What is the evidence that sox6o,z ridu;q1jxc4zc1e8b 9 kund travels as a wave?

What is the evidence t 01vejbgj38aw: z3 c-)nem.xz mu6eowhat sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string toa8ny8q wx4/ (+mn r,i l1pyxso the bottoms of two paper cups. When the string is stretched and a child speaks into one 81i8wma yxr lsy /n4p, xo(n+qcup, 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 water, do you expect the frequeqq0 pf-0 0;wb hy1loynncy or wavelengt -l1wfpyy n 0h0o;qbq0h to change?

What evidence can you give that th4sup q3:ss mr)qxd4kemv9u 7*v-k 8npe speed of sound in air does not depend significantly on frs)7equ-8x3snm4dqrvs p k:v 4 p uk9m*equency?

The voice of a person who has inhaled helium sj5 km )e7fuy9yh +j kemr6e0o6ounds very high-pitched. Why?

How will the air temperature in a room affect the pitch 1i*dnba/ /hry of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of ssm mc39l vo0z*ounds in vario3 0 v*l9somzcmus frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer rcmm5hba3( 7:h:m3 efy gk5mbtogether as you move up thrmg mbk5(::am7ec fm h 53yb3he fingerboard toward the bridge?

A noisy truck approacheupzr;7 0q-+x. krbo,+kiye zi94a wkb s you from behind 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 high0;7iiy-ukkz+e9+ rpoqb4kr a ,w xb.z -frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in p/p p-*w r7wcg,wg+pazsx2 j,space,” whereas beats can be said to be due to “interference in time j wpxa 7+p,2rgcw/ws,zp*-pg.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowerh0( * nx6m nhma0jx4ered, would the points D and C (where destructive and constructive interference occur) move farther apart or closmm *0e4hn6(an jxh0rx er together?

Traditional methods of protl pqm wv6(3*(gjjo1t)nslmd *ecting the hearing of people who work in areas with very 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, 1j* (dop(*l36m)vs glwtq jnminverts 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 if)/s/tkd fak+2sv+7ss1 ex o. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in F++/dfikv 1k/fsxsa)e 7s sot2ig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same fzv5ivj -oi i apse.,09y*eh 4direction, with the same velocity?y i.*vh- eoi4f,zp5 9ise ajv0 Explain.

If a wind is blowing, will this alter the frequency of the sound hea5xbpl5 v1z a): 8m+ paiue*n (l9oorfhrd by a person at rest with respect to the source? Is the wavelength orbon1 p 9+h :xou5pim zrllav(5)*a fe8 velocity changed?

Figure 12–32 shows v7fht5x;9xa x)7nu mfxarious positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain yo t7x;xf5h)n uaf7m xx9ur reasoning.

  A hiker determines the length of a lake by listening for the echo of her shout 9h t;p hcj,/pzreflected by a ph9;jhcpt, z /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 ship just below the waterline. He bk) b1m+ w rno(wy-om;hears the echo of-1mbw;rmn(boy +ok w) the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths i1 t balaeo414vmc 4n6bn 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 drifting just above a school ofwodxv.t (xz.n1 *em d9ic(h)o tuna on a foggy day. Without ihd9vn.c xt*o (omz(1) wde. xwarning, an 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 of a cliff. The splash it ma* h+: tlo-wmynkes when striking the water below is heard 3.5 s later. How high is the clwhm -:+l *nytoiff?    m

  A person, with his ear to the ground, sees a huge stone strike the concre:xrsu5 s6llu(woa(4j 4ujyp /te pavement. A moment later two sounds are heard from the impact: one travels in the air and the oj jyoupus6(/a(r5:l4slwx4u ther 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 d0wp7qmj 4lci.q)lerk8a -zhtvt )4u.istance by the “5-second rule” for estimating the distance from a li-t4qwvtk a047jq) p8hlz im.cu.rl) eghtning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a s3-zr w bufk*r8ound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose inthhkusvn86dz.3o ds9 9 ensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB (tbs;t+;rsd;*umhgwos 1/ w uwhen fired simultaneously at a certain place, what will ;;1so t;s /*htds(mgwu+ buw rbe the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance y30og e s9,c 4.zhrox2ct jwe6from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint:2t4 s. jeezx9cwgc, 063oo hyr Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-x 5kmmy*i id2*to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What*x yi *mikdm25 is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output ofgnohu,o 3; 2s :kspn(m sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mou k,ogsunhsn:m3 (p 2;oth. $\approx$    $ \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 st;)1rvmf c u rnkj8fg6:w r1zl-rikes 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 250 W, m3yoa.jwl 5si 3) sik9while 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 connected in turn to ea 3yi 9km .awljsos35)ich 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 whe;g;f r di qp;.5 +29dakrpccwln placed 2.8 m in front of a lo+cr;qfcldir. w 2 d5gk;p;a 9pudspeaker 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 differenc hbjw a2gpjz1sof * -fx:,+n;j1tuba,e in sound level of 2.0 dB. What is the ratio of the amj: 2ahzp, uw+faf b*1jngo1j -, xs;tbplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, q) wi apz*4pmoap87 h7hry(ll+:a c9w(a) by what factor will the intensity z* o m aah:+w 94rp a7(l7pq)iycp8lwhincrease? 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 twice the frequeqku-ja,a7l :1w s e+ x4hhju,0clt bw+ncy of the other. What is the ratio of tcjah,-1wxq lsw+u u ,abt +hkjel4 0:7heir intensities?   

  What would be the sound level (in x-ikru*km o2xk6 )ucxo+o+2z dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air mok +oiukkom6 o+rx x*x-c)2uz2lecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem v gw3.0:fjry,3kh ksmas loud as a 100-Hz tone that has a 50-dB sound levv0ghj:fyk33 .m,s wr kel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detemx5) n4 m1tlou .qg)lyct when the sound level is 30 dB?))ql4tl. 5n mmo xgu1y (See Fig. 12–6.)

  Your auditory system can y z1:p5t1 0gsnpl ttu5accommodate a huge range of sound levels. What is the ratippt0 n1u s1tg:zt 5ly5o 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 fundamental frequency of 440 Hz. The l+p9aii 1q7j+b /rbf37bak k kmength of the vibrating portion is 32 cm, and it has a mikkbm+ +rfabb q3p9j/ka1 7i 7ass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audibleblef.w* i,(tn:uun5 j overtones if the pipe iu i.ne:,(ljftnb5 u*w s
(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 across then ,4lf6ho4civ(sacz ; 7kp*or top of an empty soda bottle that is 18 cm7zfr(4 ;,casl 6 kv *po4oihnc 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 range;sp b1h(h gy++kcjp8 k of human hearing (20 Hz to 20 kHz), wh8hc+(k+gsh ;b p 1pkjyat 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 odd qb6x.3chj6f 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its ox 36jdc b.6hqdriginal length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play kclcxf 4+i:0rl-b e,e E above middle C (33 +-f rec4le0l,c:xbik 0 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an op( 4g l.qf(yijlen organ pipe that emits middle C (262 Hz) when the temj(l y li(f.4qgperature 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 n l*:t-rv*4mye:jjpl 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hole be t3 . /00ll3kagk5i glvu:qrbvrhat must be uncov3kllbli3a/k rr00g.v5q u :vgered 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, but no u0n)ns 3qr*vkt at any other frequencies in between. (a)v u3qnr*s)k n0 Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It reso;lc9nyh ) 9my bclowo3+l), fxnates at two successive harmonics of flwc+ h f 9 lx)coy,;y3o9b)mnlrequencies 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 /bo:l a:g wq*v$^{\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-muotdoe wlxfssw.tq ;:3+6-z. f2h1 ih-long organ pipe at 20 u q.t:ftwl-z2i.w+3heshd 6 xoof ;1s $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. k;uv 0c-iz/a zIt is open to the outside and is closed at the icuzkv -;0za/other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 swo7 jfsz*ju p4 *1dw1d when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is uz1spdf*1wj*j47do w the other string? ±    Hz

  What is the beat frequency if middle C (262 Hzs 4svmy6-tr, e) 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 a+mo8u yx4jd de5 ;bj1dt 23.5 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 occu;+1ydjue4 odxb8m j d5rs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning for qys vm4zebt(z65(/jhn* bt0vk and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frtne5b06sjht/ ((qb v zzym 4v*equency of the string? Explain your reasoning.    Hz

  Two violin strings are tzo8aild j+- m8ura0( juned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequenud j+la8az-8o i0mj(rcy heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each t f b--w0+l4rm:f reu buhpm4+hry to play middle C (262 Hz), but one is at 5.0°C and the otep0urmb4:mf -r hfh-4w+ ubl +her at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of pb+ wr;*m7nct7bo;3;lzpj p a441 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? What beat frequencies are possible when A and C are sounded togmb;rj*; p7a7 o c+;n3pbztpwl ether?$f_A$ =    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 sp/vljob 8e 6i4/ bhz7uxeaker and 3.50 m from the otherv/i/ 4hul687ebx j zob.
(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 vib3-hs )qnrzxn ;rating at 132 Hz, but a piano tuner hears three beats every 2.0 s w 3;n-xnhr) zqshen they are played together. (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 wrpnlnw .pt;38cu;-irpa3fe 4avelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume rp8 3unlp34 ta.rw;fe-cpi;nT = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a cert 9)a4(gxx uis;pk12o fa/bvi/ikypb0 ain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 muv k xsb/ii1f/ a0x 9ybp(;op)2 gi4ka/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire enginpl - 3t*4d8nxju r8 hb.um5yhte whose siren emits ux4h-.n3lry 5h8t bjmtup8*d 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 source is mova5swa+l: y:j iqu ym06ing toward you at 15 m/s versus you moving toward it at 15 m/s Are the two fr 5aq :+:as imjywyl06uequencies 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 the6d7 ad q 4tec8m.kev9h same single frequency 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 frequency the horns emit? Assume 9m cdhe8dqea.t4kv76T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz 9i z*:gp62)hhys/acdz40 tla z dmy 8wap(4 lhand receives them returned from an object moving directly away from it at 250lzhza sa)zpdym8p 9c*/(wgt a4 dli:h6 4h2 y m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, thiof zlsw)4/y+5zf+s iw5q 0ee e bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the o) q0ife++ s5 4 zw5slwfi/zeybat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving fla7hih 9hs-rd 1,efr//jb gbx5kt train car at a frequency of 75 Hz, and a second identical thrr5/ 1s7bhfbk/ h 9 ijgdx,-euba 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 u1te kub) bcind7,:;ydltrasound 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 is flowing in large leg arteries at 2 cm/s directly away from the sou ,i1 d:kybde)b7;unctnd source?   Hz

  The Doppler effect using ultrasonic waves of frequencyq ld+e0e1 wkat.)z;tf $2.25 \times10^{ 6}$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. When the wind velocity is 12 3zli xitn;5jty7/wn2 m/s from/lnnz yt5x ti72 wi3j; 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 moving on 8rp4vniug,g1ekv j a r*/c)yh19rv( oland 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 2.3 where the speed of sound is ami;snss/ hcn ,f/7wr9;g 0rd 310 m/s (a) What is the angle the shock wave makes with the direction of the;9sw cmag d0 rsh/n;,sf7/ir n 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 thicy hil n.1f. gju ub2ck(,/u5wn atmosphere of a planet where the speed of sound is only about ju5/kyfu2h(cg 1iuc. n .lb,w35 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 x fp /d/8h uo-vjc) 9go5b(kfam/s strikes the ocean. Determine the shock wave angle it pro5(h /j8augo-bk 9vfd )pcxo f/duces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle jy;mk(bv-r q 4$/theta$ 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 theeidqegnz bwc ifsey,1;6 6djt,8( .j7 ground flying faster than the speed of sound. By the time you hear the sonin,61wtcei6e,bsdy 7 ;fzji 8g( e.dqjc 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 + 9benn4t (/:v st fc;6dau:a7jqukjj pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is dv (duk / +n7c;:6n asj:jftbu49tea jqesigned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the 3 vlipz*dzx )+human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sy;/atxi1vvm (b7jz 6l umphony. It consists of many plastic pipes of various lengths, which are open on b lxj itauv;6bzv/7(m1oth 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 sou/+z -3os*w-* zgas2 hw-gqz8ng nvfxdnd close to the threshold of human hearing (0 dB). Wh z dv-hzg+gn*qwxaw *s 2/f-zo38s-ngat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 8zl9r;5djyw- 5m.k:khv0sv :y:c ,le,ptdkih 2-dB sound and an 87-dB sound are heard simultaneousle.cskmhdkpll:h59t5v-: :dw0 ,zjiyv ; ,kyry?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whmy-;g4lz7ys- z-a zzsat is the acoustic power output (W) g zms--4z;y saz-z yl7of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. +6fpcbc dmut 8 y6h dqul1n0;1The power output drops by 10 dB at 15uycdp f0 b n1;6d m8+hqlc1tu6 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typicqk h)a9lealz1 , vuq *sh628afally wear protective devices 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 21 al vua hzlk,e*f69sh2a8qq).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 communica: 5jo+(iaoo83mcyy)fpab 6z ations 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 isfc gsrr.8bhr 5y,/ )yz 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 fixedcf nk *)9zzme+m)ltla -ox ,9f points with a fundamental freq )ol+fz*f x)-9 mm zectk,9alnuency of 440 Hz 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 ad ,iqmx. iazw q1e33:+1mnraw bove a vertical open tube filled with water (Fig. 12–35). The wa1a3,m1wi:rqxia we3zd.q+ nm ter 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 that is open at ue85;mlf7k-z2s b8njd a dlj7one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the tj k7lz87-f25nj d8 md laeb;suhird harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fullp0jb3w)t0f 3 c*kjx hr 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 sources. jv(pg v/16veu The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is1 (jv6g/pv euv the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles.te 4 1)p4hiswo One train is stationary. The conductor on the statiw e41o4 h)tspionary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Aftebaezh3c2 l 9.mrv(1 wnl*w:tjr it passes you, its frequency is measured asl.23 ( lwa tnhe:c9jzvw*1bmr 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars jubk/89ij- xs8gahg8 hqa *ziy4st by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a cehi 4/x8abq- z s8kiy *gh8ga9jrtain 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, produce a beat frequer0ek(ap g oaj)3g qiu 0g1s7a.ncy of 11 Hz. The shorter oneapi01(s rg.3ga 7joq)ea0u gk is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as izi6q6i2jy ltpy- 1ns :t 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, jniqts6y- yz 2 l1:p6i(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/atx hgix:z:- flow in the aorta is normally about 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 r:a zgx:-/h xtied 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 moo1jpqgb g+ambdkxp53;t ( 2 g(th at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the poxk3;(q2p5ggj a +1dmbt(gb bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. Thge4369f 4,ohgdd fxs 1pcsq-xf,lr 2le pulses are approximac- ,p43sr6g sl1,9h xx gef4lfdo2fdqtely 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) was once used to send signals from *jx(9 ;o:ck,qhyg/;zwv twbe one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blowz9 hjq vo;b/ xc*e,:tww ;g(ykn 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 presence of sta;i* (q3+uni yyaw3j8q4i anzmnding 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 frequeniny *ia m uyq(inqj3z aw4+3;8cies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “s 7xsuc p1aqz j/,0+uesinging rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-/u1q +pj es,a7sc z0xucm-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 thrak66ybp uj9mg6n/;ue human ear at a frequency of about 1000 Hz is b ujn;a6/96 6gpkuyrm$I_0$ = $1 \times10^{12 } W / m^2$ 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 .j17 yj5 adfg.t7ekrethe sonic boom 1.5 jy kedret.fj .g1a 757min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is f)p g55z su(nys,zh+ rdt5p 3h15 $^{\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