What is the evidence that sou*,r7u1 1a igqk+y)k8l bnfywund travels as a wave?

What is the evidence that soun g jdz+x;5pei(d is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a stjt-j(p rl-/te w 1-znzr6,kstring to the bottoms oftpt6tj1l-/w,sr(rz e jzn --k two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do yo q 9vl9mmbvq-6u expect the frequency or wavelengt9b qvqvmm -6l9h to change?

What evidence can you give that the speed of sound in air does not depend swpkd:p4 e7:7gtd 98h (weoit qignificantld ett79( 78:eohpdi:pqw g4k wy on frequency?

The voice of a person who has inhvy() : wiec6yyaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pip0fcq0 /hfx5wn/ gi:r qrti d:3es?

Explain how a tube might be used as a filter to reduce the ampxa ),k +zz-tkj8 l2cen 6qa+nilitude of sounds in various frequency ranges. (An example ise qzj kctxzk68,)n- l2+a+ia n a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you moa /iqdpo h ie:)v5vg*59 b0alive up the fb 09)iei/ qdga*5 h:ov lvai5pingerboard toward the bridge?

A noisy truck approaches you from behind a build: )nwmt+p) bn +unbye,+wsv*ding. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear mo ,wp ): neydbwbs+ *vu)++nmntre of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interferen4rp f)bhwo3d afok/;. ce in space,” whereas beats can be said t)4p/koh fw b;.fr3o ado be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of qbdxu fb(75j 8the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move df5bb8 qu 7xj(farther apart or closer together?

Traditional methods of protecwgk/h5 7aaa;ua+ x vh)ting the hearing of people who work in areas with very high noise levels have consik;g/aa+ 7a 5a)xuvwh hsted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a sup.v2 ltnqgcr6 ,ovg*+d /sbs 3werposition of two sound waves with slightly different frequencies, as rb */q, .s olgc3nvv26sgtw+din 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 shiftmb1uz,q 8i j+u if the source and observer move in the same direction, with the same ve8 m+uiz,u jbq1locity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard bfpc(vrcuic 2 d -2c/*a 2otai/y a person at rest with respect to the source? Is the wavelength utr2v-fdi/ io c2ap*ccc2(/aor velocity changed?

Figure 12–32 shows various positions of a child in motion on aoo28tf c86w* j- e w .0;-arbqtmigqmpm0fk1o swing. A monitor is blowing a whistle in fmowm1c8ikefb q0tao ;from- *-tj0 2.gw68 pqront 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 *xh : c2h0ifybher shout reflected by a cliff at fh b xch2y0:i*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 sidetdw4l( /z/ftg1cj4cd of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floordtc(gw j d14tlcf/4 /z 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 in airkiy kriy,l6ls0e s n6,n qa4 :/.g8bmif-8vva 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 of tuna on a foggy 5yp.q uy8p/cthph7; q day. Without warning, an engine bay q;upc5pq7 t 8yhh/p.ckfire 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 makes wh3 a ;; 0klsao7mzuk pnm.zg-0den striking the water bel;ka7k0 z ao m-n.3gs;lmudz0pow is heard 3.5 s later. How high is the cliff?    m

  A person, with his eg+aog78 q vvau17u*pear to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air aa*ggu18a7 u7vev +opqnd 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 over one mile of dsyl1kl 86trl b7 nns20istance by the “5-second rule” 206ss8l1nb7nkr lylt for estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of7l i9p)nb3odh 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 sounakbvm zy9tf 5me7wd; :p 1j5e3j 2yl0jd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB whle o/o0h 0s mr2ey7j, au)8lyyen fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add in yloly rj2,/a0eom7hus0ey) 8tensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy jewuev -i;y9 1mkt engines is experiencing a sound level borderingue-1 wm v;9yki 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 s3kr qs i: hk*j2qrwx*p, 1iox6aid 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 the background noise for each x:k6i s oxh2 j,kp1qr**rw3iq device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound . xarv/lchkc,.hoz 3-z qv)ru32;dj rfrom a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughljldz2cc-z ok);xv3hv r .a.qruhr3, /y 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 1epq mlbd- qj)1o; t6 crlw17beardrum 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, while the /rup +n x9fg,o 6/wgk (hs-aqqmore modest amplifier B is rate+w ,f/6 ugrqnpxoq g -/9hkas(d 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 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 ofr6 w wweehdvfc;q3)77zi1 qc4u*nx5v a loudspeaker on the st 73wvwr e7d;fzhc w6qu5x4iq *) 1ecnvage.
(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. What6 3h cy(n;aro7jeja0e is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 116e0oah3 y7janr(ecj ;–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a 7c u/rec8s 4v2:f/mnkbx k9w :1ebcno) by what factor will the intensity increase? Increase by a fac4 f:ebc/8nek wr/ubncvc9k:1x 2o 7 mstor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one hasemrjkg *c/r(f;- :nxm*s )gkj twice the frequency of t xsf jr/e-k(nc )j mmkgr*g:;*he other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air th90v*x stkrr;u p/6uj oat corresponds to a displace*jr6tr ;u/px9 vksuo0 ment amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem asqqy9dt4k )jzm *7nqeqr;k8 x:aemeuw* h/w84 loud as a 100-Hz tone that has a *w; ex48qay9wdrm) :qjkkhe7 q* n m/zt8qu4 e50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies uggrk9s t)4ze/p9 0w cthat an ear can detect when the sound level is 30 dB? (See Fig. 12–e9k ut) zrg ws9g0pc4/6.)

  Your auditory system can accommodate a huge rangeov3 :uylv8 en, of sound levels. What is the ratio ole 3y,vnuv o8:f 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 jvwt b 3q,q56xhas a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string bev x5qt3qbw,j 6 placed?    N

  An organ pipe is 112 cm long. What are sx:i/60 g(x; ta4p,x jkscz/(bh ejnxthe fundamental and first three audible overtonx(eac(nj :;itskxbp , xj/40z h6sxg/es if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the topnb l7)px u k)f n 9ci6mrc7/4nobp+c+s of an empty soda bottlep) il7+u4mr9 nk/6nxc 7cnbfb ocs p)+ that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ wije-v r;i(8 1o1*wqjdffwy1c bth open-tube pipes spanning the range of human hearing (20 Hz to 20 1dyo q e;-*j81vb wrf1 i(cjwfkHz), 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 thiz810ewfl: mko rd harmonic. What will be its fundamental f1zk8 l0m:fweo requency 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 to play ;zyle)ldafcvtu + .-+E above middle C (330 ;la++e.tzy f)dc vu -lHz).
(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 lenrnya4njqv)w fj.1/025m v avz gth of an open organ pipe that emits middle C (262 Hz) when the tvn/5arqv 0)z2jv n4 1yfwj. amemperature 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 aj c7hm dj1:.zd r+*s y+1peamat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of c0 cle5 g jvrip:e;2h6ij zb87the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C ae 8ghj lci6:i;b20zprj cev75t 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 26z5bn2k ltd sm+ f88p,yws7, 84d yunhi4 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show k,n yst58usb4fpni z,m28 w7yld8+dhwhy 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 i: o x(rxbi5h:xs open at both ends. It resonates at two successive harmonics of frequencies 275 Hz andh(r:5b xx ox:i 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 cey8(: e4 c*ncked6jo$^{\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 presfc t. inhf3:u1ent within the audible range for a 2.14-m-long organ p1ftcfn:.i u h3ipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. x eay91h uym c49.dwi:wl*.rvw s7z7fIt is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the stanwf7da94h9w:y. u* .xcmivsz7l 1wyer ding 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 (.oq*5 3 ukishweqjjo- *.8:iulp wpktwo strings, one of which is sounding 440 Hz. How far koj wphusq*o 3i .p :wue*lk- q8.(5ijoff in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) anpjg+1v- j- xrid $C^＃$ (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) opera*echjz e 9 ais2tv1:b) ,xt*ovtes at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs whjvebcto ) ve*,a tz1 si9*2x:hen they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 0)qh5v0w)nt iy ovp5nbeats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasonpq)n05yn0i v owvt 5)hing.    Hz

  Two violin strings are tuned to the sameia8a,7kqcxbhub;+ x ,ju(ya) frequency, 294 Hz. The tension in one string is then dec+8ycb(uj ahb ,i)ux;qaxa, k7reased 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 each(ug*4i ga 1oovaax(x+z 2 /.5rgq bnkh try to play middle C (262 Hz), but one is at 5.0°C and thean r24+gq u*bvh(.xa5 a1o/ o(gikxzg other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning f.5uu -qnqll z2orks, A, B, and C. Fork B 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? What beat frequencies are possible when A an2u u-qq lzl5.nd 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 3.008 6xmy 7;djovd m from one speaker and 3mx6y d8jd;7vo .50 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrjd3 g2w5ia e9qx(u2sfating at 132 Hz, but a piano tuner hears three beats every 2.0 s wwf32ej( gd5 qau92xishen 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 wavelengths 2.64 m and 2.76 m in air. How many beats peroa j7v7m1st+fwvpp1uh0 4 bi+ sec4spt1 h wpv0+j ofm77ib+1vua ond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freqrm ngi 2*+4s(n + sh7w5um:ca 7lqaybbuency of a certain fire engine’s siren is 1550 Hz when at renu+:57 mn* c4sri(h7 mq+yglas bba2wst. What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose s.t- c tssi9galw b-y cj7k.d10iren emits at 1550 Hz moves at a speed of t igjt- aclk1.sbcsd-. 9w y7032 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward y4 n9s(w(;cd dvpc p9r htbu9/iou at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are thhvbp/sdu9ni4r (d9 (ccwp9 ;tey 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 ebh; p;p xlt /ji )id+j9s(u/jequipped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/b j(9hsj; px)ieu dl/p/+jti;s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound wave.os+mvk2 w j/j-6sj lls at 50.0 kHz and receives them returned from an object moving directmol2-+s6lw. / jjkjv sly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As e bymtvm 3*j,:nd: o2j8sih t3it flies, the bat emits an ultrasonjehi3jty: n s mv*d,:2bto3 m8ic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, agyp tg02+.gons 6ba,f 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 railway station. What beat frequency was heard if the train car approached thbayop62f gg0 +g,t.sne station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow spe-g zd0q6berbg*16epceds. 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 expectc6q -06g*zprbgedb1eed beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usingz 68a9gwz - nep vpbj6i-y/)fb ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When ttzmz b o)f u,-fkrt0wc*,+ -pqhe wind velocity is 12 m/s from the north, what frequency will observers hear who a,zzqtto- f b f,p+*)-r0 mwckure 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 l5r(woty1o id yx/u d64and 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 dtlrk*cs4( 4uspeed of sound is 310 m/s (a) What is the angle the shock c4 tl* 4ksdru(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 o94 dpv5+ipyz planet where the speed of sound is onloy945+zp vdpi y about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wa-jfx .0/ro 3x,swvytfps6nd 9ve angle it pr0pv-d6sr x,.s3t9 wnyo/ffxjoduces
(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 4; rrjbsw 9g8l1xxsfs:j .0vc$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see kz(x4 i2 0w lwo9nii.da 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 distawin2(0.lkiz4odiw9 x nce 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 downwa dkmn(hp4.bm4v5w. iyrd from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to woi4(hv.p wymn45b dm k.rk is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible rjffy-vw8 66 fxvqqb5 j(q)pn ;ange? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of man26 dn9muf ,efl-mm9q (0*huci0r xk igy plastic pipes of various lengths9 u96-hd2,(cg kxmq*rf0fi nm0mi ule, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a )ci r lzwj2ox;ah34nr 9zmg72sound close to the threshold of humz9w g 37a i2rzjrx2)nco 4l;hman hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound andk; mepyp3i;yxo2 h+u m63b ;kt an 87-dB sound are heaytp2uox k3b3 ;me;p;+h miy 6krd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB.bthunz*7f) vwd9t+ u3,ufn /i What is bizh /nf u+9tv )u37ft,u*dnwthe acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outpo /ne*b)yin3fm7wh;y gz 4hy- ut at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in w3by/m -*yf47ghy o n)ih;wzneatts at 15 kHz?    dB

  Workers around jet aircr*qcxd1bs h e95aft typically 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 2.0 cm. What would be the power interc1qxehs 5db9 c*epted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain, / iybh;k,lbj4 $\beta$ 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 viol,izhqz 1*amz1jo ybq: e*.l92t+yfrain is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamen u l 9+ xo6pyvbme 472ixktqy3-,weh2atal frequenov+ y4qype2x 2b3a ituxlke97m-w , h6cy 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 vertical open9* z j0qakdmoh/f/6m3eauos3 tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level ismozfkmj6 d3h0*qaua3 s /9 o/e 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 m4t5f aiywt*8d(p5i 0+bojkztube that is open at one end and also 75 cm long. Howtj5y4k 5oi 0tapi dmbw8f(z +* much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass wyyl-b wey h0/7as observed to resonate 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 tone in the 500–1000-Hy j3 v/5uv y5id wjsu8eqg(:a46qkku5z 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 minimaqy5 5y/(jquid vejuk85 w43vsa g6u:k l at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conducq .qexe a2winm1.y1 .utor on the stationary traiy.wui.1ee1q 2x. nqman 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 steasmos/)e -:mek+ro /x obxt09sm train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train s+:0s -exoo9 /sx)/re omtmkb moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just bywh5 mi)x3bd u1 listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency haw)1mxhub d5 i3lved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding togethw eik4;jc2-dym8c -,;dqr xmper, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. i2-c dd kwqmp;rcxj8y;4m- e ,How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car asptu65q j.9ks/nd; sbt 1*fabrv*i e4k it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he t bj6spv9k*f;a .r14q5d u/stin*bekis 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 qtknp(y8 u1ll l)q84 uthe aorta is normally about 0.32 m/s what beat frequency wlk yp8)q4u1ql l(unt8ould you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying towa,(ase 5gki )gxrd 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 bat afte(k sx5i g,ga)er that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a+: xpgkmm 8x5zd gs,x2 ov/)ak moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. Howpo+8 gkd,akz5s) vx:xmxmg2/ 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 onv y5o rzn :.wxr.l z8oya9wq/8ce used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical 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 fw/58.yrlza zvx 8 9r.won oy:qundamental 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 presenj iq,p(qiwm47 q:i)y;vv ,sz rce of standing wave,i vq qizps(:y4rq 7jv;,)mwi s, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,”vs si6 t :2w4koqi(co4 involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is iovst ik(2 qw4:64ocs 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 k /glu)g3 87pa m,rwwiof about 1grw uw 8)i/p mk3gla,7000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mac9i(t8/, .j hki yy(iaypdpb d5h 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s a5p(tyiyihk 8jpd y /(i,d9ba .ltitude?    $ \times10^{4 }$ m

  The wake of a speedboat i64g6 o lbqg a8ufaqy*+s 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