What is the evidence that sound traveibmi15( hh ;z 1dpwszh6kuh-3ls as a wave?

What is the evidence that scla .5.q+y6jty)k:b; cmeolaound is a form of energy?

Children sometimes play with a homemade “telephone” by ajg s;jfp3r2 l;ttaching 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. 12s3g; jj; f2lpr–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes ff/w2cmkov z(/mn, qq8p .d7qlrom air into water, do you expect the frequency or wavelef8q, mk/m2vdnzp(. qqol 7 /wcngth to change?

What evidence can you give tv7eqm 59 f,:ipxt 0fiphat the speed of sound in air does not depend signifi,i vep: x7mqftpi05f9 cantly on frequency?

The voice of a person who has inhaled helium12kzl *u.bj 6h,aq zlv sounds very high-pitched. Why?

How will the air temperature in a room affect k5yc;a axgg 3/0go/ o5i pi.mjthe pitch of organ pipes?

Explain how a tube might be used as a filter to reduce ths1npg p*u /,pie amplitude of sounds in various frequency ranges. (Anp/i1 upns* ,gp example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you m-g9 5sd- 37qzdplptvmove up the fingerboard ppg9d7z qds-vtm-3 l5toward the bridge?

A noisy truck approaches you from behind a builxf v;8djl diyio;k6jmm39 b7h0h hj +;ding. Initially you hear it but cabjd+3jh7 ;hh fyim80m;o;xi6 d l k9jvnnot 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 Section 11–15 on diffraction.]

Standing waves can be said to be rs)i3 v;.l1,oehvjnw 8s yt*e due to “interference in space,” whereas beats cay.,3)je8;s ohr ie*nv1ws tlvn be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the v5ar 8ofp h*f;frequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move foff; avr8h 5*parther apart or closer together?

Traditional methods of protecting the hearing of peoplel:49skjqci9 +ci1 wc r who work in 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 tlk1sic irc9c:94+qw jhe ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wrhxu 5t oxt-n93gdr hj(:*gqbcx:,07 9zw wisave 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 c-07b tn : ro ,su(x5iwzwh9jth*xq 9rxd3g:g(b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and-zxji(82wi7 n i xwj3pplj2 h: observer move in the same direction, with the samwx8jpj(z 73 i2j2hxlw: i- pine velocity? Explain.

If a wind is blowing, will thib,ac u3 9.ni/lfb9kdn s alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity can ubf 39d./9n,iblkchanged?

Figure 12–32 shows various +o gc2ipmfjm-9 z8*udm hau 59positions of a child in motion on a swing. A monitor is blowing a whistle in front of the 2goc -m*5u+paim9 dzu8 jmf9 hchild on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by lisv;5d1f5q se;hq:09bhtfvpr etening for the echo of her shout reflected by a cliff at the far en: 0e hqb;t dpvv9rqe;ffs5h51d of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the watehx8n g2 fsm-a8rline. 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 1560 m/s (Table 12–1) and does not vary significantly with dem2ns8 f8h agx-pth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in q.t .e(f;f1idknkv5tc qo /2gair at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on f3: /d;:t3vv w5 jclko1po ,7y onikwva foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by k1/wtn 7ojk;o3fi :35w voc:dplvvy,the fish,    s (b) by the fishermen?    s

  A stone is dropped from t. ep3md58se.bp 7ln mghe top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the cliff? pm e7glmd esp3.b8n. 5   m

  A person, with his ea jlsr3i;kic.) r to the ground, sees a huge stone strike the concrete pavement. A moment later tw)j;3. rici lkso sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance b/ci 3duw cs8xsz4)jq;y the “5-second rule” for estimating the distance from a lightning strike if the temperature is cd4xj)ws u8ic;zs/3 q(a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soundjoq/k.v xqc3l.-kj:fi2 v y-o,k1 wfh at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensil*7qyb5mo o fg*+ 4wodty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneousgt2 /r 9,o*h9zreq*iuj)mexvly at a certain place, what will be the sound level if onlyq*t,r /h jv) em9x2igu9ozer* one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane3rhswo) * +y0bl qu2)cj a9rds0dis,s)u+wk j with four equally noisy jet engines is))u o0 w i s2asdksrcjwqhls0 3jb +9r+*uy,)d 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 vgl 0 i *jsac4-i .ri,d,isu)xto 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 theic),l .,i rd*g4 vas0jisuix- signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power ouaguk9) o*l:q ytput of sound from a person speaking in normal conversation. Use Table 12–2. Asa oq: ul)y*g9ksume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eard:nxg w*h4z wa,l)fa 6tune.i,9 l rj)qrum 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 amplifieys/ gnc4qetq(*/cfp 5*yl.a.ay i -mbr B is rated at 40 W. (a) Estimate the sound level in decibels you would(yq cl/y5 c4sybpam*e qng.it/ -*af. expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front s*:8yorjx ysk h3,9gnof a loud8,ksr *h3gy:xs9yjn ospeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level0(o:oarlh6/mg;cprbfe 8 9h k of 2.0 dB. What is the ratio of the 6r mgbh(;0kla8/h feo c p:or9amplitudes 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 fj,gbt;.*usm e actor will the intensity increase?s; m* gebtj.,u Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves havesd zo9pac2w/1 equal displacement amplitudes, but one has twice the frequency of the other. What is 1adp2wos/c9z the ratio of their intensities?   

  What would be the sound level (in dB) of a so zb+ uwpt4wfr1n7s b27 9ncl or/l-oxe.0 t*tound wave in air that corresponds to a displacement amplitude of vibratingtps l-rbb+7 oue.*1t2c 0wzxonwt9 ln4o f7r/ air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as av.8n7 +1ixfkoh(d g gde2+tdv 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6hn dte. 8d71fkxig +g2vd(ov+ .)    dB

What are the lowest and highest fh, ql *-ckp4yhrequencies that an ear can detect when the sound level is 30 dB? (Se 4q pk,hyclh*-e Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Wharh 2,zoi.)ikd4rbgpotw,+ 3kt is the ratio of highest to lowest iz, 3)ropokh+dkb4 ri.wtg i, 2ntensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The len ka-h(if0f:a g.zeo;cci wd 2o;4 d(ifgth of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the strinf cfg.2ioci f(:adkiw4h;e-a d;(o0z g be placed?    N

  An organ pipe is 112 cm long. W t0edws- bw(frn0b.;mhat are the fundamental and first three audible overtones if the-0s webm dbnt;r fw(0. pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequencyy) e; xqclcdyg6s2 n5w52x/fg would you expect from blowing across the top of an empty soda bottle that is 18 cm xy62;)fy dl wg5gx2c q/ec5nsdeep, 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 s a f-ip79coi6,.a jssthe range of human hearing (20 Hz to 20 kHz), what would be the range of the cjis s 6.a s,p9o-fa7ilengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as itvaw 1mos(- q1ts third harmonic. What will be its fundamental frequency if it is fingered at a lq-1( tsa m1vowength of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E aon5ax h(e9 i2s.xki9 +f+agf ibove middle C (33hxa 59(isnk2+e i.+ 9o xffiga0 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open orga/ fk.3zmit 7sin pipe that emits middle C (262 Hz) when the temperatutm3i ik zs.f7/re 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 kt xc6:qtjy.47y qzr720 $^{\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 be thm 1vqtb/ u phl*:1qpp/at must be uncovered to play D above middle C lqvmbt:u1 phq /1pp/* 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 notxoeje0tc ac6v2c.- .ue6e sp6 at any other frequencies6eejc2t0v-x6o.6e s. ceaup c in between. (a) Show 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 succ ,di:xxsvg n1livm0b0,vu0u( essive harmonics of frequencies 275 Hz and (vnusixlm0 di,,:bv01g0 vux330 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 r*xzg :lpn;:i:g8e b m$^{\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 xz9jl3)zqghj; ;wm(sstk,o7 pipe wj 3zgx(oh),klz m7 t9;j;ssqat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is ow.sp 7 zy0ag4wpen 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 canal. What is the relationshipw7.yw4sz0 gpa 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 tcmo ha)a54 b 6-i2ccmwrying to adjust two strings, one of which is sounding 440 Hz. How far off in freqbma65c ac4hiw -) om2cuency is the other string? ±    Hz

  What is the beat frequency if miyumx1 v9tk6q )ddle 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) oper k 8evf0tku4,kkkqy/b 5;ilu4ates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill 085k/;,4keft uy kkbuvl4i kqwhine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beat93jfxbzqdd l 75j tugt:*zv68s/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. Wlud96jx 5 zvb*q:dfz 3j8tt 7ghat is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the sa 4qz bh 2y//vxwb54nul8g7tdeme frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played togetd/ n h5v47yb eltg482zqwxub/her? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flz sme7)c/+na/jk )oarutes each try to play middle C (262 Hz), burkjn/ /7o)+ze )mcsaat one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, (xpl0en8w*qfk x n6p7 and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible f7 fxlx p(qwn 6enkp0*8requencies 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 and 0v.v/c .iuj, ibhdg7mh/ ole13.50 m from the othbh.,odcl/ie7 0 i mv v/1jg.huer.
(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 pip s;s.: z5nfxvano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating 5nz p:s.f;xs vat 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 wavea5-/vx s lwfuud*0 j *hy23jjdlengths 2.64 m and 2.76 m in air. How many beats per second will be hearx y 5d-v3fujd/hu a2*jjslw 0*d? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequenc:q1 jf6yyeg+ee k/.rjy of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a spe 6eeyf/+.q jjrk: 1ygeed 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 g 82w)ol um(8gyuo:vu (c2vkxfire engine whose siren emits 2v28um(o wgk)l8 :u uv (coygxat 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 sourc/f iy:x)pl ;/vlp1v: )fx zhjle is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are jz:pyil xf p;: )vll)1hx f/v/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 same single frequency horn. When one zt rt) -o5hx-ju ktpg9+vjgy9m 6b0)ais 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 frequencgxo-) j )brmghkp0ztauyv j995 6+tt- y the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them rct,.j.0s/b.k i e6vd mx3st)r (h ulqweturned from an object moving directly away from it at 25vuhw . sertt6,cs k(qd.l imj 0).b3/x 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 it3he oev1t .w(zqc ls46 flies, the bat emits an ultrasonic t4zve o(sc6hw3. eq1lsound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopple5h6xs3y:p q5adq u/lrr experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest inxl/q3ads 65h q5rup y: the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow fqg y bw4:-efxko;2+-k sv(w.7qpbfq 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 expected beat frequency if blood is flowing in large leg arteries at 2 cm/s dir72:(.qfoeqbxfy4vg p; bk- sw w+q fk-ectly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves 35az6 juvm:j svh3z5 vof 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. Wkze;-g;k /hz jm ih(mtft;/v.hen the wind velocity is 12 m/s from the north, what frequency wkm/f z.hegm -/h k;jv tt;(z;iill 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 speed z uedcr 7,: 3)rmffsz,j7h-jm 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 (ifzoug;3 g y-fb4;n; ba) What is the angle the shock wave ;bn g;go-ffib4yz3 ;umakes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of sound isaxwu 6 kk5gl -f18:k7sw, jkwl only about 35 6 w:j akf1lu75kxlws kk8gw-,m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Detel vkxs/ii) oz05e;*vqlsb4u / rmine the shock wave angle it produs4)s *;iioeq/5vkuzxb0 l /l vces
(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 vsbpi o n.jr+( 8+j,cl)4 jcbo$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a put,+ew *kj5c/ ivj vk.f9c5e9o wfp/4w(awl llane exactly 1.5 km above the ground flying faster than the speed of sound. By the time y5w5 9 v+ /wwfjcktvi (4o9,a/.fcl ejuewklp*ou hear the sonic boom, 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 downwa7 z m d;ebi/xu:e +1br-zboym+rd from the bottom of the boat, and then dezy1x om;b ++ z7:e-/u ebbimrdtects 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 8c h-oij4a-;; azybvz+qmhf. range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists ofe)v2l4qg bi2g 6 ,o mggj:zw-i many plastic pipes of various lengths, which ar,-b4v q )i6g ggew:g2m jo2lzie 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 aav10 dn(om2ke9qn ,jl sound close to the threshold of hu(v qekm29j non1d0 a,lman hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant soundwl ld8bchzw4k/u.k 6st i+.p o(3 ty(v level when an 82-dB sound and an 87-dB sound are heard / i(yot84z6pk +w.tkwslu3vdb h c(. lsimultaneously?    dB

  The sound level 12.0 m from a loudspeaker, plac yop7m2et;jo.ed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming pt2 7mye.j oo;it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The p .+mwrxsan78d ower output drops by 10 dB at 15 kHz. What is the power output a8rxmnw+d 7 .sin watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices ovhouw jkh)h(xede7-)n7c 9 /reer 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 unprowh cr7(xehj neko9 -euhd/) )7tected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sysb-scx8y/i8 ;rq(u kgjwebj- 7tems, 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 freque mipieh b+9iw ;izovqg f(875kj+s7y 1ncy 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 fixedxn: gz8vzrc*/ points with a fundamental frequezcr*xg n/v8: zncy of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube fil2 m3kj51y m*xg.e cpjlled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, th 2 5*mlkj.xg ypcemj31e 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 mass 2.10 g is na; :p4kyhr6mfitr.bu, ggp 7*ear a tube that is open at one end and also 75 cm long. How much tension should be in the stri hg ,*fk4mb6p:yptg.a; 7ur ring if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed t, ubgv-+e2n k6uhl78vht 7rfk o 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 rangpqj6c(tw4 w x;qn2x np3(bd2w e 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 anb4(6p3 wqx 2jwnd2cn;(ptx wq d finds that 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 is stationary. T,vr om6odf n/ov tt)95he conductor on the stationary train hears 9fdrt5 ont6/ vm,o v)oa 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches yo bw2sa ji,*h1cu g()dkzj+)iru is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assumb2( iij u,+z gsrh*)kj1acw)de constant velocity)?    m/s

  At a race track, you el4uoq0qmc*dz11c+ mq b d+6:0cucv acan 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 full octave*cc ++ 0abeuzd4:6vcqq0 md1 ulco1mq (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 frehw2 ddes88jp +qg+yl)quency of 11 Hz. The shorw 2)g8 8h edqsdy+jpl+ter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroadtefz7 9y9b t5g car as it moves past a stationary observer at 10 m/s as shown9ftzb g 79et5y 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 between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood fv y suhym2)(yp 9r2*hjbuj6 *mlow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves *pr yv9umjs*2(h u)2hjmy 6yb were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while thp tm w9c.o7:xtas)5an5 gobso7 x;7bs e moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off thet7sxt 5xoa:m.7 onw;acbs s 9 5pog)7b moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. .jsgfin..0qfvo y1; aThe 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 q1.v s 0;.yn. oaffjigso that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. hi;h h8i.xg07ak ha4i12–38) was once used to send signals from one Alpine village to another. Sincehk7 ia;h0x8.i ahhg i4 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 this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can44f uhf /c r 7cwv-,cljxs 1:d1rprdw( be compromised 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.j/7dpl1r:cvu-1ww,f dc rrhx c4 4f( s 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 d;w/xjo4q(j aop(fx2 a long, slender aluminum rodajdwp2ox4;(fx q o/j( 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-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 h8oe;e xm yh8k;hn , sd9o+m6)iax yri(earing for the human ear at a frequency of about 1000 Hz is 9)6om(;yxhe ah is nm+y8rei,8dox k;$I_0$ = $1 \times10^{12 } W / m^2$ 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 hears the sonic c 7 d:7esl3gh9 )spbchniz3.-jzp.z mboom 1.5 mpb9s3z. ih: gnl3d.ze zms7cc h-p7) jin after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat i)7vi3 ot- hke;anasn)kzxjg pp 2e,xr5t w301s 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