What is the evidence that souj0y ,)yhzi vunxh 698,:k6zqf ab x s8jj+s8khnd travels as a wave?

What is the evidence that sound is a form of enwc+fx )fa/ 6rvergy?

Children sometimes play with a ho,lss)i . b:hewmemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child se,wss b.i lh):peaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequen/mgn *-ztu / .jrcae+mcy or wavelength tm c tau/- n/.e+*mgrjzo change?

What evidence can you give that the speed of sound in air does 25mtx nbev ;3unot depend significantly on f m2nu3x vet5;brequency?

The voice of a person who has inhalu; s mc(.2k)lq1x- ot4krzhized helium sounds very high-pitched. Why?

How will the air temperature in b9l v rx5dzd.pc)9qg)a room affect the pitch of organ pipes?

Explain how a tube might be used as a +v/uxd i euk* z*i xr4(71rdxlfilter to reduce the amplitude of sounds in various x4+vxxdii/ *e(u1*7 lrrkzudfrequency ranges. (An example is a car muffler.)

Why are the frets onqk:a7g91lor97 b v)-wi z oika a guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridge?17ak vk9)9rzib-glq:ooa7 w i

A noisy truck approache .qis :-c+7ctt x,7osmvtvt .vs you from behind a building. Initially you hear it but cannot see it. When it emerges and you do s+ isqm cx, vtv.ts.vt t77o-:cee 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 due to “i4u.kdn rpxvjow j)7 -3nterference in space,” whereas beats can be said to be due to “interference in time.” E7-x)v3 kd wjonru.p4 jxplain.

In Fig. 12–16, if the frequency of the speakers were lowewde4 w ss /cahix,t/;6red, would the points D and C (where destructive and constructive interference occur) move farther apart or closer tog/6s,icx a4;dhwes t/ wether?

Traditional methods of protecting the heac-6ma8 u dghx-ring 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 thcmd uhx6ag-- 8e 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 k 4ucz )vg*xhbp/. 3k 5x8qthethought of as a superposition 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 farthe3e bzt v .5)/uh84xhgc xkpq*kr apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sourc ,y9xvhg0)ook0:j8 qdc+ ,3so qdbxsryl1m1ye and observer move in the same direction, witsb3 ,s d,oohj8mrx:c ql9q y)dyv1o0x01 gk y+h the same velocity? Explain.

If a wind is blowing, will this alter the frequency of tlg,p(5 juk+qt he sound heard by a person at rest with respect to the source? Is the wavelength or velocitjuqk,tp l +(g5y changed?

Figure 12–32 shows various positions of a child in motion on a swing. A)jj(vbr* xyhmu zk:)k-sl, . s monitor is blowing a whistle in front of the chilx (rk .huz):v sm,yj-jkb s*l)d 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 echo ope7ji+yd0 n +b52qh q.zllq9gli :m e(f her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of tl++blgij. i72qp(5 qedemy nq09hzl : he lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his shi jw)l:h5b 9odtl *gv4uzd2y5ep just below the waterline. He hears the echo of the sound reflected from the ocean floor directlyj9z)w*dvogul :2 e 5d4lbyt5h 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 wavelenglt n o,ong0zqt7(9zhg- *lv-hks(4jaths 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,(+u*l:di (kmwsye 2 min 1lyu 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 the fius 2l1:(ku*y l, myw emind+(ish,    s (b) by the fishermen?    s

  A stone is dropped from the to:kxg1/z sj 9igp of a cliff. The splash it makes when striking the wat/:xgs1ik jgz 9er below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear x*k.c*a b nk5pto 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? See Table 12–k.xkacp*n* b51.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance:ku,4 qr2vpkna7k/ le by the “5-second rule” for estimating the distance from a lig,ek:pk7 kr4a2vn/ul qhtning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain l,fcth .u pgsyd6 f)-gfv) 3fi/: lzm9tevel 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 so4g+qj d0;e guqund whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired sim -rhcf.gr gd;s;j1 ag*ultaneously at a certain place, what will be the sound level if only on-rs agdrfch;; g.*j1ge is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally no9kk sqd e(lk-l8 en,b-isy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one enklb k,l9(e -8d sqk-engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-ts6+x(/ ydqmau o-noise ratio of 58 dB, whereas for a CD player it is 95 dB. Wuad x6sy+q(m/hat is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a perlh7/qxd4d2j;cym4lj 0m)ovwgk ia- 6 son speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly ovm;x4i kaq26 wy 7d-/lmj4vohgl c 0dj)er 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 eardrum whos9f-t vlwa4sc(e 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 mhovfn0v::+,uw-: p )mvm w nqlore modest amplifier B is rated at 40 W. (a) Estima whf) uwlvnp+ov-::qv0:, nmmte the sound level 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 -iqivyh7;5.+ ynq;:sns jzjpin front of a loudspeaker on the st y+qj:s;zh siqy5;-ipn7jn.v age.
(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 typic*1y3xk8w mz+r mtglby1k zez70txj0+ ally detect a difference in sound level of 2.0 dB. What is the raz3y18+zlz*x +j0 gyem7wkkt r 1xbt0m tio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is trid6( +edd89gqlynd.zxpled, (a) by what factor will the intensity increasg.eyd8(qzdl+n d d96x e? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacembi fs-l:0goql a1k:*t ent amplitudes, but one has twice the frequency of the other. Whato*g1f-ksqia:ll b0: t is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds to(gt uryw)q4p90 r, +rcr5j ktk a displacr(t+q,u 9rg w kp)jy r5t4ck0rement amplitude of vibrating 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 q 0s.)kgshtc1cf dm+wc /6qh8tone that has a 50-dB sound level? (See h6c0m q ) s +h81tfqscdgkwc/.Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can det:3mk. iqcwax5ect when the sound level is 30 dB? (Seq :.kx imwac53e Fig. 12–6.)

  Your auditory system can accommodate a huge range of soq8 tncmd6rat:t,gx *p2fi(j .j9 /kizund levels. What is the ratio of highest to lowest inte nrt8ajj 2x.pt/z tfcgi6d:q9m(*k,i nsity 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 fundael-qn3s b z8 y w4dzqi.,8khj+mental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0. d4w biesl ,k3zq+z h8q-ny8j.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm laz 9* 1fxx7qhbyl.t5 thw,)yuxu8h j3ong. What are the fundamental and first three audible overtonesh 7x qazhjuwu5x1*x yybh tl)9,.t38 f if the 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 t6:a(yvdv9te 3hf 2 qkyou expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a cl(hev9fqt k v3t a:26ydosed 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 spact2)l0 db ggt;nning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes re;0 tcl2tbdgg )quired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its thirdc h .0+sr)laxn harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original length?rhn)s+a c.0 lx   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E ank f,e;b6t a5tz 3krqh+6t+f pbove middle C (330 Hz), ++ ktbpf nt63hrk;teaq6zf5.
(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 :7l1yw)v o;-cv1nwqo :e yhe aorgan pipe that emits middle C (262 Hz) when the temperatuhnoaw7) ec:;ql1y 1wvvoy:-ere 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 206ejp)t)(o0y. hry0i ari x4oz $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouth2no og0y7 ,algpiece of the flute in Example 12–10 should the hole be that must be uncoveredy g2oan07,ol g 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 pipa1qiy ,2sa:gy ahyvsi;e7)5r e can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Showhgas5v a1 2q7 yy;as y,rie:i) 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 resonat5vfteih rfpx*,99 d8ues at two successive h8 h ft5rpfv, 9id*x9uearmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 trxe ) l7y p/w7.zov7z$^{\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 ra+, vre7 -l,bts7u 1ffud)yafcnge for a 2.14-m-long organ pipe at 20) f1 dftucar+f u7l7y,, sve-b $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2tom( 3nty.e 0a.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible 0ytm3t.aoen( range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to a gzoyu;e.ia1 ccbr,. .djust two strings, one of which is sounding 440 Hz. How far off in frequency ioey1g c..au ,bcz.;ris the other string? ±    Hz

  What is the beat frequency if middlg +czk7 1+ vyqxfc11tbhq34pge 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 )21poun+ zl,he:qu i , y:z ,kymoals:23.5 kHz, while another (brand X) operates at an unknown 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 simultq u:zs maiylue,p,y+z)1olh : ,n:k2oaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces ks5;s z:ax6d8;; d9ijnjm hsp4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency xp59:zsmjajk8dd;;n;h 6 si sof the string? Explain your reasoning.    Hz

  Two violin strings are tuned to 0 (x)q 5t9hgrb4qpe.az hqp1mthe same frequency, 294 Hz. The tension in one strinq) q0(g.qphtr ebx5z1 ma94hpg is 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 ea53uuptpz fo)ko9q7 za2bl li3 7xe:3ich try to play middle C (262 Hz), but one is at 5.0°C and theza e3kbql7t)o7ip: x3lfo2puz 53iu 9 other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequehdj+u,b8v7kg l . alpn 6.hf3zncy 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 frequencies of A a.,7 j 8k.u6ahbzhgdlp3v +flnnd 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 zfw::h06 f h:h+di knhperson stands 3.00 m from one speaker and 3.50 m hi0khwdfz::h6+n hf :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 -:aav+v 2i+qqck , stibq)y6vat 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 : i,6kqbsqa-vic+qyvt )2v+ aHz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and: ifjd ph5j)a3 2.76 m in air. How many beats per seajp5hdf) ji 3:cond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequ,5 hsae8pz3hyiru ktuo l4s u:l 55*w2ency of a certain fire engine’s siren is 1550 Hz when at rest4 l2s 5touuehp, u3hw*8 a5syk:rz5li . What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you de3b/lixdww 8 rk qy qq:,-3b*cgavtv( ,1kc7w utect if a fire engine whose siren emits at 1550 Hz moves at a speed of 3 kut,v lw/vbw1q*wr-3ycqq 8,gba 3i7:dk cx(2 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hzgtqa:pu4tj* q50 /m jq source is moving toward you at 15 m/s versus you moving to/tm q*40j: qp ajqtg5uward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same singl(y0 (* qtvu v7mziiyh4e frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 2t( (mhz v4vyu*yqii07 0 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound 4 2-rxr;czs4s kr) j e8vzjw 7.ylxli2waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the r44j7xr 2lr2yc. rk 8s v)z;xiwlejs- zeceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall 4qc:;buaj zg:-dby ;u at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat heb4-;uyz jqga;d: uc b:ar in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played e1fm1 7 0 vyssrbict:886mhrn 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 10s810mnif:7vh 8 yrc6 bts1rme m/s ?   Hz

  A Doppler flow meter uses ultrasoui 72fmx 0ao:km;;ipnq nd waves to measure blood-flow speeds. Suppose the device emits sound at 3 f0ak2xp:;7oimim ; nq.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 directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frevn2 k)x i412nlgmht;17u f jvwquency $2.25 \times10^{ 6}$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 veumnmbf2a3dua5waf* * w.9-p( rs /voflocity is 12 m/s from the north, what frequency will observers hear who arb9m (wudru2am3*. fnw fpso5a -vfa/* e 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 movq: wy8i: xu+r5 +fo7g4nu oozxing on land if 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 2.3 where the hkqp-y-;46cvt 8yv vdspeed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airp8yy -dk4tp v6hcvq;v- lane’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()slhjknkn/x cgboi77 * qu6n-; y c:t sound is only about 35 m/s cinn7kouxgt cb: knyl)-j;qh/* s6(7
(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. Deterrt /xlawx9lk -sl jd l9,5d4-jmine the shock wave angle9-l jkr-d4lw 95la /jxltsd, x 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 dc lus3 9+p*gi$/theta$ 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 groun9p5 mwjeh5m a;y7 ca7ld flying fasta9wm hl5;7cmepj y57aer 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 ai0, 2 zdprbcd- sonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum deptrbczid- 0 2dp,h 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 areju+t h(.lnme7 there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display calleovz4 q lhd47gd*1 5 6kfha+w pa;6kdjmd a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on botha7 *od+dq5k p 6 1 4lkv6hmajf4zdgh;w 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 mad- / hzu)ehay)kes a sound close to the threshold of humu)h a)yehdz/-an hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when ahyz-qq97 ga-+sjm g,yn 82-dB sound and an 87-dB sound are heard simulgsm9-yqjzg q ,7-h +yataneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the oso6yg(7yq zh4 pen, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it s6 z qyy4hg7(oradiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drvk l(jz7d 21jtops by 10 dB at 15 kHz. What is the power output in watts at 15 j ktzl2d(7 1jvkHz?    dB

  Workers around jet aircraft t1fgb ha0 x*:qxypically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unproa hgxb0fx*q: 1tected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sys7y rh9t)n+xnv8 y yqg-tems, 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 frequency 1x/tz+m3qyhp kugg/ s s7 7/t+y$\frac{1}{2}$ 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 betweauwot5a9y;xpu o (u(nv h 1c67en fixed points with a fundamental frequency of 440 Hz and a mass per unit length o6 ;xhvwpu(yo on95ua(7 c1autf $6.1 \times10^{-4 }$ 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 k:hyn7)v n bp1a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is 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?ykn 1nbpv7:)h   Hz

  A 75-cm-long guitar string of mass 2.102imh 0, z1tn rlcx*/pc g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with ccmlrh,t1 *0 pi n2/xzthe third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to15q.ixmq rj )d b:-lcl 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 5umo c*)z1kwla6hy6x - 00–1000-Hz range coming from two sources. The sound is loudest at points equidistx6y*6w)a mhoz-1 kl cuant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary bp)sdq,8ytt ,. The conductor on the stationary t,)tp8qysdb, train 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 train whistle as it approaches you f 5.lk i 6vq(( y:i8 )vjsystzrp+3zn6mw :fbris 538 Hz. After it passes you, its frequency is melfvybp (+.::t v mz 656i sfy) r8snijw(3rqzkasured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estima ewf bd/ gc:/e,b;,nzs1sdpy srxlp 7;1a0g .hte 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 (frequency halved) as it goes by on the straightaway. How fast is it goingsb splhx s.7/dr1ng, ; e1g w/edp0 yba:cf;z,?    m/s

  Two open organ pipes, sounding together, produce a beat frequep.(, sb,ehps * zmob;xncy of 11 Hz. The shorter one is 2.40 m long. How long i;bsp .ps,m *xz,(ebh os the other?    m

Two loudspeakers are at opposite ends of a railroad1kh) qoxlhe;/ car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency 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 hi/q);x hhel o1km, at C?

  If the velocity of blood flow in the aorta is nok;ke0eh7y/ ptvwa z8,oi:*agrmally 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 cells? Assume that the waves travel with a speed o khaz,e ;ga08wio 7/:y*kveptf $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s whili5o ) y4wnrcqg+u12gje the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What r4u ny 12gi5 j+q)ocwgis the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency soundi;ednjk9 9c6 cyne 20v pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each ic0ykdn 2v96ieecn9j;s about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine v2a 3mp * hy3i6jke.lrzillage 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 je3zkl ipm.rh326a*y 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 compromise+bt5 eamb1ul.twz) *e0*ogvv d by the presence of standing waves, which can cause acoustic “dead spots” ablw*vg0tb z+a5v .*et ou)1emt 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, c spwfy9d *kk1s9/t q3zalled “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. Tz9 yp9sks 1d3 *tqwkf/he 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 3;l*t1 dx vcs/8giijxhearing for the human ear at a frequency of about 1000 lxtg3d*js1;vi c/ 8xi 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 ground .euhz1u 1+zeyv6/eb9*rsnpq hears the sonic boom 1.5 min after the plane pae 6q zub1zns/ry1 v.ueh*ep 9+sses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1cvxs2p;iiq/xl h90vi7w7(n u2 8 j sce5 $^{\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