What is the evidence that sound ,) - yysdwij)t51 xnfsmi:rt)travels as a wave?

What is the evidence that sound is a form (/f msd.p, een;vfkw24u 2ogq of energy?

Children sometimes play with a homemade “telepho(+jkwj u: lgo*ne” 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).(kolgj*u:wj+ Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air inu0wk,)mt2 x 2qfg2l7 :zpoxqkto water, do you expect the frequency or wavelenggqwpzuqltk2ko m:2)f70 x x 2,th to change?

What evidence can you give that the speed of sound in air does not depend zg 2n1qbbm1 4ysignificantly on fr qb12ymg1 n4zbequency?

The voice of a person who has inhaled helium sounds very high-pitched. Whzmg(bz3c z0aif9/.vb 9qg ix(y?

How will the air tempera9rv ryc4p;s6 eture in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the am.ly f oc1fq .2b:h7kgarnn;-xplitude of sounds in various frequency rangel:nxakyg 2f.-n qhcr.b;7of1s. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer zt::khlg9n:8tk b:op together as you move up the fingerboa t tn:lg:bp8zkkoh: :9rd toward the bridge?

A noisy truck approaches you from behind a building.f (t8m.2 xqlqs Initially you hear it but cannot see it. .lfx(8 s 2qtqmWhen 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 day3ki e,(fvj0ue to “interference in space,” whereas beats can be said to be due to “interference in time.” javk0ey3, f( iExplain.

In Fig. 12–16, if the frequency of the speakers were lowered, wouln0/ 8ddm6j4ewmtopy ,jop3:casuz/ mq , w0h1d the points D and C (where destructive and constructive interf/ 1on4 mp3mwca/6,: m8,qtj 00 pezuy wsddhojerence occur) move farther apart or closer together?

Traditional methods of protectwm*azqt.7i txig(r3fk:7 cc/ ing the hearing of people 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 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 thex wi:.rci mt7 zfqkt3(g a7c/* ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a sup8cr* js:evi-t ubh4 zxeac*,2 erposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.c,: *c-b2eja 4xsute vzh*r8i
(12-31)
(12-18)

Is there a Doppler shiftsxpnq ; ws z i,br(nc//;(.1myhb wgi. if the source and observer move in the same direction, with the same velocity? Expgmh/c/w .p1.n izssb,n qriy; ;( (wxblain.

If a wind is blowing, will this alter the frequency of the sound 0/1mppd3v. f y octn5amut c5)ccd0m8ij vf43heard by a person atm iy5om0c5j3vt. 8 / d3mucfv f4c)da0pcpn1t rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of amlagf fqx7s0qhi9,ei * k3q2m2ort/d 2f rp; 9 child in motion on a swing. A monitor is blowing a whistle in front of the cr r23ieofa7pi, 2q09gq 2 hmkq fl;x/dtsm*f9hild on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echoqsibfx/gl 9e ms/ .x)7 of her shout reflected by a cliff at the far end of bxlim. xs/)7ge/q 9fs the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes thetu33)r-1kw8 l jwqtl*u)qbef side of his ship just below the waterline. 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 s8 l3fewtuq1j w )b3)-kqlt*ru ignificantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengthvjc lzmdjy;n+0qk:2n pl /4 4ds in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy/6md / jqrm.plc+ kc.w day. Without warning, an engine backfire occurs on another boqd//.rw lj+mc6pm .c kat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when stric-t/ rc,*qgkdfunw 26 ty9/rpking the water below is heard 3.5 s laqu2np k6wy ct dfgt-/r*rc/,9 ter. How high is the cliff?    m

  A person, with his eafam2s0jt6rr z yqr0c)20 .d cpr to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur?qarrsy0j0)22 dp czcfr0 .t6m See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one miled(jq9zrf.7 sxj8qpl9oh s3*e 8xe5djza p (1o of distance by the “5-second rule” for estimatjxs9zp(z d o r (h.8d89jf x3epeq15oa*jl7q sing 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 whf( dr)wy;j 5the 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 intenmb*h1f kqai 5 q:ealq1.ibu h0or /*e9sity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95*h tlj4e/ b1fw dB when fired simultaneously at a certain plac*hbf lw1/4t jee, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with fzkdgm d24 v(3uour equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person gdm(kv24z3 udexperience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to havjx-t qyl e,73 o6fw:;njd/mf le 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 ba7fndy-tw3 o,jm;l:/ f jx6qe lckground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a persc5jet- (fds e;on speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a 5cft ee(;sj-d 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 eardrum whose area,:bgo *pj3ggy 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 amplif,: 1mflijy-.dln 0z ngier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in.yjim:d0 l -nfgnl1 z, 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 whejte99s u 99cvun placed 2.8 m in front of a c et 999uus9vjloudspeaker 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 dezr3:oin-ybt . tect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ :.yn b 3zoi-trby this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the +ysl;zl5pof vd*6vo; nux 6;g intensity increase? Increase by a factor of dps*x f zv+g5 o 6l;;y6ulv;on   (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement a t/-wcw2s f(21vcy,5mns jkdv mplitudes, but one has twice the frequency of th5fss -j,k(vvcc 2nyw1d/mtw2e other. What is the ratio of their intensities?   

  What would be the sound level (in dB) ofhun2bwck w9*4 a sound wave in air that corresponds to a displacement amplitude of vib4*ckbw2uw9 h nrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone t. ijeo:g5g ;vgvu7a)(w; wal shat j :a5;sigg.w(wau;gve ) l7ovhas a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can dete ic9ror)pt,0nct when the sound level is,i)rt o90 cnrp 30 dB? (See Fig. 12–6.)

  Your auditory system can acpm*n2hmdh k 02me w1pj+8mw4 jcommodate a huge range of sound levels. What is the ratio of highest to low+hepm h4jnk 0wpd*mm wm2j218 est 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 frequency of 440 Hz. The len8,p n4xnstz)hv( g,ib gth of the vibrating portion is 32 cm, and it gbn4n z s)i,vh(xt8 ,phas a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the funda hv. si:*.zfjg3qs8-8usvhxbmental and first three audible overtones if the pipe vvsgq 3s.jxubsh*88fhz :-i.is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing acros7. ,d(tr5yudu1qdp* 8n 18rksfd htxbs the top of an empty soda bottle that is 18 cm7d*1.dd( httufdsnr8k8 xb,5 pu qry1 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 organl-znb 0h8hg4 r with open-tube pipes spanning the range of huma4zhn0rh- l g8bn hearing (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 fr4urf0wx t vky5)(h nu-equency of 540 Hz as its third harmonic. What will be its fundamental frequency if it isu)n( 5f0kx4 rht- yuvw fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m lov2:)yj09oh 9occcd k ong and is tuned to play E above middle C (33jo ccc 9yo o2v9)k0d:h0 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 z8txobq-s mx;s ;z9+e8hy1tgc3.v rwof an open organ pipe that emits middle C (262 Hz) when the temperature ish3sv9m;8 tzo grstx-qz ;yx18 .ew cb+ 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 atcuqa g 7;l12ad 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of th sdsa1t62 a4hhe flute in Example 12–10 should the hole be that must be uncovere 6ad14ashht s2d 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 cmu+a8ds k8neu;3 v- presonate at 264 Hz, 440 Hz, and 616 Hz, but not at adpvs 38; kcnua u8em-+ny other frequencies 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 84at srjl,hscon dt;0r9 x rt9 *o9o3ztwo successive harmonics of frequencir* 3talz tros0csrh dx89 t9no4 9oj;,es 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 zg:-hdr i*qlqt2zsj l; ,y l20$^{\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 rand bhr r6taxh+zqo81-/ge for a 2.14-m-long organ pipe at 2xbh-q8o +ht6/ r1radz0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm lo3/te,ac xtvy ) hxa0z/ng. 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 canal. What vxt)x a/30z /cate,hyis 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 stri:8ljxyh.p sckto(f5 w- z)z1sv..emp gqfp 0.ngs, one of which is sounding 440 Hz. How far off in frequency is theq1pzps lsfm.:5c.pe 0 -t(f hz.xk8)g. owvjy other string? ±    Hz

  What is the beat freqnt 6 wf ggl(f*/pio99duency if 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, while9+;8ndi2eh 3mbh+jh 7w ma *ghx xedc* another (brand X) operates at an unknmnwh*c72+ xdbx9 ;ah8hdjmh *i+gee3own frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and p;c m f9k+nv t/(dvhou+lz c539 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? c(5u+c +tzp3 h9 lmvnkfv;do/ Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in obb ;f:7kestb0(d qox3ne string is then decreased by 2.0%bd:qboxk 7sbfe( 3t;0. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will h /ps/jg/4r ip6diqr6be heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 2g ridqs/6p /rj4 pi/6h5.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C.yvw9m ,c +xj-l Fork B has a frequency of 441 Hz; when9mv- jywc,x +l A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A 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 onejpu-72pa /4u0f ngvl7 vk8iz j speaker and 3.50 m from the oth-vaz724 u/ 7fplvgp kiuj j8n0er.
(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, butrawn8 dm( )g+d a piano tuner hears thrn+d m(w8)dgra ee 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 wavelengntxl0o.ao0z 5hf99 u hths 2.64 m and 2.76 m in air. How many beats per 0o9.5ltxfnho u9 ah0 zsecond will be heard? (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 w22m e uxo:,pd9(jj-gzxq-v mqhen at rest. What fgjompd ve,9m xq- 2uzxj( q:-2requency 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 i+q t hw954uf.w/mn4t6w r mytaf a fire engine whose siren emits at 1550 Hz moves at a speed of 32 wfw 6n a5 +4mthtm4 /y9.qwurtm/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source ic.cj9-h b coae9z.crdw1tw3x 2/ 6xc +kd,ccts moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they cl.cx9t6 k9xe2hc oww1drz.ac+3dtcj ccb,- c/ ose? $f'_{source\,movine}$    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 is at npgvauujkkx79 7* /,7yo9tpy rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the hor77x tja9 7uyvo,g/k9nyk *pup ns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kyc 7 :kx2jmdap963xbfHz and receives them returned from an object moving directly away from it atm9 7xkb:yxc d326f ajp 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed)wzv,e )3/zohb+v cv f of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.03bh z))vcvvfw +z/ ,oe kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a motq/ypt +(d*bvving flat train car at y*vb/tt+q d( pa frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ul sytrs 8add3 5cbca+92trasound 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 13ssatay+ 5brc8d9dc 2540 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 ultrasonic wavvr p )*c)egbts bw(b76h-ihy.es 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 veloc,ur ir9sb((3 +vd el vy0cr:8peetr2x ity is 12 m/s from the north, what frequency will observers hy3s,l er(e+r09 2xp rec u(8divbrtv:ear 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 at 20+5 sy.wjdhy f 0/tt9yj $^{\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 (a)g: 8abf/l(q rc What is the angle the shock wave makes with the direc8 lgrca(/fbq: tion 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 thirp964 zvh+uhe thin atmosphere of a planet where the speed of sound is only about 35 m/s z irhu+4 69pvh
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave anv*ymlr 1fr 9ivl 3pj.1r3jp 3cgle it produlpr vcmv1j*f3i3 .rjr1 p9l3 yces
(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 (jnin( yv43 cvhq 9d6w$/theta$ 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 group e7v1rswdbmw*6, .a hnd flying fastebh .*6w ,awp 71vsdermr 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. 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-Hhmi na7 o,og8 ;4rikn.z sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is design.8r okigih 4,mn7o;a ned 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 rt9 5ysm6aturmo4 ui2*ange? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. (vd ;sxif1,wx1jk3o1m cicg2x 8 fju6It consists of many plastic pipexgwj18;u jsv1 f2oc dx1i,mx(kic3 6f s of various 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 dv033qxwp.zgojagr8 9x rv 6.a sound close to the threshold of human hearing (0 dB). What will be the sound level ogx3davr8 .g9 ov xq0jp. zw36rf 1000 such mosquitoes?    dB

  What is the resultant sound level when azan43,pu0 zrud3w 1v an 82-dB sound and an 87-dB sound are heard simultanuda0,3 r1znv4 za3upweously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What i25yq6x.mxk9ib h 9ajis the acoustic power output (m kax9y6 iih xjq259b.W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 15j q2)pnnj1 z m z.+-z6/ptlja,uyas5m0 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz? y5jns1ju6n/qm+m-)tal j z. 2zzpa ,p    dB

  Workers around jet aircraft typically wear prot.n1 .mvkdg f,7tmhlp8 ective 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 lndt, pkg m.. 1v7mhf8power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systemss1 (m yaj.a6s26 v*po ysayvj(, 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 tuhv,t82r9r; nld+ias aned 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 lonl91hy ngxzz0+ky .t ;7w; atnfg between fixed points with a fundamental frequency of 440 Hz and a mass per unit leng;twkg+hy.71azyx f 0t9 ln;zn th 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 filled with xnv9bk/ t3wmsoxc f,szoyfjc1a6g4 x, 9:, 7lwater (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 heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again atal6s9wtxx,vs 7co1 fxocjfk4:,z ,9gnm 3 /by 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one endlbny1+ ub:3( 8jp rb8+txmb fy and also 75 cm long. How much tension should be int p byxu+rbjn8lb(f8y1: m3+b 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 was observed to resonate as one full loohr6 wqc9ju,0k3,xwb pp ($\frac{1}{2}\lambda$) 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 tvt hvv wy5l5s- l; 9o:mq9la3the 500–1000-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 f q5av: o;lhw93ylmt v-t9vs 5linds 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. The conductor onx.waa,y5k:p0 zfzn 6 x the stationary train hears a 3.0-Hz beat frequen 0xzaf,a.5ky:pwz 6n xcy when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it vkq0ci)dcfsu4/ *4mmu .lto+ approaches you is 538 Hz. After it passes you, its frequency is meac/msf d.ui4c4+ mtqu)0 ov*lk sured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the dif 5r0dq neqw o75a+3y00xcfbtfference in pitch of the engine noise between approaching q0ce+bd tf 3xay o7005rwqnf5 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 11 Hym )78pzfk jmj w*o(4bz. The shorte j)f4po *(mjkwyb8mz7 r one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of zq4y)edpr +hop,lynu,3v 8 l.a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identiy,r.3np 4duo,l hzlq+e v)y 8pcal 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 flow in the aoroxqg2 rn:t7 3rta 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 c nq72:rrog3txells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is fahh*) lsi.w)el7ojh lu2- c2tlying 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 afteos )l h7)lh ujte-*li2ch2wa. r that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as d ucd (3h4g;ffit approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms lcufhd(fgd 34;ong. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signa0ratejmy+ -zbh1i0 efr (-)yxls 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 this horn, and which overtone is close to F sharp? (See Tablezyi( je -xb)1mhefr00y- +tar 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of stajj/czbdww16 el 6zd24 nding waves, which can cause acousti wc jwzl46d/12b dej6zc “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstratiok-;a6azss*u(b i1 d rwn, called “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 clear, loud, ringing sound. For a 90-cm6zar;a -us( kbsdw1*i-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequa 7/9:*z6d cck,l g2p qxhhwfuency of about 1000 Hz i *9,:h kac2plxqd/gwz7h6c f us $I_0$ = $1 \times10^{12 } W / m^2$ 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 0oeb-rgl8rg1 syt xm75vc 8n;Mach 2.0. An observer on the ground hears the sonic boom 1.5 min aft;5yrl788 0ntvcsogb-grm e1 x er the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15/ql;k i:ll/q enu2 ch/ $^{\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