What is the evidence that sound t+sj/uy nc 5(heravels as a wave?

What is the evidence that sound is a form of )z6u nns9:psi energy?

Children sometimes pg9 es1q()(tdqy (.cem,sei wilay with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cu wi1(e sceei)mg(,y.sd(9q tqp (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 or was-t g)+ (biaf 8s.ijzsvelength to bii z8g)taf .-sj+s(s change?

What evidence can youl r8 u7kswb .7va3avv+ give that the speed of sound in air does not depend significantlyw7u ra7val 3vskv8.b+ on frequency?

The voice of a person who has inhaled helium sounds vereb+g i 73e7dktbw r) vm8is ,hxoo+w16y high-pitched. Why?

How will the air temperature in1/(jcm5bqg jl a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitpl8 1*rtds p5uci(iq 5ude of sounds in various frequency ranges. (p1ii5qs(5r ptc 8 l*udAn example is a car muffler.)

Why are the frets on a guitar (Fig. 12pb8atq3* fac6/scjf/( y wd*x –30) spaced closer together as you move up the fingerboard toward the bridg/scd/p*ty fxfq(ba6j3w8c*a e?

A noisy truck approaches you from behind a b)y-y+odu, bu ukn8)t oj/ :+l.ytxcgvuilding. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — yoyvt c8ny yo +:u,).t/dubgok+-)lxuju hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas ixxf:p 3b /gbl vmv7f+5z 53yrbeats can be said to be due to “fv3i5yxp5 f g:mr3+b vb/7 xzlinterference in time.” Explain.

In Fig. 12–16, if the frequency of tdix t7ju 1e.9bn mew3y) x8+eu w+7jbvhe speakers were lowered, would the points D and C (where destructive and constre7yd9 bb ni e+v)17 uxxmtue8+3jjww.uctive interference occur) move farther apart or closer together?

Traditional methods of protecting th*0 ;mx+oe;zx3 u *wrkxao 2qtye hearing of people who work in areas with very high noiseo*zqkt;x2o3mw xauy x0+ *; re levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in ;l0fl cudcz448bi cd/Fig. 12–31. Each wave can be thought of as a superposition of 4fid8zc0c ;ldclb/u4two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if t gkgkcb+ xo0zvz/v)1oic.3 d;he source and observer move in the same direction, with the same velocity? Expl1gv);kzcg3dc+ ibx z/v. o0ok ain.

If a wind is blowingbfws/nnyhy, ma4q uy(;(( e,wofs n69, will this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocitymhsnaw 4/(nu,s6( yw(;f neq ,oby 9fy changed?

Figure 12–32 shows various positions of:g tjo1y(jq0 q 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 c(0gjyot jq1q:hild 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: yf 5 a/wolc3yu/fp v::jtpz* her shout reflecyc/jy:fp:l/ :ofpw*53va uztted by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of (lm . jc:+n/v m+xnp 6h5/)crlbnhph whis 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? Assulp /r /hwm) n hmcj .:+lvcnp(n6+5hxbme 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 wavge+ gz9:zwnm .; cj*dn)db ow1elengths 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 dr9 ziw+a so7bl,ifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km aw z9owa+7sli,bay (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 makes whnxr yg lqeqvz*:x;9 .3en striking the water below9 yg.ern;:3q l*vzx qx is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the conezkmmifw0 zr ( +2 ;nv.f4lj+qgoks 50crete pavement. A momen5ljf02ko0(msw qvz.zrg+em n4f+k;i t later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made oveya3:mme 2 g+pjr one mile of distance by the “5-second rule” fay2 3 pgmem+j:or 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 o y82hx,i ;ptmm,tpa .zf a sound 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 intensity z2*pn wp8duobdt2 ;s h *,shi-is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when firvsfe n6nn4/ 0be) gd6i (f4mkzed simultaneously at a certain place, what will be the sound level if only one is eezfnnim4 (gd/0 )6eskv 46nfbxploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with fourjbd+ abxwt p 7yzb:3m. , :cd3rf:fpj. equally noisy jet engines is experiencing a sound level borderi.7j wpz+::bpy3dr3c. dtmafxbf, bj:ng 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, wa u0-fqybwj /.hereas for a CD player it is 95 dB. What is the ratio of intensities w /uy. 0f-ajbqof 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 person speaking in 0e v -(gft-v k)jb+imsnormal conversation. Use Ttvemfbg- i(0- +j k)svable 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 strikes an eardrum whose area is jk-) b8z5/qibru bsu+$5 \times10^{ -5} m^2$ (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 amplifier B isztp* ph.a2ld 7:)o qyov id;h8 rated at 40 W. (a) Estimate the sound;v.yodi)ld ht78p ho q*za2 :p 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 p r3nrz.h -aiy4zqu7 (qlaced 2.8 m in front of a loudsr3 unqq i -a(zhyrz47.peaker 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 2.0 dB. Whpr ol*q vigu*m44, rs/at is the ratio of the amplitudes of two sounds whosel*uvrio/ 4,sp qm4*gr levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is 3m2/nunkub+npv* so 8tripled, (a) by what factor will the intensity increase? Increase by a fact2n+mub p3n/vk8 uon s*or of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one hash 3ozn) qh on,gb2w9vky3a5+k twice the frequency of the other. What is the2)3w+5v9ob n,3zgkk h ynq oah ratio of their intensities?   

  What would be the soundu /wqllp wy4+6 level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?4 uyw6llwq /+p    dB

  A 6000-Hz tone must have whk-.m uwqlf 78fat sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level?uq8 fl7.-kfwm (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an egke(jlb64 g p6ar can detect when the sound ljgk4bg(l 66epevel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of qpmd;n: nc(+8 gc7fsp sound levels. What is the ratio of highest to lowest(8 fgn +n7:ppmqcd ;cs 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 lengt5 s; xopyg/ry1h of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string bey;gor5y/xps1 placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first tnogrj3 vtn*qym-(1j2hree audible overtones if vj2*(ngt r -j1ym3noqthe 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 w 6m5:2k yb 4fmsccjm(x m*5ey, awrq+jould you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it wm mjms2e 4 *q5+jaw5(y6cbkmf, :rxc yas 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-z+) imvlse g/ the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requireis+ze/ )lvg-md? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harpl-kcq3 l+kop 18.a usmonic. What will be its fundamental frequency if itq.p3cka +ol-8u1lps k 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 to play E abovm.k mdkc,;v+e e middle C (330 ,kdkmvc;me +.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 open organ pipe that emits*8cwa3x0d/jhr:poz k middle C (262 Hz) when th*: ohckp8jd r 0xzw/3ae temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at jvb z)w u;q6np0uj6z+ 8rotb-on r, j820 $^{\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 4ggligu47*w sfvey iv)xgh a**hd 0 hhr*:9z8 be that must be uh:gydvlw8 9h )g vi4fi*g 47ra* *0hughz es*xncovered 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, an nwix -wuz9 :2c4ivo)j:0yt:c qc wq0zd 616 Hz, but not at any other frequencies in between. (a) Show why c0:q)y0cz:2t:wx ionv - jwuqz w9ci4this 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 lo0 0u: vab q9z5xj vliouqqu1:9u bkg7*+b,oegng is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 i9e,:1a qvuu*q uo0 ux glj+b9 bbvq07:gok5zHz. 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 k3n;rxzjkmx)e cxm.1-c4 2xn$^{\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- ,hnd0 3fovc4yact;+o m-long organ pipe at 23v0 ,odc4; ao+cn hytf0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 8 awn)q(e -th+wgw 8ki2.5 cm long. It is open to the outside and is closed at the other end by the eard aht-wqgki)8nwew (+8rum. 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 s when trying to adjust two strinmr ,/v-wa r nz-;9fuj+s(wftx gs, one of whic vs-nxw9at w rzm/;f-+(u rj,fh is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz)-*p0j0 ivt o(ff7a pvr 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)+ :vsj,gatfa4 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, estimate the operating4a: ajvt,s+f g frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 0q-n(h2pv5umrutad4 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is that5p(-vu du q02mhnr4 e vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensifx5a hpdex -6+61lqeeon in one string is then decreased by 2.0%. What will be the beat frequency e6d pq-le5+fx a e1h6xheard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will t t8pvwa*a-46 lludtciquz7/ dnl+7 ,be heard if two identical flutes each try to play middle C (262 Hz), but o tu/6adl8l,t 4u+a dqilpz *ncv7wt-7ne is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hzs,co a bg7 htz52,rt-j; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are2oh, b7-t rcjg5t,zas sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker andea 6dyl 6bt,kpah32l8 3.50 m from t83a 62de lbhtpky,a6l he 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 bfd5c.p f:x zn;j43s cge 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, j3.5zsdcn g pfx;: 4cfwhat 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 ai6jk.2p7zo 1jrf lp;6 c1lt rier. How many beats per second j.plfr1ic6zjtp;7ro k1l e62 will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when aas4r o-l6w l+ot rest. Wh+rl6 4-lsooawat 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. Whb/nje2g1/m0- :dd boms iv z)uat frequency do you detect if a fire engine whose siren emits at 1mvbbo:-nd z )mus2j/de1ig / 0550 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 2000-3l lcarz;ze1( cs k gz1t3e6r1j3tyz0Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencis;r3 jattc13 0611g(k yrl3zzcleze zes 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 u csw( zd+cizey96,:y with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver atdz +,syc9 ( wzce:6uyi 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 ultram) (5g*hw1 zu e 3eio,cw wmji5jy9 z,z1uwrx+sonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the reczu +j5emumxz ,hw 1cw9*wew15)j g(r,yz3ioi eived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it uwt:q3(cmok/ xu9x6 0+rqak uflies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What fr0x 3qur:u/q6aok t +cw (xu9mkequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experim4a n)ivra ulazs0z91 .ents, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the si u4s arlanz 09)azv1.ame tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bloo-rdt7 rpux u oip08d-9d-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 expe-r0 8odd97 uxtpr up-icted 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 wavr,g f,u-nji0q es 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. W n)0l qy8lj:w+u-o.g rv uf8gdhen the wind velocity is 12 m/s from the north, what frequency will observers hear who are locatedl )ru: gvjnwld f08 u+yo8q.-g, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speedcxgc8e1( wbtfq2a:;n 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 atg 6m*xf )alob:4 pcp+a Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle the sxml+:pp6aa)bc*4 ofg hock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed69e2l*cbldpi e47;asb qqo 6p of sound is only about 35 midp s7q6eqbal6 bl9o4 ;p*ec2/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 strikesnt gn0n+f x d7pz)y*ire08nw z/cc++ b the ocean. Determine the shock wave angle 78+z0+zg/) cn wbnt0* ipe n nrxdf+cyit produces
(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 j*9qpps45ew jpv81o h$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead anzc;gfufh,z/;fof ;1ps; dl;w d see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 kpc/f; ;hzufw; gof;fd1 lz;,sm. 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 sou(.3m nm ,i7s9 yyseykcnd pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is desi39mkmni 7. syc(y,esy gned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves alwuz ++ly k(b voh7z:,re there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphvij.7 90.uw3ekhules)dkn 4 v4up+ it ony. It consists of many plastic pipes of various lengths, whiclk4v.ui3uj evi uth9sp.d e04k+)w 7nh 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 6u pa9p kdw*k, k76h;3ntxwwtab(z/wa (pzx -from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level ofwtb p /k*wdzux 9xaaptw6w zp ;hk76n,a(-(3k 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are h h z xz1 zsqx/l6s(8qcea2vr,j:en z,rb.n* +feard simul + nz bjzexsx(fc 6z*rh2szq.val:n8eq,r ,1/taneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the t x: sb-2 s(kb6rf(iubopen, is 105 dB. What is thbsr6f tu :b sb((-2ikxe acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output a 5 so1qxhz0rb2l; yl55z/zuvmt 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at ol15 0 q5x2bu5rlyh; svmz zz/15 kHz?    dB

  Workers around jet aircraft typically wear protective devick*9 v+ivgwwo y7(izjki 77 .yres over their ears. Assume that the sound level of a jet airplanj7go ykwv.+ ziwr v7ii9 7y(k*e 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 s:z)keu9ztr k 3ystems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequency 1lpv .pi,);c rgpc7e kbx6p50 d$\frac{1}{2}$ 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 lon-+f975r0l,xydavlg dnv wk3og between fixed points with a fundamental frequew a7o93dlgvvd0 k l, n-fy+5rxncy 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 above a verticudn 48ij: z7hxal open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in 8x4hn: juz7di 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 :cd,9)arubcw2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce cc:9ra,) dwburesonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to r6w: h( d wn2/jk7miywjesonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure d*d .k8nved z0tone in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 00k edz* .dn8dv.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistlemcs lov2 ll8* 1y8kmeyx/u75rs. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving traincr kmul*y e17o m82/lvy8x 5ls?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After itlqf (p-y (64smgn 1mxj passes you,- fmxyln1qsp4jg m( (6 its frequency is 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 b *amj-7a g7xuty listening to the difference in pitch of the engine noise between approaching and recea7mt-7 a ug*xjding 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 it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency6dnqz2jmc4ua 4w rd( 8de*m zz2d 9wg6 of 11 Hz. The shorterqw6d* ewj42amu z68m( zdrg429dnz cd one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as itva qb/ /cjwv61 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 beavq61/vcaj/ wbt frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally aboud).ibj +wor 2ut 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directj). +odwiub2r ed 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 ciz 84b r0w 3dha.,jwrwhile 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 derzwwa8 ,j di4cb .3h0rtected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high f* v0hjnp u 7oaph(,8zhrequency sound pulses as it approaches a moth. The pulses are approu hz8 j ah*,(7vohnp0pximately 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 signala6;jb 9 vi1*y/orjds ykgl)3 as from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity lo3 s/y;9aild j6jr )y1bagk ov*ss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compr 8i5pd msn,/im-hi4 qb .nfl4qomised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodq4linp4 .bsq/h mi8i-fnd ,5mes. 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 demonstrationu*rrfis2 lq st-..ei9 , called “singing 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,..2 re-*i quri9tl sfs” 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 eamg*xkzd;6u v5c0u x1ar at a frequency of about 1000 Hz is xc1m;uvuk*z5gxad 06$I_0$ = $1 \times10^{12 } W / m^2$ 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 9vkkzqg ) n7z:on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitu79zk zn gqk):vde?    $ \times10^{4 }$ m

  The wake of a speedboat izy2+3yq+ hkd4uwi q.4bq5d it8nh3 sus 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