What is the evidence that sound travels as y0yn p4(p -37ek qfdcya wave?

What is the evidence that sp )jky9ms ir78ound is a form of energy?

Children sometimes play with a homemade “telephone” sk kkwmd59nzd+ w,q.4a9 o4qlby 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 thesq mn4o dk9klq4,5dw+az.9k w other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave pasg3v7 7xomtj* /)oyhhkses from air into water, do you expect the frequency or wavelength3 ohx7/vkotgm *h)y7j to change?

What evidence can you give that the speejm4jihyj8f7 ctt 9fj -snvi0jv5( ;1kd of sound in air does not depend significantly on fmtv5 knji1jc9jvy- ;ji047(8tf jshf requency?

The voice of a person who has inhaled he t3zwsrtapvp3 r578 w9lium sounds very high-pitched. Why?

How will the air temperature in a 3s: xk+z0l auqroom affect the pitch of organ pipes?

Explain how a tube might be used as a filter to 5bopod.ndzq ;av3pyrs/ 0mz+yh a1n;;8b*dc reduce the amplitude of sounds in various frequency ranges. (An qay.zhd;o+3d1bbycn vo* npms5 ; ;ar/0 z pd8example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spco7; 6 y)zdkm2ord x7raced closer together as you move up the fingerboard toward 2ky7cd z ;o )mrrxd7o6the bridge?

A noisy truck approaches you from behind a building. Initially you hear it buk,dl;ldi8 y5 k/dxr9dt cannot see it. When it emerglkkrd /x,i9ddd8ly5 ;es 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 oh-5 ;qzo-jq du :zj*gto be due to “interference in space,” whereas beats can be said to be due to*zj zgq-; dou j5ho-:q “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakb7,fvdn)4s rb ers were lowered, would the points D and C (where destructive and co ,)vbnds frb47nstructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people wig1v 9ziw ++ rdr1la.oho work in areas with very high noise levels have consisted mainly of efforts to block or 1o1ria+ .ivwgl+r9 zd 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. Eac- qxzk uu7x0s:h wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In whi x:q-x70uuszk ch of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shqj- );5fh juduift if the source and observer move in the same direction, with tqfjh-u5 ud )j;he same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by aau7qdb z/,3e/n3dr w s4/nzz z,wvvn, person at rest with respect to the source/n,w ,dvvd3w a,z/b7u4/nns er3z zzq? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitq2xg,qxlev 8 m5 -9suwor is blowing a whistle in front of the child on the ground. At which position, A thro,l vgxqe 5u89wmx-sq2 ugh 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 liste/aktaeb g (y5sizl*2esr 1+q/ning for the echo of her shout reflected by a cliff at the far end of the lake. She qi *g 2e+sz(ya1t5l ka/rb/ eshears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterq b.ccmkh.:ye52h8 mrline. 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 speed of sound in seawater is q25 h rm:c keyhc..b8m1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 2g c;:(meuodjxowcrga (+ y/ 540 $^{\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 day. yzi 8 w3x::aqaWithout warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How mi 8:aa3y:z wxquch 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 qjjt90* q:mcj when striking the water below is heard 3.5 s later. Howq*tj0: j9qcmj high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone stryxjkcdm0o )ow:)7jw * ike 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 impact occur? See Table x7 d:0c j)j)kw*mwoyo 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made ov5 irhnpf 4j7+fer one mile of distance by the “5-second rule” fhrfn p5 4jif7+or estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level o4(db ((6*oqkq gwpowv *;ewxjf 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 inte zyu.6u(,i xdensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaee* p d9vl5-csneously at a certain place, what will be the sound level if only one is exs *e9dv-lc pe5ploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distan+n m 6yvr8gi, chsla4xe ul7g. 70c/syce from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensiti 6mlg7x08 g .succl v/eyi +ys7a4rn,hes, not dB’s.]    dB

  A cassette player is saidtq y clm72.nd:;wni2tmr6 js4 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 mwlt724t q6rn; n .ij2m:yscd noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output7 uj*8nqbx21m1dbix n of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered x811 uqnx *mb7jnbd2ion the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area in(z j8.byra*jcksh35lrw. v-;v,e rcs $5 \times10^{ -5} m^2$ (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 amplifiwc)o8zz (k;g8wq al k(er B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeake( kw(a)zq8o zlw;kcg8r 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 *nx9jkg,*k rs meter registered 130 dB when placed 2.8 m in front of a loudspeaker k*n,g kj9 *xrson the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound le/eg wg obqr946vel of 2.0 dB. What is the ratio of the amplitudes of two sounds whose lgb og9e 64r/wqevels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of attre xz);2c z( sound wave is tripled, (a) by what factor will the intensity increase? Increase by tzrcxe)(z2;t a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have eqkw voiio,d 9t,ff 8-h9v;0jmnual displacement amplitudes, but one has twice the frequency of the othehj9mvdkv8fft-w 09ni;oi,o , r. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in ammer5 7j :j t)ryeg/z;ir that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm atrt7 :yzgej rm;m)5ej/ 300 Hz?    dB

  A 6000-Hz tone must have whaff9j0(2 nx zyw.0: bbbfl0ekft sound level to seem as loud as a 100-Hz tone that has a 50-dB soundfl0(f .:enby w9bfxj200 bfz k level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an iw)*dby w.4qp/dnz/lr q 2m5pear can detect when the sound level is 3* qpw)dyb.zw2r/ 5d /mlqpn4i 0 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge rkfy0/4dnha(z2j-atjt jv 6 2pange of sound levels. What is the ratio of n jafhdjtza2vk6/yt4p-(20 j highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequ x8/wfyh/( hrmency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 h( 8h rfywx/m/g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first threeum tf x0h3yj1(q7innl9yr/(c audible overtones if the pipe is /hc3i fnj xmr q0y 91(yu(ln7t
(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 thefs:p )pnx-/+g -+t6 c zqgyd7wzyl2 nk top of an empty soda bottle that is 18 wk7 fp -:z+-qxlyygs6 zcnp+/g)dn2 tcm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning to*- fu lx0sqc)hd.j : )qx(nxdhe range of human hearing (20 Hz to 20 kHz), what wou( ufhsjnldx0)x:.*c o dq qx-)ld 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 freque)*dmy dn*mzn2e7 sq1ency of 540 Hz as its third harmonic. What will be its fundamental frequency if it isnm1y s dnz m7dqe)*2*e fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar stringz)c3dvaput: 4sx g )6c is 0.73 m long and is tuned to play E above middle C (330 cs4dtuvxz)6 ag:)p 3cHz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits eruts71ou e-w0 y2q)h middle C (262 Hz) when the tempoe2suyt1e0h )uwqr 7- erature 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 20l 3 e+i.,hfm3zn/mfjq $^{\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 y(k8u8nud)gssy (o*c should the hole be that must be un n ksy(d 8(u*y)gsc8oucovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but 3csx*w qs ,bs,ip0zz3y3 uu-p not at any other frequencies in between. (a) Show why this is an open or a 3supq ,zi uz-b*ss0y3,wp3cx closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 mqp6z d5 ;y:ltinoc, 8s(1w fnep8sz7h long is open at both ends. It resonates at two successqcle,ws s6pnzo zn;h78fdp:i8y51 (t ive harmonics 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 0otfp tr 3e))hch1t i;$^{\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 wr7 *-7vthj jagithin the audible range for a 2.14-m-long organ pipe vjh7gtj* 7-ar at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal 2 v.m lmi(co1.nwy5ma is approximately 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 ear canam.5v ylwcm(.i2o1naml. 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 strif g a;d8.*g25(fww09j. dfwfo sgnt jungs, one of which is sounding 440 Hz. How far off in frequency ;dtn0wo ja( fgw5s2df*..wu jfg 9f g8is the other string? ±    Hz

  What is the beat frequency if middle C (22sdg( jnd7zyox 5.zm 8ul(r-e62 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),hvbl) 2t**)gm:ev z .fpmji u operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of fieft*v h2jv)p ) bmugzml:.,*requency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 bea vszz+p)6t3y bts/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 yourz by6 vpt3z)s+ reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The uqy pc;qs(s-k :m3s9wtension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strin my-qs;s3 (p :w9qkcusgs are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will xxcv z(/b5hqnykcf66,wt9/w be heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other xfy/,ch /6b9 nq 6zw xckwt(v5at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C.(u (wxekgp 42s 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, 2sxpwg(( eku4 the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker anch v1t j7mtq27d 3.50 m frt 7 7cjt2hqv1mom 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 vibratingsr*7 6t ;qdfka at 132 Hz, but a piano tuner hears three beats every 2.0 s when*r6ksf7 aqdt; 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 wavel8 n5yqqb24z qgengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 2 5ygq 2q48zqbn0 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain oli*e -.9/v qjfqk7yb fire engine’s siren is 1550 Hz when at ree9 l*fkj./7 -ovqybiq st. 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 ady l71m vekd0q7dfq /; fire engine whose siren emits at 1550 Hz moves at a speed of 32 m7e0 /y1qlq7;m ddkvf d/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency i29ip vk9uhy6 ij0wnj 5f a 2000-Hz source is moving toward you at 15 m/s vhiv 6j 59ny0k 9iuj2wpersus you moving toward 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 with the t0v41zz.q ud66b ilsksame 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 be.zld ik6 q ub0s14zvt6at 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; rf9ukyw.b5*tc uu7n at 50.0 kHz and receives them returned frucu7fwkyun9b*; t . r5om 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 s1/v7djf0a rllc4frh4e1 u 8.m)net qcpeed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. f m)j7/e .0cdc4l8 4laur hvqt n1rfe1What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on au,4 ap1x31zvjctl l1q moving flat train car at a frequency of 75 Hz,u1t114z3xlv c,qpjla 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 useu cm2gky51j7jvt9 vgi/j0r* as ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be vkjuryv t9 217gj *5 0cmgj/ia1540 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 using p(chfwhg ;map0v lf+iq7/0 9iultrasonic 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 velojjj2p 3n hfr 4i;w/)arcity is 12 m/s from the nort w3iphaj4r2 j fjr/)n;h, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its spfpp 893;phm,b4 ivm xgo u,0lheed 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 1,//v,pu u qdv4 kbpl ld/xfl,where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of thep/,u1k/qllu xfdv/,, lvd4 pb 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 thinejy4/fbg* .:ib j3 xs7nwnwo r, (8mcp atmosphere of a planet where the speed of sound is only about 35 m/3: y jjw8 i4n gc*7p/(snxreb,wmfb. os
(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. Determi j(v: spprg;5smrw 5,bne the shock wave anglemb5g vsrj;p,r ps:5w( it produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle ll o*.k5n; :ln:z 7 xbbttgf(r$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plph-dj jdo3g byuat 0aja,56i+ rb3,d,ane 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 Fig. 12–34. Dead-rd, g3j +oa phbu3d ,i5jy,6j0battermine
(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 downwarq 0 jar4clhs5r5k;z5 rd from the bottom of the boat, and then detects echoes. If th5aj;45hzkrl rqsc05r e 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 ar. bm9s- iewau1 f2pz;ne there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipenhbzb47hw0+ aruv47r) q jor: symphony. It consists of many plastic pipes of vari wrb7z4rqo)buva h :7 +n0jhr4ous lengths, 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 sound close to thegxi, t:h9k 9zd threshold of human hearing (0 dB). What will be the sound level o9xh9 zi,:gt dkf 1000 such mosquitoes?    dB

  What is the resultant sound s+srit 24vwendp.e ; 3level when an 82-dB sound and an 87-dB sound are heard simultaneoeie4drs+s pn .;3t vw2usly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open,a4azb hht- sqz1-lcqe0)- f g,l-d/ ny is 105 dB. What is the acoustic power output (W) of the spegdl)-h-0qqczl/ 1-ns fayb- he4 ,azt aker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. d77 ffk( (;njgrjac2vThe power output drops by 10 dB at 15 kHz. Whacdff7v7jar kn ;j((2gt is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protecvs oi8)87 7dpm 2jfthytive 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 fs78phm oj8d7y v i2)tthe average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications slpbpx0+ az h p/..xu9eystems, 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 violi sn2d9 vjf70 6n lawcp).s(vke(yvvz;n 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 fu6;ef ytgz2 ;p83s;vell 4a ipoints with a fundamental frequency of 440 Hz and a masslpt2fe8f;;i4v6 y e; l3aus zg 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 verg.lxhy-i7 h+ atical open 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 is lagx.yhh7-i+ 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* )z*j mjxhk1i ceg63qv)z-tnd ew) 8q near a tube that is open at one end and also 75 cm long. How much tension shoulv8 xe nd)zjgeqw kjh3z-m*6i)t1c)q* d 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 wasf: r w+j9fmi.p 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-Hz range coming from two sources. The40ue.na46i g qa okj(o 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 0.344kga4nj6 aou(. qe 0oi 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 stationi c2w 9agqlfji 94o+v2ary. The conductor on the stationary train hears a 3.0-Hz befa+ li24iqo9vgw9 j 2cat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam9m7t+.2hi*z qi: mgh7 nrgilp train whistle as it approaches you is 538 Hz. After it passesg qn: ighm97i2 *ltzmr+.7 hip you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you cqn:hzv z9le bnv-038 oan estimate the speed of cars just by 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 fulzqnv -9lnez3 0:ov h8bl 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 11 Hz. The .g birj si--,ff:.w/anqipyt5gx ,e, shorter one isbgyf,f ,-.je -qw .pig:itx ,sn/r i5a 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad ckyqhzzw. dn9u ;ef9 :/ar 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 hekzh ;zuwn f 99e/y:.qdard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aortmbo57 exzvi wf ,hkee) ;0osbd9-,oj9a is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cell90 fmw z ids5e,7hoobk)9xv-j;eb e,os? 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 su7hl1gzs6yow+o eeq-f 75n2 a peed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave oflzqu7wg+faono1eh -s2 ye657 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 fg3zpp;:ml./l9 fengd requency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, anen fll.dp;pzgm 3:9g/d each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was oncjt kqn:231hbs e 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 fundamental frequency of:tbk31 qh2nsj this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo list;vn3sefe o0d4s +9)uo vqu8 fpening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living du s9o4snfuvp30; o fe+q)v8eroom 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,” involves a long, fbbz:w u, ac) jyil428u)7im gslender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-longlm fyb g)u:a u8, 7i4bjciwz)2 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 uavy +lxpxm9g7 rk zf6e*1+*qear at a frequency of about 106 ervqm+gyak *9z*lu x p7x1f+00 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 Mach 2.0. An ob h-cua9mn lql2/ gkcg7t/,jm )server on the ground hears the sonic boomk 9h,/cg7mnqu2 j cmalt/l)g- 1.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedb8u)uq9*qg3x jj .wqsqoat 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