0e n7wi1)ua9-a takmupux- *soning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in oneu 20u-wd1ta ah jb)jhmb6 m,/m 2:alyr string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are m2tm mua-/hr2h0lubw)d16ja:b jy,aplayed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle C+ ey2d*fj.ql j (262 Hz), but one is at 5.0°C and thel.q 2ef yjdj*+ other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency oe86b l ;3ponczf 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are soundcz3; npb 6el8oed 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 speaker wntls e oi7w h*1ch-xxm)8)g0and 3.50 0)x1hs8n t*we hmwi )cglx7-o m from 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 b t0wb9jps8m 5se vibrating 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 bebsw 8st095pm j 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 ul+m 2s to8op+m in air. How many beats per second will bpoou+ 28mtl s+e heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 15v cz5p/*sp6uwadtt4p 6y, :zu50 Hz when at rest. What frequency do you detect if youz:/y*twv tzp,6p cd p564ausu move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing stilfv2kyb*g j2 sn s*rp8(l. What frequency do you detect if a fire engine whose siren emits at 1550 Hz8s(yg v brnj*2*k f2sp moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shifp.; ,xmfpi h7et in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Aim 7pxpefh. ,;re 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 theh2o /e km+t7dd5py )yn same single frequency horn. When one is at rest and the other is moving toward the /d5h+)2 yn7toe pmyk dfirst at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz anv0ng6igr5/( e;8rpkbz /vf f zd receives them returned from an object moving directly away from it at 25 m/s What /( e8/fvgnpb5z 0kg6i rvzrf; is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits ana)ujvvd -4-h4 :wima w ultrasonic sound wave with frequency 30.0 kHz.-d: u v- hw4m4awjavi) What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba w- 2yoqp8v.xx)of t zid1b8kt/q4g p+eas played on a moving flat train car at a frequency of 75 Hz, y8b 4i+kz-q8./ vtgpo2epftox1)xd qand a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultr s.t0syxz 6kz/;/qygfasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood 0 sq.yz gfst/xyk;/z6is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultr* c,py1e 37r/b 4ig+vfcfbbr iasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz.e:w6 . d)io zqox3mue: When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest, :i .)e mx6ez:ou3ow qd
(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 spe5sc:hup80c chb,s tq 8ed 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 whoas4) o9 *ou8w0lufgk0,v md mere the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’4a ws0oufmm)o9gkld 0 o,u*8vs 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 to(n2/7 3zdrgbd e0.;tehelr p cyyr1* he thin atmosphere of a planet where the speed of sound is only aboghee bc1yyzt ;o(d.lr*pr/e27 n3d0 rut 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 lk*t twit 9:a-d z9)oem 9*bt0tiy8vfocean. Determine the shock wave angle it produces v: mitte -bo9k*itt 90)y8z9 lwda*tf
(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 - 9f 4ma6p8 uok7cy(wa236egotmtzef$/theta$ 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.v pbv+4yp/o2 k5 km above the ground flying faster than the speed of sound. By the time you hear the sonic b v2vy/4kp+ob poom, 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 tx/d nxnb mku3nc6du fkts/ 65 ,j:4xc;ut 3yt7hat 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, wh3 bk3uxy csxdtmku:c,n n xnfjt5tu7d//;64 6at is the minimum time between pulses (in fresh water)?    s

  Approximately how many octavecr+r 9+dd t)oi0t3r 3npmlth-s are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display callj/qnfz5.k55q2n5fh4sr .c2;fo6c tiuk z onmed a sewer pipe symphony. It consists of many plak5fcinon65hq n 2qf/ojk ;umzts45zr5..c f2stic 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 person makes a sl 84 /y:howd84enx dpwound close to the threshold of human hearing (0 dB)w 4/8y :4oxhdnde8 lpw. What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant soq)0+zhu y9 mgpund level when an 82-dB sound and an 87-dB sound are heap h9gmyz+q )0urd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, i hn8(kxyae./. 8s jnqys 105 dB. What is the acoustic power outpuy/j nn(8aex. q8 khsy.t (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W cm3h 7s)4yxdz output at 1000 Hz. The power output drops by 10 dB at 15 kHz. Wyxszcd74 3 hm)hat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective dgq,t0*nt p r0lrch qyb1+ 7x4aevices 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 u ,qbh +t0nqy*4ltag7 cx p10rrnprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, 2met3ri .by n*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 i sdulb0c .;lon2v. /ums 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 fixed s(1 be4crf ndmv6b jq k)h65zdhv-s10points with a fundamental frequency of 440 (6 e5dvh1zjh m4rk0) q16ns fdcv -sbbHz and 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 ver qq/i/ud6(yvmrvkl j5+7ng v+tical 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 yiqv /vrm6/qjv gdn++l7( 5kuthe 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 a tube that is f+hvj;z;1j76lw4wtn e rwyb0 open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in ie rvl whwj6tf+bz;4w70njy 1;ts fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full l7mps4 8 o3c:f8xp xlaxoop ($\frac{1}{2}\lambda$) 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 from two sources. Thq420 uaf- w3bw na9uple sound is loudest at points equidistant from the two sb -40uw9aqnul 3fp2a wources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationaryyv fprscw,1 hf-1:jq8. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speedf-h:v1 yfcj q8 rw,sp1 of the moving train?   m/s

  The frequency of a steam tihz2 8g*dy.mq rain whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity2i hzmyq.dg* 8)?    m/s

  At a race track, you can estimate theezo * gz(j)jir h) z1n2j.,0qi,uln cj 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. How fast is g eo2zj0niq, n)1 z*.,(hj)urjl ijcz it going?    m/s

  Two open organ pipes, soundinguv:k oz*j*tlloj15 . b together, produce a beat frequency of 11 Hz. The shorter ol k *jzjb:*.1voul5tone is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a rg:(0nsyh84 , v/zimfes b6qprailroad 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 the position A, in front of the car, (b) he is between the spn8b(hs eiqf4 vzg,/0ms:py6 reakers, 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 about 0.32 m/s what mjed u 8p6)stgu*t g638wed k0l/cq2s beat frequencj6 0wg gm de)2t p8cu 8d/sk3q*lues6ty 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 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 f, dpeyod9vi t,7:l w+en4 2irthe moth is flying toward the bat at speedy7,rn oti:4w2l,de f9i + pevd 5 m/s The 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 pulses as it approach2f*;te,dp9 dhs; lglhmt6 ) otes a moth. The plts eo2h;h96; ltg m)ptf,d *dulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) wa(fxnl94o3r ju+cpyo. n gn+f*c1dut75 (ebizs 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 instrumyj f7 ou*(glbfx+5+ c pt4.r1e(zunin3oc 9dnent, 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 compromised by the presa(h55vnhi+k f ence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nn 5+h(ikhav 5fodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slend2(fex/kwj d(;fq unv 7er aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod canx7( udf wfjneq(/2;v k 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 hearingzy/hy y; z(d9zdyr(r 4)t:y clec w8o* for the human ear at a frequency of about 10004) l/ywe(8rr(zd;zy z*oyyh9y d:c tc Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic bo 1zggevg*si8u+1/iq2(d h orh 2z8wfwom 1.5 min after the plane passes directly overhead. What is the plane’z ghfeoqwhgv uid (+ 8 2wzr*gs1218/is altitude?    $ \times10^{4 }$ m

  The wake of a speedboat isov dly4x101 c:dl1dp p 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