What is the evidence that sound i 85brext-xop56bv2fj9e xfe lep7 11travels as a wave?

What is the evidence that sound is a for:ns+;c 4.o qut4 y; wb-wpoiezm of energy?

Children sometimes play with a homema 2dzix-do)j x8de “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be hea dxo )2dzjix8-rd at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency oo( )zr6owh4yhz,7gjro uui 9yjz 2n7,r wavelength to hoow zjn,h,z( 6zrjuoy9rug247)y i7change?

What evidence can you give that the speed of sound in air does not depend signifm. /oi nyuadtft (uvf2,s3snrc6/.2 yicantlym cit/.syu2n(f.y6a2, f o su 3tn/rdv on frequency?

The voice of a person who has inhaled helium sounds vy )j 6;lfrue*e3cxw;aery high-pitched. Why?

How will the air temperature in a room affect the pitch of m dnu1 j -apj/.girvb;1at eyw/z8 7t,organ pipes?

Explain how a tube might be used as a filter to reducefnua-+n:w)31 :tmjlikpx9,wc+m e axa . ts v* the amplitude of sounds in various frx9+ +nm:eu 3 t al.xt va1*wfn,pcam:sw-ij)k equency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer b;*4j*bwoe vickugn jm 978t/together as you move up the fingerboa7 ;g8j jtvbnoiw *e9 kcum4/*brd toward the bridge?

A noisy truck approach3;oj l1qqeue p-4sa 0fes you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “br ;e3q ofal1u0s-e4 jpqighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be sai biml50 h p1l5stf11j7ywe*lg d to be due to “interference in space,” whereas beats can be said to be 5j1l f pyb5*e tsl70w lihg1m1due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speake . v)ui ois,+a2e cza1t+wcbs:rs were lowered, would the points D and C (where destructive and constructive interferenuiso:et,ac +z)i bs+ .v c2wa1ce occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peow eo3( 4zo.i1lpn8kk./tpdq6 v* cszr ple 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 bloc p.8pkr3 4/o(i*lsknw tvz1oz.c6 qedk 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. Each wave can be thought of as a suu2svls ve(:cp 7,ll7pperposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of th(llsvlspe,c7p :2uv7 e waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same dirqa ;ltk g y,,ee, hq/y:5d.gtjjcln):ection, with the same ve tjy ::tqlj;ka /qc,d, gen)y 5egl.,hlocity? Explain.

If a wind is blowing, will this alter the fre8zln a6jkvzcwk13 q 8 i/z-p0equency of the sound heard by a pers31ja8pvie z0 kk c8qnwz/ -lz6on at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a zj+il -x2( uklswing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequenl+ (izlxu2 j-kcy for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shout raz t (c3hc;m)sb6yi2qaj9/rneflected by a cliff at the far end of thezq) 6 c;jynsa3ri9tcm2b/ha ( 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 ju4 :q) os10xa1s eylrxcst below the waterline. He hears the echo of the souny4 r:s1)xxes0c q ol1ad 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 depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at x*wmxbxnyr1g 4-8 ev()ol 7ty dd:bi4 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 driy9/humeh m1f;5(mjql fting just above a school of tuna on a foggy day. Without warnin(j/yhmu1mhqf5e m;l9 g, 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 the fish,    s (b) by the fishermen?    s

  A stone is dropped fe whr2bnoc; 7jt0-s:v rom the top of a cliff. The splash it makes when striking the water below is heard 3.5 s laterc w0 -7rtsn2:v;eobhj . How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concreig si )kbcs*9:te pavement. A moment later two sounds are heard from the impact: one travels in the air *sb)9:si igk cand 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 dista-n; l m tvo ;98ymjmawvzhz//uida6 +2nce by the “5-second rule” for estimating the distance from a lightning strike if the temperature is6-298 movhdy/z;wjav;/z mm ainul+t (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity oh 8n )lepvs9fg8 o,m/b. qoof4f a sound 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 leveikbtpalq*: ,;e b :j02+8zjpi 1jgyi7* v lfcil of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound leveytnajpnur 3+45gs q ;1l of 95 dB when fired simultaneously at a certain place, what will be the sound level if r3y t5u 1gj4+spnnqa;only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain hqt-v+yamm,+ distance from an airplane with four equally noisy jet engines is experiencia,-ytqh+ +mv mng a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ral-fx+psoxa w5e y 9.zpn)09uftio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal andsea-znu fp.xw9p5 o+ xly09f) the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person sp-ljez/w8en. l eaking in normal conversationzll e8w/n.j- e. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikesl js2:,qapn1d gf3r 3a an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amzthn4db o4kg;k sr+459l ikic(gnkj6 +:8jntplifier B is rated at 40 W. (a) Estimate the sound leve k4tz ;n+bg4n 5l:oni k69igstc(djr+k4k j h8l in decibels you would 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 of orq og0w25y 5ta loudspeaker on the2 gy0 5qrto5ow 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 level of 2*y s3wv9f k pb5v6-zmx.0 dB. What is the ratio of the amply9zxw3mf *vvk b-p56situdes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a souq7b ow9d:b2tlg z5 4pu5 jv(hpnd wave is tripled, (a) by what factor will the intensity increase? Increasedp bw2 5oq9z:l(tu5b7hjgp4v by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equ3x: gr-2ybsm val displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensities?b xvrs 2-g:m3y   

  What would be the sound level (in dB) of a sound wavef 1 b4-c1lwinj in air that corresponds to a displacement amplitude ofjnl-4biw1 f1c vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seemqzm+q9hwk to76-r 65om;ydna as loud as a 100-Hz tone that has a 50-dB sound level6+q7d -o ymm ;n56kzwth9rao q? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear l) qnza vqb9wo1.zj.o4*r2 utcan detect when the sound level is 30 dB? (Sevan)b uzl* tjq1w2 ro9q.zo4.e Fig. 12–6.)

  Your auditory system can accommodate a huge ra4u dm :0a j7xbd/wb-ok6lv+stnge of sound levels. What is the ratio of highest bjbot4dv- lmskx 0 wdu /7+6a: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 frequency of 440 Hz. The +nss2v de0 ovp2+;h sf.vh;uzlength of the vib ;vvo;2pu +hzsnhs0s+2ev.fdrating portion is 32 cm, and it has 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 -7gm2jkpgjpe vkkm h2 b els)p(h92,,fundamental and first three audible overtones if tpb)(s7 hvmkjk2m-ek2,9 ,p jleghg2p he 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 frequency would you expect from blowing across the top o3.d.zdzevg.;k0 cnvo f an empty sod 3. dgvz0kven.zc.o; da bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes sa 7w fmu/6j cu:g8(e 94aptxtjpanning the range of human hearing (20 Hz to 20 kHz), what4(peamfj/x6w u agt:8c97 utj would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. What :u;;f g ev4bpj myb6r:will be its fundamental frequency if it is fingered at a length of only 60% of its orige:uy6;4b:pmr g v;jf binal length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle llpe z)h 8 qg9ctyh;;1ajk 4o.C (330 Hz). .;c94kjlh yol;ztqhe1g)p a8
(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 em(:mz akef-jq/of jb ;*ya, -cmits middle C (262 Hz) when t fja-aqokfmzb:c j ,e y(/*;m-he temperature 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 2kpb ww9ohy, .(0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of uj uosy.4*p + 6c,oalpthe flute in Example 12–10 should the hole be that must be uncovered to pl*os. o6l+u yup4 cajp,ay 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 264lz dnl1u/ 5ki x29bh6p-4 qlsg Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pipx l/sk1bi95-g4n lq6 2ld hzpue. ----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. ibg:sm692mr/ecm ndt ) zw-72.bnwknIt resonates at two successive harmonics of frequencies 275 -gb m/dzkci76 n)rw: 229 twsbn.emnm 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 oi:n1ud o/n-e1 lly3q$^{\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 audib2 f 1arw6duz,1j2 onrlle range for a 2.14-m-long organ pipe n6122afd1 rrwo , uzjlat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm ls -6xzw6+jlrt7 *tefd og 5zx/ong. 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 is the relationship of your answer to the information in the graph of Fig.r gwxtjxsd5to7e/z6 *l +z-f6 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 strin 72hvmh5vble. gs, one of which is sounding 440 Hz. How far off in frequency is them 2v7hvl h.5be other string? ±    Hz

  What is the beat frequency if middle C (262 Hz9kzy4zm) nup6rnj 3-v na9r*w-bca(y ) 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 operaz1yje. (bh-ottes at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans why.th-o b (j1zeen 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 sound :ojzwlqk-sgd) cvz c2k8 -bfq,8,8kbed with a 350-Hz tuning fork and 9 beats/s when sounded wk8j8qbl--,:swk)d kqc8o v ,z cbg2z fith a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency9bh pqw(o-apcor*r r+tq ) godb844(p q7n8lr, 294 Hz. The tension in one string isr8bopplro-(tw )hn pqgdr7* +q9r a(q484cob then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try rahzpq9ii g*v ,3cy )6to play middle C (262 Hz), buty v g*6ap 9rii,qz3hc) one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuningy9- g+rpvky(oe3q* ky6 muri+ forks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz -vykuoi9y(g3qr +emk y+p*6 ris 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 1.8h9 ,vim 5l6lh2tsffi 30 m apart. A person stands 3.00 m from one speaker and 3.52i hs965mfh,tlif v3 l0 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tu.luvzm)tyw6. 6va rd; * +cxybner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequencyywm.v d 6ylxt.)zab6;v u*r c+ of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in airsu:a7zu4 k3 aubkha+ fv//vm1h, dx p.. How many beats per second will be heard? (Assume T = k 3 x/.s u h,da:uhv+/a1fmp74abkv zu20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a w5lpyp zz9ys8 fw3v- 1 zv8(hdcertain fire engine’s siren is 1550 Hz when at resp-v3yzfs1 lp98zz(dw8 wv h 5yt. 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 fre e /0x97exhp*52g hesd+c euzrquency do you detect if a fire engine whose siren emits at 1550 Hxes0xuh/7+ 9 p2c gdhe5ee *rzz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in f ed4l2ca j4ti-requency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the t4j2dl-i a 4ecsame? 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 same single frequenc.*ymcr3qmqw d75 z -dby horn. When one is at rest d3my7q-* dcm brzqw 5.and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them ris/bkg ,l6 7ydeturned from an object moving directly away from it at 25 m/s What is the received so,ikbygd/ 76sl und frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed cy-pgyfu8w -p;d5mv0 of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30y0p;f -c8-w dm5vygpu.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler exper5n wq2x-ndm8b iments, 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 in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 qndx mw8n2 5-bm/s ?   Hz

  A Doppler flow meter uses ultrasuqqjjplma. 3z)** )a v6a+jmkound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and +*.vj kp)6)*qjalzmau 3ajq mthe 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 directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequencyels02,sdzju482v il y $2.25 \times10^{ 6}$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 frequencc*wiur:l5 le(pbl x.o+ j)fu)y 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear whr flub up*5io))e(: c x.j+wllo 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 kos17vb 9 (v5ajba1d vif its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2 )pxt)kmfm+.x tg a,f2.3 where the speed of sound is 310 m/s (a) What is the angle theagx+mf),m 2t kt) p.xf shock wave makes 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 wher;x s/l-4glejre the speed of sound isx4;s /l-re gjl only about 35 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 striiqo )) 3e zpm,jlguopq.ig23 .kes the ocean. Determine the shock wave angle2qi.qjzpo)gp,.g3 uome3)l i 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 /a hdltu i.3ld2q;x6q $/theta$ 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 abov kbtq;;nz)y o1 drikrxjm 5kn8l ;,;w;e 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 Fi;)nmzr;rj8x5ydnwt ki;q; l,1; kkb og. 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 down nbp ,0mx1;duay.cbii ah.x05ward from the bottom of the boacn,b dh .up1i;0ay.5ix amxb0t, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the 0f1(p nayu iw jt.y/8hhuman audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sympho. 1wqab,;t ss) ehmpu5mi-6lany. It consists of many pla)amt.1;qi a-6sup, wehsl5bmstic pipes 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 makezu.rln 80*ezd 1kcv m-s a sound close to the threshold of human hearing (0 dB). What will be the sound levekzn*u1 e-zcm.8v0 l drl of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound .kg62be z f-*gl0 excz3ucas3are heard simultaneoug0cg us* 3-k2l.c zafzxbe6 3esly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 of9swlw3uw ng qurk5*zb79-b2z+r/n dB. What is the acoustic power output (W) of the 9 w9grln*w2ob75u+ z/-uswqzn b rf3kspeaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output (z8pps131 )br ycz+ kxu7nd ekat 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power outkcknxr 1zy7bp 3( e+u18 dz)psput in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectipwas ,q 9cah77ve devices over their ears. Assume that the sound level of a 7pa7wc ,a9hq sjet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications6 yz+h2c 0fozq systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a :pse8)m uzjj2 1;belns)iufmr15. y s 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 points with a fundaw;gapg:k v 6k;mental frequency of 440 Hz and a mass per unig6vkg ;:ka p;wt 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 fqb*;2kl olz-u +p.iywi6b0gswdw6 p3 illed 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 heard to resonate with the tuning fork when the distance from the tib63sk6;-p 2l *l yz.+0bduwwpwq g ioube 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 near a tube that i9:oa54 yzym pps open at one end and also 75 cm long. How much tension should be in the string if it aypy59mpo 4 z: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 l58,ln rl;aphfull 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 rk-.4n 1saoh4 q*:qqoroa,hg lange coming from two sources. The sound is loudest at points equidistant from the two souonaho* qh4graq,4-:os kq1l .rces. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. Theu+ )cyf(0amfd:n;ds n conductor on the stationary trains:0 d;nm+n f(dafcy u) hears a 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 traiwsdpr0 xb; 1xs.rruy(.,ue .rn whistle as it approaches you is 538 Hz. After it passes you, its frequency is meas,;y.rur(xr.dxu b0rs p 1swe.ured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speel4j w uq+b0)/g :pghjud 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 (frequency halved) as it goes by on the straightaway. How fast u)g/: 4puhj+j0wgl bqis it going?    m/s

  Two open organ pipes, sounding together, prodvkv// va7h uj4uce a beat frequency of 11 Hz. The shorter onev uk //hv4jav7 is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a v5q*l3d7 ,)ct,ka5q zf dbx mcstationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after t5addb,7klvt,qcm3 qcf* z5x ) hey have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s whatyh2cm.18 zgkr beat frequency would you expect if 5.50-MHz ultrasound waves were directed along tkc1zmr .g 8y2hhe 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 the mo2 d- lzb.rjl,ith 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 rj2,di.- lz blwave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a z : xv /k2hv2pe1homl;moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echozmokh: /xv l;22h1epv from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine villyhu8 ; * .v phxwxo0,/wh3g 9fkg;foalage 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 mu; uf0yhw.xggo *,w3hlo;9kp vhf/a 8xst 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 can be compromised by the presence of stanh9ts)fbk yz*aq 664ha zjsa(/ding waves, which can cause acoustic “dead spo saab *k (fhzhaq46/z96y t)jsts” 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 demonstration, called “singing rods,” involves3n(i hxb r7vqp3:.:gdecxgh ojyv2 0opd /*x0 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 axn*3.j 0 odv2d pg c hvi0xgo(x3:ph/re: ybq7 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 thre+cqzz/* sa f/ishold of hearing for the human ear at a frequency of absq zcai //*+zfout 1000 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 observer on the groundf rqt0xc5xmq(jd 5( /i hears the sonic boom 1.5 min after the planiqjmf q5r/dc(tx x5 (0e passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboovb5 i)+q)to sc5qsm: at 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