What is the evidence that sound travelii1mj:l ft :s:s as a wave?

What is the evidence that sound is a fo+9dacfaq1 pn8slc/- 6ax:6zk umyn)wrm of energy?

Children sometimes play with a homemade “telephou- s p*fy(e4.)ou 2fxa m6a/ .4z1tbhngfgb phne” 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- p6.m4bta)4x yz1g onf *sh. fauepfug /b(2h 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 air24thz4x;w rok4 ds9ev into water, do you expect the frequency or waveld4 osz;xvh9e4r24k twength to change?

What evidence can you give that the speed of sound in41:afq*i 4vgc8j s.hmd6x drg air does not depend significantly on frequenc6 q: hi*j14as fm.v cddx4g8rgy?

The voice of a person who has inhaled h/cjuy, 1z(wolelium sounds very high-pitched. Why?

How will the air temperature in a room affe7 qjolszw 8vy.z 7yclrzx((-,ct the pitch of organ pipes?

Explain how a tube might be used as a filter to m7nda7 c1)jhsreduce the amplitude of sounds in various frequency ranges. (An cm)jnh71d7sa example is a car muffler.)

Why are the frets on a guirzyd pz4m/0;0-uslc star (Fig. 12–30) spaced closer together as you move up the fingerboard towarr0zdyl4s;-0um/ cpzs d the bridge?

A noisy truck approaches you from behind a builu-bv9cxrhn 28 ding. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly h 8cvunb-92rx“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 ujbdej ,r,7k k..o (qbin space,” whereas beats can be said to be du7rk,qo d( ekj.ju,b .be to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speaker)ul (pvr6;hz: xxwuvv: x3zsoz nd 1n0.ly8v,s were lowered, would the points D and C (where destructive and constructi uz,v 8l0yrzvzx: 1x6 .nv)wo:; u(pl n3hvsxdve interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with v(9wwus5mr5 vjery high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levelswu55wj9 vs(r m reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wavad8-z stk*r7frsv8-8 yz si0 ne 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 component frequencies farther apart-kt n sz-as y87s* v8z0rifd8r? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sm dy3,rrx0yvt-w/ zm + b4irx3ource and observer move in the same direction, with the sam,tyv-d0xryrwxr+4i zm 3b m3/ e velocity? Explain.

If a wind is blowing, will this alter the frequency of t ek/dk3f+zai;d. c v4e+5nghbhe sound heard by a person at rest with respect to tnb hk ceki/34v.gz de;d+ a+f5he source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitpr /k.fq3)ba2 .knhe oor is blowing a whistle in f2./ o rke)n.bk phqa3front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shout r01ncr ly7i nxzd0vp:5eflected by a pvnd750cl zn:ixyr01 cliff at the far end 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 side of his-v/z 0x;fif c5e f5dxj 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 does not v/zf5 xfv 0-exf;5 cdjiary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20 y:ag3 xhz/y:q $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above aq( 9icfj1 ytj6 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 backfir qfcj6(1 9iyjte is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. * bg-o ;om:k3 zloq ;cfju2-jcThe splash it makes when striking the water below is he:clkocj*qfbj3z;2o-;-u g om ard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge g(pq t)uu*6y zstone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and tht)gu*yq( zup6 e 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 errht wy+ u9gs;(vor made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 3vw+ ts 9ghu;y(0 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120xt l *e/b55sru,vri5dg ta938cxog k ; 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 inten wdh2pv)i:*rodzrou (ze-. ;y sity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a moa t w kylm 49n8d1jymz2/w0.sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint ma 1ok.lwj/nm02z y89wmtd4y : Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with q+gg5 e(yjy z9:s :xxw/l:zzc four equally noisy jet engines is experiencin xxlge zgs (:w+:/jcq:z5y z9yg 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*nugeq7g a,s/sh p n.8 to have a 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 and thn,ae* 7/uhsq gp.8 nsge background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person spea+6z)a kogzl m7king in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centeredz7 )o +6kmglaz 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 p: mwx.m7t(( 7 ezgycjwhose 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 250 W, while the more modest amplifie c*j6vv(bmx dyi .j.j;r B is rated at 40 W. (a) Estimate the; v*bdj.ymj.(xi6cvj 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 front of:t/nkx n0jyi(z sg2pgz(;.x r a loudsgtz;nxi:2gjxr s ((. zp/ny0kpeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 6k,nlsi/y z) h 7hk2rppn x+,-*h yzkp2.0 dB. What is the ratio of the amplitudes o hp6zn l-,iny)kp*2kh +p ,hr zxy/s7kf two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a)9n mky x528efy by what factor will the intensity ixn k9em2 fyy85ncrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twids-3qf94 ;n-.ce qpk af1qncrce the frequency of the other. What is the ratd ecq 9p- 1raff3-qsknn4 q;c.io of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that correspondg21 *o qmmyd*w dp+u:jmn qw9)r 4xsq9s to a displacement amplitude of vibrating air molecules of 0.1d)9qpgwumd1jqrm*+: 4 *m nx29sqow y3 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tonxknl8 2 +/dyml7dhr ;he that has a 50-dB sound level? (See Fig. 1 h+y rmldhx8d;72 lnk/2–6.)    dB

What are the lowest and higheushyh5 do-t 9z: e3ubb50 /chifx(bt+ st frequencies that an ear can detect when the sound level iss 3hye:btu 5co+tbhu h( /db z9x50f-i 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge ranglxl hp:88fbn(lt(z v0e of sound levels. What is the ratio(pf nzt8: (0l8hx blvl of 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 fundamentaljl/nl e/1dt u/ frequency of 440 Hz. The length of the vu 1ne /dl/l/jtibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are thl7u(:ld o7 wh-kv v*/:xmhfp be fundamental and first three audible overtones 7 hvl/b(- uf:hpd: 7vlw*omxkif 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 blowip-u x*2ty zhplwqn n+9ik lbk383p9f+ng across the top of an empty soda bottle that 9l*k3ty nz pk+ixu83hnpl9 bw-qfp+2is 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 s0js( p v4sqg a*v6 /x3exkhd-jpanning the range of human hearing h/k3v6 e jvg-x a4 0sdjs*qp(x(20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmon 0kyle/ vj)v,3 * uncxc,.xsdqic. What will be its fundamd3e* n, lj x)v0,c.u/ xcvyksqental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned tovh0fkhdd-w(ph*k s7md* :9ew play E above middle C (330 Hz)fhw9 kvh m7p0 hw*d:-( ddes*k.
(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 op.3xs)e tzw) mren organ pipe that emits middle C (262 Hz) when the temperature is 2)rtsm)wzx . e31 $^{\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 20 , o rpa6 nd-a/qg:xc)z of//oa$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of 4uss77flq9ab (w:bho w i:t1a the flute in Example 12–10 should the hole be that must be uncovered to playof 4u:q ab:it9ass7(1bwh7lw D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at a ka5uo9+ e6esbfvh+nyw9 g4g)ny other frequencies in betwf v)e g+bo 6 9ga5k4uny+e9hsween. (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 endsk xaplc*7p 29hrfn;m3ti29 zt . It resonates at two successivekt *2 7f;ilthcamxp9r3p9 z2n harmonics 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 v srvn k8z61y1$^{\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+vo 0r,yyotq e5s0hf 1 audible range for a 2.14-m-long organ pips h,r 10o0qot+fvye5 ye at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatelyo y5,wnv1pz 4oow /xpyg65-3b (zkhbx 2.5 cm long. It is 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 your ans6hbbw op-no(yx,/vp4z gy kxo 3z15w5 wer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears o(wp42w uk vxw4ne beat every 2.0 s when trying to adjust two strings, one of which is s4 xwvwp4(w k2uounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if mw(6 gzbn* r9ouxhj9 4 8n/fbwniddle 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) opv o9awl 4k2f-ierates 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 simult-2wko4la iv9faneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning f3 .; ubz/nsvwdrl;jxpyo2:7iork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency ofi;;p: z 3/v7rdbw2sx nou y.lj the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. i7ox. 0 qbsod6The tension in one string is thendx b.s7o0 q6oi 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 heard if two identical flutes zv n)5s3w/tls each try to play middle C (262 Hz), but one is at 5.0°C andw/s5stl)znv3 the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork 3nf eqa)d8/ksB has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? fesdkq3a) / 8nWhat 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 pz/ b 7 l.iuxjhht.2,u9dblt2person stands 3.00 m from one speaker and 3.50 m from thb.2.ij9dxht/ pbu , l lth7uz2e other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a pian b2 fyf6m2,- e8lmnjjuo tuner hears three beats every 2.0 s when they are played together. (a) If one- f2b m6y2,jmfuelj8n 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 aj(zfc82/i mbfir. How many beats per second will be heard?8fi(m fcb2z/ j (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of aj xw5tf *t5lnmqd.s pog4(sieqa;s*,4w9v 0m certain fire engine’s siren is 1550 Hz when at restsvimjmxq 0sqgtf 9s55a * w;leopn.4 4, dtw(*. 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 h .x-tmvscy1yo7 o2fy : vjv)2you detect if a fire engine whose siren :jo7v1h vtxv y 2.fysmy- 2oc)emits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sour/xnted*jv xdp j *79,zce is moving toward you at 15 m/s versus you moving toward it at 15 m/e9* ntj/ pv,7xdxdj *zs 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 frequuo6oyd l7:i8* iqi t d*h3y:-eoq .uqnency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frq 7oyodiu-nt3*eqd*y h. i6l o:uqi: 8equency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 k- /wpd9v7lwbqHz and receives them returned from/q9wp- d7lvw b 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 ph 9vhxxahs- 6rtal99:vp(6 pwall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wavh p-pv r pt9sv6hx:l(h996aa xe with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimeycl0 9 sdr);mdnts, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the rai)ms d; 9r0lycdlway 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 blood-flgz z6ed f*(-qzow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1z eq*dz-6 fz(g540 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 frequencywveq8t6qth c4nhj2 g (:16c7nak ;asc $2.25 \times10^{ 6}$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 frequencvuhu)7 7aw6rc)y1xztokjmsk :/ zd7 (y 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observerudc w:z r1j6 7xyhmuko(k)s z/t)v a77s 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 .,;y*mdyd0l *jf itc 9o7zrmtif its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of soundi ym h/6+27sbswsndn3 is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motioh3 + i76ysnnss mw/2dbn?    $^{\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 atmosphe5kovst3)cwj )6e (xeyre of a planet where the speed of sound is only abojwk 3s (c5oxy6et)ve)ut 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 sh./oxdnk-xw7 jo a0p u-,ah vto:1cvp0 ock wave angle it produx -:. n p0wj1 h/cv0,koxto-d7 ouapavces
(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 nm9/ 9bdlr,a z$/theta$ 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 es)/xz/x p4 tgixactly 1.5 km above the ground flying faster than the speed of sound. By the 4/g xtz/s ip)xtime 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 dow43tz z8b c0fxddb)4n. -t5eldx ym.ax nward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work ie8 f.t)bt.z y4 xd3-mdb dzx05xln4acs 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in th8ch x*,w 9eiuqe human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe 0sm ge+g:g; nusymphony. It consists of many plastic pipes of various lengths, which are ope gn:;gs mg0ue+n 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 sound close tj /bnuubf:pv z,)*it ,o the threshold of human h vnzpi u bft:*/)b,j,uearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and ansp0.tuswkf c 6twtn-7ac07,n 87-dB sound are hear7w 7sn,k 0c 6w-tt0.asf cpnutd simultaneously?    dB

  The sound level 12.0 m from a l 0it+an9xt7x9tnlr -wv 6gs 5goudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it 0g-t a+rw7tlx gixt 99nv5s6nradiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000-msmu;n)2 a2yzf djtgp1 0w1o Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 2go1 0paw 1 t;mf)yzdmu-nj2s kHz?    dB

  Workers around jet aircraft typicall3y35iyaff6iomf:/t l1k uig :;nu* dn y wear protective devices over their ears. Assume that the sound leven; tf i/udykg1f m*y653o ::3 fiinalul 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 airplane engine?    W

  In audio and communications systems, the g7:bljcf i8i h,ain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned i;1c zcy+7xex-.y94ck,s 1 zg jhaebsto 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 with a fundamentyz,a6fs.m; ke al frequency of 440 Hz and a mass per unit length of mf,6;sayzek. $6.1 \times10^{-4 }$ 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 witner 2l y7-7hbn+g:cq,unj4h z6hq.tph water (Fig. 12–35). The thpg- c7 2n hnz.uy bhnj4,e 6+:qrq7lwater level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube tsx5c hjow- n(,hat is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fun5os-x hjnw ,c(damental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fuyd,;yybtwd 38h :6kb r w8w)fzll 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 from two xpiliop+ 2dgt6 su (91e2, vbvsources. 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 pv ei1+lgo2i(,t xsp269 v pduboint 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on +/hyp /b:a/ sz 2dnhftthe stationary train hears a 3.0-Hz beat frequenbh/h//ny d s+fp at2z:cy when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches yofkpz) )hherm )pfr;6(u is 538 Hz. After it passes you, its frequency i phkfh;e))z)r6 (fp rms measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by lidnwcqjl/gw89+ i 3e;* gaxb4rstening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the s ijq*e;a +n 3rwx/ g8dblc94wgound of a certain 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 together, proto.i5o5 c f;mxduce a beat frequency of 11 Hz. The shorter ontoc5 o i5m.;xfe is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a stati(o q ee agtfk8iw47 3:un+fr3gonary 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 heag 7if4e3 eao:3nt(8 u rg+wqfkrd 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 about i n;r)mu e;g1bwa2wo) 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 waveu o2)e)rmig1b;;n wwa s 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 flt3y( t gmn./v/zxps2 wying toward the bat at speed 5 m/s The bat ext/z ptn .ym3(wvgs/2 mits 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 h 78cts)dy e7lgmi4zy 1igh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by tl 87cm714)id s tyzgeyhe 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 Alpine9svq6xo4p w 1b village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played9vw6sob q41 xp 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 compromised by t7 wdbsfw)0sbmtvm;z6)80cx/- p thk the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a livib ds/-f0 6tmxtkc)wbmw z t;p80v7sh )ng 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 demonstrata*pj/6mb+flsh z) a1uion, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The abzjhpa ) 6fs/l*+u m1rod 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 human ear at a frequency of+n:y 7 5elswi/zy 8zquk ,pua6l f+7s:mkapg4 about 1000 Hz ywgp78z/47ss ik la6 qlmz,akuf+ ::+ueypn5 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 soni8 m xiwpmx7 45ds8k,dac boom 1.5 min after the plane passes directly overhead. What is 78md m8 daxwxkp4s, i5the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatzc; uemgdm;j- tca+se*q,yf85( o 9bo is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h