What is the evidence that sound travki)r e5m x/t 7ww.kqvmm. ru c;-,rw(hels as a wave?

What is the evidence that sound is a form o-krax60 fqxp3 mr0. gaf energy?

Children sometimes play with a homemade “telephone” by attaching a string h on2:8aw rb*kto 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 cup (Fig. 12–29). Explain clearly howb:wr h28o* ank the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the freqiqg fb .4iy7*p,zb 3opuency or wavelength to change?y b7z3 ,*.fpqipg4ib o

What evidence can youjfk. o(ydgnl;. u9 ih 5e9vlpu0k 0w(q give that the speed of sound in air does not depend signific;hlf lkku o(5j09w.i.e p(u yqd gv09nantly on frequency?

The voice of a person who has inhaled helium sounds)u lrnj -;(e1:kkmvey xig-p - very high-pitched. Why?

How will the air temperature in a room affect theobv; x*s9j;ix pitch of organ pipes?

Explain how a tube mighkp(- s4amjo 6et be used as a filter to reduce the amplitude of sounds in various frequency range(km epo64j-sa s. (An example is a car muffler.)

Why are the frets on cw m3s xjz(t*i;/+, modlys6 za guitar (Fig. 12–30) spaced closer together as you move up the fingerboard towardo/mms*6zyx ;( sj,c +tw iz3dl the bridge?

A noisy truck approaches you from behind a building. In8 f8twp di1v,h3 i..i+rau iq js2,hfiitially you hear it but cannot seef.,trsqi ph3va iif.w8,1 8+uiijh2d it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,5+m39 beqt( qhq4jek5ttqz ( u” whereas beats can be said to be due to “interference in time.”t+54 9(bm5q e utjqteq(3zh kq Explain.

In Fig. 12–16, if the wa .dt+ v(mdbax) -by7frequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farthet7w-bvy dx+)dab( ma.r apart or closer together?

Traditional methods of protecting the hearing of people who work in:t ryn5j2b hy7/* kt(v2v sfah 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 wh :ykvha ft(h/5vr s 72yb*nt2jich 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 shoit;v) uowyk6+wn in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequenv+ o; 6iy)tkuwcies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observery8lhlu 9sguupzoox i;((3j p a8*9st0 move in the same direction, with the same velocity? E8o(us9 l z9yjlg (3 ou;u0hs8*aptpxi xplain.

If a wind is blowing, will h94 svw. .ic2nuaf1w nthis alter the frequency of the sound heard by a person at re1uwa.w4 ci sn2 n.v9fhst with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monityl.7 -w :tjbrbq9g e5mor is blowing a whistle in front of the child on the ground. At which position, A through :w7-r lbtyg.b 59 qemjE, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake syj q2z +7b0r 2ethn/yby listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length oj2b /ty+en20ys zhrq7 f the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the wamu3: t/qup,i,uhf ,f 9hhhu4lterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the spee:u thh ,uuf34hl9hm,,/fqpuid of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wave 09 d4 x4v1dwbws3m9lp/d5cqdff, th nlengths 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 drifting y4 zdc/r htk is1 iv3)nvr6x*6just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses k4i y1sc /rdhri vt63nv *z)6xbefore the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. Te-mm qhe8ob(hf q4(4phe splash it makes when striking the wate8me-4eq p hoq (mb(h4fr below 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 tgc h+twnhk6,vo 9t) fqt jg- l 0:7hc(wmhrt26he concrete pavement. A moment 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 Ta wwtfhj(o: gk6r9h+t 2t)ml -gv h6 nh7qt,cc0ble 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “gqngm:z;jc5jm5/ e / z5-second rule” for estimatin gc :g/jq;55zm/mjzn eg the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level vzr0*ky)s 5;7h,h3dtxpme wx 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 intenax8w*u ux0w o-dou1c0/,ip itsity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fire)nc+a o mbvohq859+i;5v rxu ed simultaneously at a certain place, what will be the sn x +) 5ovi8obqv5h+9 ua;cermound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with fourk q)n,8: nfssx(vqk-4b-2owrq*l wi m equally noisy jet engines iv( ,8w*4-x-s nmfo:inbq2wk lsqqkr )s experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, where:s3kbbbcrel ,)js ;c3as for a CD playerbsjks3 3:ebcrlb c,); it is 95 dB. What 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 powe27mxga7hh:i h 9b5uo rr output of sound from a person speaking in normal conversation.:ha7xuhi9b 75hrmo2 g Use Table 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 strike8gic1 p srd/6ss 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, while the more modest amplifier B is 49c9fepzboh5 hjrj i w1/m.*i rated at 40 W. (a) Estimate the sound level in decibels you jbwio*p zi hmf 51j.c/9 r9e4hwould 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 metl/ kfxqqv3uxo+)6)b;ez0 lamw r) i+ xer registered 130 dB when placed 2.8 m in front of a loudspeaker on )w vxm)ezxx f) loa q/r0bk+qi u+6l3;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 diffej grh.92ht, j-jmlz6 qrence in sound level of 2.0 dB. What is the ratio of the amplitude2 hg,zjj6 j-9.tq rmhls of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fa jxp()gf0s3ze,0+ iv15nksq3 ydimx cctor will the intensity increase? Increase by a factor o0k+ zeyq im, 3s1cj)vs x(0in3fp5x dgf    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice t5ldi ngr/u 3/zhe frequency of the other. Wun35rz dl //gihat is the ratio of their intensities?   

  What would be the sound level (h / c.mw42jpikin dB) of a sound wave in air that corresponds to a/h ck2j.pm w4i displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must hochl4 .avutd +42ky*k*l fb v5ave what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.) avk+ .2ol 5bkfc*4vhd4ytul*    dB

What are the lowest and highest frequencies that an ear can det.6b v pzyju1n1ect when the sound level is 30 d6b 1v1ynju.zp B? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of so:og( q-q9 htij2d 70sb pq)jzmund levels. What is the ratio of highm9sq )ij2-: o7q h0(jqzdgtpbest 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 fund;uebisgxd 9 9c7b5x0y y./c a7onn/pqamental 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 be placed/cabe9x7.xqd /5c9g u ip;nnyy0bos7?    N

  An organ pipe is 112 cm long. What are thex7ulf 0ou ,hl2 fundamental and first three audible overtones if the pipe, 2ul0uhl7o fx 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 yf-bjsul1rz- doa42 q0/k0 divk c0,piou expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closeddq kd00 c,zupsk20 -/oi1b vla-rfi4j 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 sp02kk1fbj( 4c8xhmmf qanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipesj(cqm814b20mkf hkfx required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its thirduux77av.bg on7kxa, y6w wjn t l/83qm;06cdu harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% o6o.jm n6/ynavdua;g w xub k7u37x7w08t qc, lf its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play 9 ufqo. w tdoykr4ff47 ;il;)xE above middle C (330 Hw ulr;o7y;kfo)i944 f dq.fx tz).
(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 e: dnc; ;aplx cui zd .,-po;ihl;6hn2umits middle C (262 Hz) when the temperature doiipn, uhld-lh;n; 2;p :axcuc6.;zis 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 iesj4)1m 1sq lat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpli20(9ptlhj;s,0 y*i7fi vo.pe lpbz iece of the flute in Example 12–10 should the hole be that mui(pl,0 yl*hfvjpt is zb0 ;.27loiep9st be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pip3vm0alofxn z -gh*) s9e can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show whyl vo nf)0h3agm-9 szx* 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 opwovh ncsi/ yu wjp,1636 ,ts0xen at both ends. It resonates at two successive harmpiw0nc3swj66s , t u,xvyh 1/oonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 ephvpw9eve *8m, bo 5dy zr/1yyt5.*u$^{\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-m-long organ lcn bwms5j1w9vx-:0) beem8m we 98jc- nmw0v5)bxm:e slbm1pipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatelm8i 5w v .7cp.zx4xtqiy 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear5.ct7 zv wipx 4i8x.qm 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 strings, svzt/;w / c89.urah0f y+xdal one of which is sounding 440 Hz. How far off in frequency is the ozftx/8s09y/v + ;d uacarwl.hther string? ±    Hz

  What is the beat frequency if me8osnbx( 1 un6iddle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operate)3yfvcdf5qc ) s at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill3 d)fc5 )fvcqy whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beatt yi:0e;epqga v9 ma7m0i8w- hs/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 m 7 08hgie:m-ivqwtpae y;9a0 frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hzll, ;dv7.znsq(y du4g. The tension in one string is then decreased by 2.0%. What will ;d4ldv(n7l.,u zsy qgbe 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 identic ,li-4dl9r tqv;udlj u +-owzw-o),n pal flutes each try to play middle C (262 Hzow)l 9;wzr ,o-v -q,tdlljpid+ u u4-n), but one 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 z cm/2w9j-rvhk 2el+q441 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 ckw/9elq-m2hvr 2z +jHz. 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 speakjoi 0/,f*c )t7wmz wiyer and 3*i y,cjm)/0ofw w 7tiz.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 vibrating at 132 Hz, but a pian q9n6v8wv zi ugq ;z9:eh5gsp;o tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz,pizhv8q ev nw: 5sgu9q z6g9;; 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 perv -mo1xtky4:c. -egtl second will be heard? (Assume T v cgoxe:lt.4 k-mt1-y= 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a ceroyayapf rakqbvc s p 35;68668tain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect i ;aqoc6rb8ap53 a y86 vyfk6spf you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing stillh6qm 6w-f fcbbsm 4+ iw)gve);-a6uiw. What frequency do you detect if a fire engine whose siren emits a 6 w+ )w) ;uwsm6qh4 evc6gf-mb-aiibft 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 st;o/vi 9z zog3ource is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are tzt/9vi;3og zohe two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped kw h )(5cp: caqkbv47jwith the 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 horns7 aqhk):cwck(4p b vj5 emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrason09jjj0yyjd k+jcb2r4 5 mb ey-3zih/kic sound waves at 50.0 kHz and receives them returned 9jy+b-/dkjh4rj ey z2m0yi jjc5b30 kfrom an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, theef 9)jp8udo 9 7jr2ag*gup4 ja/tz3q y bat emits an ultrasonic sound wave with frequency 30.0 kHz. W2oaeq)j f*8 3jgdj9uy9 a /utzr 47gpphat frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the origin;2p vk4 5lif ew0-k rwp llte6opr889mal Doppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz,kkivrr;p0- 6mw 4wotfllppe85 le 892 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 the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves(fof7j9v5r9owd1 sb k 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 ex1ff9o 7dkb9 jo5v(swr pected 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 ultrasoniv x;otp3qkxxrs 82,ze/ow u +3c 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 ofiyu abmy3b1 a78k(5mv frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency yka1v87b b maim(35yu 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 movin:25s q uh1ax/5mlgdyjg on land 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 310 m/s 35snzbv y*yp+dq/ k1 kie(d7k(a) What is the angle the shock wave makes wipv5y/ kk dy(qe7ki*1 d+zsbn3th 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 plan i/- ihwm7-eerqtsq84et where the speed of sound is only about 35 m8s -ee -7 iqwt/mqh4ir/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 ocjp.fw d /ldwyov1)1j 1ean. Determine the shock wave angle it producefdyw.j)pw1ov d1/ 1j ls
(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 2veaogqmv)v yua) ;x, 2z3a+g$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see ah3tou u.q 6g m4ek0m/q 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 km. See F uk3mtq6mh /.0ou4 geqig. 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 downward wd8zcg+g-ynu h m7,4kfrom the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum timzwd c+84mk7g,-n uh gye between pulses (in fresh water)?    s

  Approximately how many octaves a crrway 45xck3 y/v./are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a l b)id,+9b 75 bib.nv-ni mdctdisplay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both end5d+ ncm. 9bbidi,tbv n)bi7l-s.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound clo;w :0uiqfe+eqse to the threshold of human hearing (0 dB). What will be the sound level of 1eqqu ;:0e+ fwi000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound *x- t lt y1dueq3b+p9fand an 87-dB sound are heard simultay xq+ef1l-tp d3 u9t*bneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB.xjt- c*m6vs(7vqp. to What is the acoustic power output (W) of the speaker, assuming it radiates equally in all direcx6vv(os .*tmqj 7p-tctions?    W

  A stereo amplifier i *5,ueoiqx2tja (b *lls rated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output ai jbteqo**u5(lx l,2in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear2 9 wje-yf2dxo 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 rade jx22o-9dywf ius 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 communicam-dqg52 (,ilq uuy: xotions 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 is tuned to a frequpch/ 7xhlk-5.il+/ u2tgm rr vency 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 - lmh:yhlbd +/long between fixed points with a fundamental frequency of 4 ybl-dh:+ /mlh40 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 vibrao9 k4yat6.ua1 )uw1rf6lp jkstion above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the aikl1 sawok9.ju4u ra 61yf)p6tr 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 91:83z(bzh zk hegd1wbl/qyy2.10 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 resonance (in its fundamental mode) with the third harmonic ib/:31w zz hg l8key(zq1d9hybn the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to re) h*oas nd-ev) mq1r/g.yj y.-gtgm7esonate 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-Hz range coming from two so wz-bpw ws) 1bn;su(,kurces. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds tbbw z n-ks,;1w )(puwshat the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train if4s. )p 6rjwj2uqhia/s stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other rw2u)qis4 hjpa6 j f/.train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whipr kkpk5/g:5vstle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486vkrpgk p/k:5 5 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can es97p7p ci og;fftimate the speed of cars just by listening to the differenif;c9 fpp 77ogce in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequencywje9gk cu7 z1:xs-t,z of 11 Hz. The shortgs7ze,9 xw uzjc:- 1kter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at oppo m2qvwp/0e zxv+;toew-p,) wlsite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is betwe p-tpvwe0) vwwmz x2;/qe+ l,oen 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 nxi ,s ) ty(vu *qm24btetxm) 0v7omh4wormally 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 red blood cells? Assume that the waves s )vyw4 *mot2umxvmbqi04 )7et(, thxtravel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/g2jyxrem u;0+ 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 0mug;e2 xjyr+is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it apprnc v+.mwuz 0:c2lc(peoaches a moth. The pulses are approximately 70.0 ms apart, and each(em:w2cl n.pc+c0 z vu 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 y6-wkh+r poa7an e27w 1h ap;zsignals 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 alpenho6a;7ak wea1h-2w poyn 7 przh+rn 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 f* sen7wpfpu ,t.5p3d18pi 7cuc )wao by the presence of standing 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 p c 7fu8i* ,ndp7cwwsa.p pt35ou f)e1frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long c/7c/c)vw9fpf /jvju, 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, lo)7f/uj/ jcpfvccv/9w ud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequency of qc g3fv ug+of4ib)-:m about 1000 3f om v4g-+fqi)u: bgcHz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground :)o )tphc-x;5u rzju) vrhr qr,ic(h9hears the sonic boom 1.rhvxu)) ch :q(rp9- h j5u,r) ;tzroci5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatt+y /1klbmk*l/s*nz) czd3)i ijt5db is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h