What is the evidence that sound travels as y vut rucb8mng4 7(//ua wave?

What is the evidence thae d/el e6k5i0/9g e+ dtsood.at sound is a form of energy?

Children sometimes play with a homemcsd65vhqtq .ul3 n7qr(2 kcd5xx 9p5 zade “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 cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other. p6tx9l 5( q3cdsucdz2.v75qx rn5khq

When a sound wave passes from air into water, do yoa)w h (o/pyo9ou expect the frequency or wavelength to chang)p9w/y a(ohooe?

What evidence can you give that the speed of sound in airis 6 xatm9);vo does not depend significantly on;sm6it) 9ov ax frequency?

The voice of a person who has inhaled helium sounds ve-i yge9 l 0r79nfo d(k1hljut1ry high-pitched. Why?

How will the air temperature in a room affect the pitch of oq:5iw- 7ocmn wt/ fwxll-s;3d1jco1/fhsf w,rgan pipes?

Explain how a tube might be used as a filter to reducdwr ,.z8)s n gz,d*pzk( g*(zcveb3ct e the amplitude of sounds in various frequency ranges. (An example in(v)d8rc z *cwk p*e(g3btdzs ,zg, z.s a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced close3 pz,1k q3a) kxyeh1rdr together as you move up the fingerboard toward the b),3kp q hkea113yxrdzridge?

A noisy truck approaches you from behind a buildingk)f0g1yxh7uyzbr8,q . Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See S8y) b0zkfq,yhxg r 71uection 11–15 on diffraction.]

Standing waves can be said to be pv1lqjsp3vw (31a)vf due to “interference in space,” whereas beats can be said to be due to “interference in time.” Expla pfjp31qsv31 (vl )wvain.

In Fig. 12–16, if the frequency of the speakers were lowered, would thm u, 6 8uwz3o0sib. ni3mv,rdfuo1.qjoaa l50e points D and C (where destructive and constructive interference occur) m.qroluuia0wzmdj, u3o o ma31b6, fni05s. 8vove farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas wzai axn1u /xj)999hp aith very high noise levels have consiax/9n9 pa)i 1az9ujxhsted 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 yjx y;1p e5zpcrym6v6 ; nh3*ashown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different evc6yh5zpp;n*y ; a x3yr6j1m 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 the sourclj,5( lmf bsn2w,ny2g ,zdj+xe and observer move in the same direction, with y, wj,dlm5js(2fb2lzn g ,+nxthe same velocity? Explain.

If a wind is blowing, will this alter thjcgvc5k(i 3od(/ey11 jwr )onw *t h*me frequency of the sound heard by a perso w d3wi*)e to(1ckyhrmn*( ojc5gj1v/n at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions o2 8q uiq0f:z ev2xg6fff a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whis q2f:80e 6vuizxfq f2gtle? Explain your reasoning.

  A hiker determines the length of a lake by listening for ucbwuwue35:k7ux.jfa7o/mz6 9uq ;i8evv:ythe echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s aftujwyf.qmx 8: ue u/9auw77ie;65b ov3zkuv: cer shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the watera(bh. .d fei ukz+-hc0line. He hears the echo of the sound reflectedze..h- hf(a+ udki0bc from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air atpbw1kx . :(rqt 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 drifti+;fnd*39uo gkmb ; yltng just 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). Howyo;u d9kg*+f3;nml tb 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 ma70x/zl ez,u ctkes when striking the water below is heard 3.5 s later. How high is zc u,7xt/l0ez the cliff?    m

  A person, with his ear to the ground, sees a huge stone swjy8 rm9 83ieg5 9ldeztrike the 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 ijr385g89lmdy w9zeeimpact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by ztww 7;6) dy55ico+e.gio by*4/ 9acouupmtx the “5-second rule” for estimating the dis yo 4;i.u5iobtto wze7x6d9 cw5 p*y u/mga)c+tance 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 9:jrpmh sp2m4pain 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 whosell kb7ht8d m f1gtm;pfdnf,1w1 01q; r intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously ogfon;mziu ov03h)1 *ley aj*+ z: ch2at a certain place, what will be the sound level if only one is expl)o3uj y nzmlgc ozvhf:oh2e 0 1+ai;**oded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplaneg9use nv y4/yh*4u;oj with four equally noisy jet engines is experiencing a sound level bordering on/v nj yogy49heu;4s*u 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.wwy ym1)oq6 n of 58 dB, whereas for a CD player it is 95 dB. What is the ratiywm1qo )ywn6. o of intensities of 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 normalhu a76:: (w6bwn nwhhl conversatiob:a:7lwhh6n uh 6nw w(n. 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 strikey g5i s/vfv vo8pkd(*)s0 e:wus 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 .qb le jzfgw(k(/2+rj ik6-moqpw +w0 B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudsp-(zb+ogf +/i pw6 jq k0j2(.qmrlwe wkeaker 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 w0bii5c - pcb,shen placed 2.8 m in front of a p-bb5 ,ii 0cscloudspeaker 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 typicru g*ri7 oii(8ally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hri *7(8 roiuigint: See Section 11–9.]$\approx$   

  If the amplitude of a soun9ns axnv6yuy-7d 5tohw6 hc 62d wave is tripled, (a) by what factor will the intensity increase? Increase by a -7hy n9wxys6 ouv 5cnat66dh2 factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, kg h2e/ch f0cp)a*:ol 2v+exdbut one has twice the frequency of the other. What is the ratio of their e 2f/+hcv da 20le)cx:goph *kintensities?   

  What would be the sound level (in dB) of a sound wave in ssagrdw) l-c9+lw1 2hg ;g*nbair that corresponds to a displacement amplitude o hdw lbsgc+ gw9gl2*-nr)1;s af vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound levx.ha n)jt6q4bb6yb)1h uk3vm el to seem as loud as a 100-Hz tone that has a 5 uhbnm) 41t6kax.b6hyv3 qb)j 0-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect wh/ gf gnle-3(zoen the sound level is 30 z/oggl-n(e f3 dB? (See Fig. 12–6.)

  Your auditory system can accommi)c4o u7nxbwi-b)v5fsz m1 4uodate a huge range of sound levels. What is the ratio of highesn iovu14fbw)iz4)us 75c -xmbt 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 fu aqr -+4kh)u4lw4oaqf ndamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. ah4arkqwul4+-4oq) fUnder what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundah fnd ;t +2*k bgp,rh;lj32vbpmental and first three audible overtones if the pipe is; *bbpn 2+kj;v3, frthhgpd 2l
(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 jtc;p3e9*bd :mw fo0fyou expect from blowing across the top of an empty soda bottle tfecm9:oj* 30ptfw d;bhat 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 with open-tube pipes sh,cll(v9z9*. 7yo+spaqmqb m panning the range of human hearing ( *bc.vmq oq7lm9hs+ 9apy(z,l 20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its mp4 u5q,5va7zl cp/ lpthird harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lengqlapp,mu 75/z4pv c l5th?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above qut2fnf894dd middle C (330 f d8t9f u42qndHz).
(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 opa+h7wzg0 tx jws4s (gj-ds8 r2en organ pipe that emits middle C (262 Hz) when the temper+r sj -g40atss7djh8 xzwg2w (ature 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 2ij; n u,zn hf07(tba9y0 $^{\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 x tga+++qu ph+be that must be uncovered to play D x +h paq+tug++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, 440i/q h 4+dgf8fkuhj*a 5 Hz, and 616 Hz, but not at any other frequencies in between. (a) Sfhd/gka *ij4u+qh5f8how why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at two e6 cwb24zt xwcgp2e78successive harmonics of frequencies6ex8ec4wt 2c bgwp2z7 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 :slor i2sc 3y2:a/ zuk8f1zzl$^{\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 thvh5id0 9 f32lmx2t c2hig bf4me audible range for a 2.14-m-long organ pipe bgl42t52mvc i2ff im0dx3hh9 at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 k(8 3jj)oaqj 9ucsk1bcm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (s)8j9k1b(aj3cuqok j 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 trying8ix8b +.a q3g)kdih4morp sk 1z 8+glu to adjust two strings, one mi3+ h8.zk 1ogp 4lskx8i burd) +qa8gof which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if nd(b vk0 tu0n/middle 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, whil)7d5oy kkcqofgx7ph1+.( +gkosi r(pb. e 6rre another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine kfr7o61bhkkp+ yxoqe sgg.7c5.oir )( +prd(of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 b6(z o aetkau73eats/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 e3to (kau7a6z string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hq xr5y7x ;fs1tz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when thef xqty71x5r;s two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play )q c t*ccv,:(7:hkoqopet1cnmiddle C (262 Hz)h 1qoc)kc *v :p7qcn o:t,tce(, but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, bze)yl02f/z 5w xq9x hB, 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 20b weq9 /zfx5)zhlxy4 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 ap fixvy;1bhk;pl0i xbg o-::1d art. A person stands 3.00 m from one speaker and 3.50 m 0 ;xp xi1 :;-yl:kfi bdbo1vhgfrom 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 supposedm:+wvrj, 7m7r ay9vu8 b p kkxbs0smox.ml/*( to be vibrating at 132 Hz, but a piano tuner hears three bamuk/mm, vxsr8y.o: lpk0 (vbsr9j+7x7 wm*beats every 2.0 s when 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)z:7aff r ,74ayyw-ur v 6tzsu in air. How many beats per second will be hea7f-uutz7 w:ay)zysv,4a f6rr rd? (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 at r8c20 uu8r8ec oc/h jcdest. What frequenu e hdu8c0occr882 cj/cy 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 firei.f+3 ha sqf6e engine whose siren emits at 1550 Hz movessq6ffa3+.hi e at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving to4 nkx(fidb 4v5hhe,(eds( wi3ward you at 15 m/s versus you moving twx f(b4 d(,nd (hei 4hi3es5kvoward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped wk(xms8o7 r.x 1r 3m4uvttj3 zfith the same single frequency horn. When one is at remxzjor 73k u.(3t 18x vfrmst4st and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and rece9 hs a1m9ba6a-kzpd+p3ll a+o ives them returned from an object moving directly away from it atpbz p3 al9m++d1laaak h-so96 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at k3 s0p -he4w3ixkumyt. d*as 8,kt,a :av(v wya speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the3at,-4p wa0:wey.s( s,htk*vdkxka 8vi y um3 bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a mp+- o)5tyqbmyr .kc-ioving 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 freque-r+)pq c o t-mky.5ybincy 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 bloo2/8sy (+ fs7faabpet md-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissup/ta( 2+be amy8 s7ffse is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usi- f 2fi3vssy :xfey+r .8kj jfp3xt2-cng 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 the wind velocity is 1l s 8 ydzpiog 5ru3p65h--y(tk2 m/s from the north, what frequency will observers hear wh ghyp3-yr 6uzk 8ol-(s5pdti5o are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed atcv2 . 4kv,dl)loqijx; 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 3ft kx7ps89f6 g10 m/s (a) What is the angle the shock wave makes with the direct 6skf79xt p8fgion 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 speed offe d(l 5o9vp2hw7s(40ltuggh sound is only about 35 gg(vpw (l94d0u hl7fsht e5o2 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 ocz xa(h js(vkj 0q40e+zean. Determine the shock wave angle it produce azj+v0(4x0jhszk ( qes
(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 s xu *4zg0m1ai3p7azvxwq( *h$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the gro4*dynnx0yflz.ld 6j, 2sz gc+und flying faster than the speed of sound. By the time you hear the sonic boom,ygsyl6+jcf0nz4*. n x2 ld,zd the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downwar6cl, r 2bv g84zf+zcuak. rng.d from the bottom a+ cz g28fvbn .r 4ulkg,6zc.rof the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible range?m va syj)/;u(a $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called ah:z, u1t+qaqifo5xsi)-b +j k sewer pipe symphony. It consists of many plastic pipes of various lengths, which are ojoi5qxu+) h -bt,az1:q fs+ki pen on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the thre9d pnb((cbvd /foy/2ishold of hufiovd b /b( (d2cy/p9nman hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultantq1a;aki*4dg l3o*nll sound level when an 82-dB sound and an 87-dB sound are heard s; qlalli o1an4d** g3kimultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open,-b9koxi7 tpu1;dwn,(mv j+dx is 105 dB. What is the acoustic power out+;xu kxd pv-1,(toijn m7bd9wput (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Thu,-f 2z u+z)i et6ikxhe power output drops by 10 dB at 15 kHzkf26,) htizz-u +eu ix. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typicalj(jmz p .w7eo805yh:; jmcmculy 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 intercepted by an unprotected ear at a distance of 30 m from a jet airplane engij(uemz0jy 7pm m hc8co .j:5w;ne?    W

  In audio and communications systems, the z0;)qgc)op p wi qkl49*9+s .ykkd pzfgain, $\beta$ 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 frequencyxsk055,hlf- yl3 k jdd 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 violi2xx o,utj s4q 56jc65qxrhzp6n is 32 cm long between fixed points with a fundamental frequency of 440 Hz jpst6q42 z, uhjo xx55xc6q6rand 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 abov(d nh2/e/(aet 6de memqts;b.e a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As ;s 2(m 6.a ebeee ddt/qh/(nmtit does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of massg .(qr h(istk3j 0vkg1 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string ifqi( sgrtgk13(j0. hvk it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observe pbw+(-q((n4szm twwnd 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 500k*v61 vzlbgkn /c+mm 3–1000-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 0.34 m farther from one source than the other. What is the frequ1 m/n mk6v 3k+bglv*zcency of the sound?   Hz

  Two trains emit 424-Hz whistles. achexvy7,2l fk(k t s91: 7cchOne train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approachestk:c1c fv yl,7hk2 7e saxc(h9. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 H2*(wxr2nk i2f9v yv rhz. After it passes you, its frequency is measured as 486 Hz. How fast was ( r2 x knwyrvv9h22f*ithe train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by list+ a +ruxn1i ,mk8s9ee dk7ye:cening to the dif xmku8aecen7e,:i k+9 syr +1dference 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 frequency of ynau br(0x2ax3b .vz( 11 Hz. The shorter one is 2.40 m long.ra y(x2nv(b3b auz 0.x How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a stat.yf 5kyul w/f*9 db3kkionary 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 carb *ykd3f9k.w5/u yfkl, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s wha4cogk;)a6 yb ojtla-1 zcu.f3t beat frequency would you expoozag-.tly;)3 aju14 fcc b6k ect 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 4 mh3qf88tnart,wkfw 92pnu56.5 m/s while the moth is flying toward the bat at speednn4m28kw8tq , twr5 p3ufafh9 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches x8bqt4pd/i pfuvlgt(1p0;.jg1 n 8ut a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so pjpl.unb4t ;qp/ftd vg ug18 (1xt0i8that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals fr. xdgrhpg-gy ktj+in*9 :/ bk)om 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 funda-yndktibxh/* :g) .+g 9gkj prmental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of standin+ke7s2 x)0ae hv wazpq ;u.5hng waves, which can cause acoustic “dead spots” at the locations z2pu ;ak s0x hnq) 75e+vh.aweof 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, callizju +t z30d5ged “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,” or emit a cleartzji5 u +dg3z0, 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 u. 0i0lu5tdk fa frequency of about 1000 Hz isiu fktul0.0 5d $I_0$ = $1 \times10^{12 } W / m^2$ 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 2ikq/b59 a.mvm .0. An observer on the ground hears the sonic boom.am/5v i 9bmqk 1.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat x c -vbn90oz qiq9m;v5is 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