What is the evidence that soun ;5w3mn3ntlox(livyi kp 22j /d travels as a wave?

What is the evidence that sound is apw utp+: xyuhb l0cnufd.) )3- form of energy?

Children sometimes play8 mh3upxwt 5*x with a homemade “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 u83 mtw *xxp5hheard 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 exp7jko(z 8g)a;z4 gl0gajf6myw ect the frequency or wavelenl; g7kzgyg 0j48 ow( za)6amjfgth to change?

What evidence can you give that the sp;p kg u*v.de3oeed of sound in air does not depend significantgp3ku*od ;.vely on frequency?

The voice of a person who has inhaled helium sounds very higkjajy7d2 k( ,ah-pitched. Why?

How will the air temperatat38adg-7./vb bwin:jdq 4 n bure in a room affect the pitch of organ pipes?

Explain how a tube might be usedm0d8 w p eil,)u-vig6przoz6 6 as a filter to reduce the amplitude of sounds i6zvw ,d-)ipr li866mep0z goun various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) 706 c8 a:a )yck8ri(z6ljfq srk uukq(spaced closer together as you move up the fingerboau ia6kkrfcqsa8q0lykjr8 c )(uz7(6 :rd toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear iflxf( dr-6a4 xt but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on di l 4fdf6ra(-xxffraction.]

Standing waves can be said to be due to “interference in space,” whereas *+oenk . bxcpn +w-v : sr;-ljvj8hxtk,bo/(ebeats can be said to -+:bosx./w ,be; -otk phn(vjj+krl x *ecvn 8be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poi6n20dc /bt lj2lge 2tfiq8fr 6nts D and C (where destructive and const 6fb22e dr0jql/6c8n ltgtif2ructive interference occur) move farther apart or closer together?

Traditional methods of protectilmc+8flv2 vb 3+*b)ipbxbm,i ng the hearing of people who work in areas with very high noise levels have consi +c8fli b2)bm ip+xlbmv b3*v,sted 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 the ears?

Consider the two waves shown i*xf2k7 f qpn-qn Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies f qp72*f kqn-fxarther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source am()6efai:c pn / ;zfemnd observer move in the same direction, with the sammc ni)z eapfmf(e6/;:e velocity? Explain.

If a wind is blowing, will this alter the frequency nd(j4bkvd r5b3ak( t +of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity changednt(+rv4 d5k3kaj bb( d?

Figure 12–32 shows varioum. fztydkj b.1-u: fb.s positions of a child in motion on a swing. A monitor is blowing a whistle if.ukyb1: dmjf-.. z tbn front of the child 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 e 6bwkosioxcnm.-a/5 )cho of 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 theasnow-i /5b) mko.c x6 lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship juskgig- azggxq 7xn+735 t below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2 +3axggnzg 75-kqgix7.5 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 wavelengd7nrlo 5v6o*95e jfdfths 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 tunc;g g m:u9laq.a on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (F;a gc.:ql9gmu ig. 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 fnrnj v gouam9u9:6z1q;i5y4am /me 5 when striking tham ;u5i ajne1qz:6mr9go m fu/5y94nve water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike t-y a+ 4bliyc/jy3z0nohe concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the0zjoay/n yyb c4- li3+ 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 mlwea .a,hn-t7jo8 anwoy09x34fra jgez 441kade over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if theorx3nnel4 0aeh w84z .f ya-w,g7 k4jt9oja1a temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the paitp ngh1sm6:7 vdtt7+ nn 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 leverkj8nffa ,;k mrow9r 11v(c:xl of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound le 7;r zx o7 :ll7r5fmgtxf)vev1vel of 95 dB when fired simultaneously at az xvr7lxte5rog7fm:v17; f )l certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a cerot/ 2lub+ ;d frrk/bx ,hh/0ertain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all ;bh lt /h/ 2bk+r,/0drruxofebut one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a si*omqis1zjvii2y a19x 5u5 t, wgnal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal anztxi92s*1qijamoy1 v,w 5i5u d the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of er.z *g-zug;fengkxn5( ,9 svsound from a person speaking in normal conversation. Use Table 12–2. nz5eg;r ug*v,sz9n -. gfex(kAssume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum wodjn0hnxa+jq +d/2(l hose 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, whipov46 5+ yti60zac dbl/lah 1wle the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeakeralvz i15/oc yh46bd0la6 +pwt 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) mgiyg5x4;d occv2 +f a loudspeaker on the stav;fo)ggcm +45 y2x icdge.
(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 typi: f9lxpq(l;jp(z.v zos itp ;;cally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of pv zx;jo.i:;p;(ftlzl 9(qp stwo sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intensi,7j)ls / ub qz.u6ervdty increase? Increase by a factor ov jzbl6ure.)qs7d/ u, f    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the 0lncjp*u -:bw s (j/hhfrequency of the other. What is the ratio ob 0h(:hwjljcpu* s- n/f their intensities?   

  What would be the soundlz6n aue5bd9 + oniv/7 level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm bzu5/i elvndn7+69 aoat 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hzs6 ,3ah x ztd**zy:*,phv gv7zmyteq 4 tone that has a 50-dB sound level? qdhapvt4zy 6*g ,v7xmy*z3s :,h*ezt (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the st 5c3ftl q6v kbee- a6(o)lh)pound level is 3 (et56k ) qoafe3 phcb)vt6l-l0 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge rang lo/hqm3n.:*yukpqm ;tr ni z9p ):0yke of sound levels. What is the ratio of highest to lowest inten3)m p0n ;ypz9nroql q.k:y:*iukmh t/sity 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 *)1geekfmfe- length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Uef-me *) gf1kender what tension must the string be placed?    N

  An organ pipe is 112 cm lou9q:wo.gz/ s8d8yt b gng. What are the fundamental and first three audible overtones if the zq :og 88.bg/usw 9ydtpipe 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 of an *(, n tfop1t s4lwnn2vempty soda bottle that is 18 cm deep, if you assumed it wasf2s, 4 ownntp1*(nlvt a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of humnvb20lvibmn0i6xr vik6ad 9v sv5v2 ) l0c88van hearing (20 Hz to 20 kHz), what wblivrv8ik6s0 v nv 0bi2x8d )6n5vva0m29l vc ould 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 th 7genlrw .+tj m *.421c1 ax8udfybv36thmuvlird harmonic. What will . .vutecmfmj21h3bn7vta*8 ldl6u1w 4 x+yrgbe its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is t1m2vhi+k 0;fac4f5mjv v9wyguned to play E above middle C (3305;iw2m+4jk ahvvg 0y mvf91fc Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of ehydm+b :gb:/ zml) u*ows o4n,2/avban open organ pipe that emits middle C (262 Hz) when /u yw o)*mzo/lbb2b amdv4sg,+ e:hn:the 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 209h+4hk bi)pf: zbc3eqy4 r 7sc $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 shoulu4 p yar+1)7ta-gtnjx do. qnog ,v9n.d the hole be that must be un1q u gpxd)n4vjgt oo.-. ra79+ ,tnayncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at y wreql0zcw ypc6*b*4ol,g:: any other frequencies in between. (a) Show why this is an openq l*g*lwzcw4c6r ,pe:y b:oy 0 or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at two c9rg8- 9wvcpwl q0 4rksuccessive harmonics of frequencies 2rr-v q kg99wp 04c8lwc75 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 enhsxnj 0b3sb2 16i 2n$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-lon,fa22 fdbkp7c g organ pipe a7,d2k c fbapf2t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal i8ssueo j l l-o20/(2o7 rt qgoq+n:euugd7ga5 s approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. os7aq0e5 +ngd qlg8 tju u 7e ol-srgu22o/o:(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 2.00z+pbu,2o ult9xn); bg 2ls0u 1mecgc s when trying to adjust two strings, one of which cxn p+s;be 2ol)9g100c gmut,u2zbl uis sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if-uuebj nlw0g y3uonv; z 93-tfk(9c;p 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, while another (branhs)t9j,r yz+, cyah a+d X) operates at an unknown frequency. If neither whistle can be heard by humans when played seaaszhcyj r+t,+h9,y )parately, 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 forkp dc9+jwew7;x.uwmnk s/py/ 0w6fo*t and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibratiotk *suwow 7c.fwxdm; y6w90/j p+/pennal frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 29 ,o5jcdtov42w 4 Hz. The tension in one string is then decreased by 2, twv4oc5jdo2.0%. 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 to d s*b099xxd j /*lnfjfex,od2play middle C (262 Hz), but one is at 5.0°db0s 9xeld2f nx/xo9,j d* f*jC and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequc zslaqm . 7dzq5i9.+::g nwgkency 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 and C? What beat frequencies are possible when A and C are soua9wlg:kc zz.dmi5q n :s7+qg.nded 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 3.0*he-w9s;i 0h4nk3r4d nin gjd0 m from one speaker and 3.50 m from the other. 0h nndwijd kh4-e irs;n g39*4
(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 on5v6xh taccpie((/ ; un0f9dtuner hears three beats every 2.0 s when they are played together. (a) If one is vd(i 0vtex a;9/c6(ncufop 5h nibrating 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 soundn3wv qk7 3+yvy kq*2mx of wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume Txk7vyw n mq3+ q2kvy3* = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequenc)pnd3* fka5lyfk v*(py of a certain fire engine’s siren is 1550 Hz when at rest. What frequencykyl5 ff*d *vpna k)(3p 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.i ipvmst d e:rul0h ,hv* d5.dao()a;4 What frequency do you detect if a fire engine whose siren emits;5u .mv pa( :le)ihord d4havdi*0 t,s at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sour:yh. :t3kqql/sor fe8n;e/xkce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are t ytks// nq8or3flkeh.::e;qx hey close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one is h(2-yn qw0 15jx gq4sp2or pn)st+a3zit8yimat rest and the other is moving toward the first at 15 m/s the dri40tyn ypst p8 o-gm i3iaqrqznw5j 1h2)x+s2( ver 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 ult(hwp *oe 6/txerasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 *ph/et6xo(ew m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s Aep1c d 2v6ofls3( 0nyos it flies, the bat emits an ultrasonic enf3l o0pd1y2cov6 (ssound wave with frequency 30.0 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 movc9g-t ug/* pyb.1julying 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. Whatugty1l/j9 pb gu-cy*. beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultr5+-za.t b3 fi xtyj-biasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound tt-zb. ia5-+3 bfjy ixin 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 uzgc*8e4p1 rgdsing ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity is 12 ) enlg3,.c ,r0y2jirb kqrl4nm/s from the north, what frequency will observers hear who are located, at resj.)2rbr3iy04 , grenlcln, qkt,
(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 it xjlr/nkdq32. 4 +daony+ 5fkis 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 speed of sound is 310 m/s (a) What i2vy yrd 5rg: *0 (utf9rxhm4vps the angle the shock40rx uyf 5vphrm(gr* 9t ydv:2 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 where the speed of sound lo:/x4h3zhdxqe1 2bmis only abbx h3xoe z/4q:m12d hlout 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 strikes the ocean. Det h0l51;t))rv pevnc f(pgk3sjermine the shock wave angle ()fp0kv 1;c3hv)g 5enptj srlit 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 qz 4q)heft-, q$/theta$ 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 exacd 0 m(xyeu.j-qc4naod+32che tly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizon- m j0xcq 3oe.nadce(d y2h4+utal 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 dev xvdtk8b)x-i3 ice that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth foikd xbvt-x8 )3r 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 na:jnbd 0i8 , 9lz)hr) izp(cthuman audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display cah+ ;xr. h4k*t7mr2si o*jorxllled a sewer pipe symphony. It consists of many plastic pipes of various lengok7siro; rx4.hxthm2* *r+j lths, 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 pe 4xh:nqlw0bi3 rson makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoes:q inwl4h03bx ?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dvjv bc76 jnj r2(2o/ 8cob;wlkgj)f 4lB sound are heard simultaneousl k7wfvrj cl4)26ln2jo c;8vbb(j/ gj oy?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 1 aq2( i6+hr5ug3d vvcm,s.fm o05 dB. What is the acoustic power output (W) of the speaker, assuming it radim.c 2vogv ,+sq5ruh6( afdim3ates equally in all directions?    W

  A stereo amplifier is rated at 150 W outpci 0p.f8bg( /uj3yxfx joz25 rut at 1000 Hz. The power output drops by 10 dB at 15 kHzf ( poyuc3b5j2xj.gr zfx/0i8. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears. Aiha22f)zo w xg6 8y9ut21oxamssume that the sound level of x6ft2gow o)ym2hiu98 xz2aa 1a 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 unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, thq ks2jaf5 *7imbk0. bde 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 freqq3qr-18 polir uency 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 anel9tcy)zud7 f7x: r: fundamental frequency y 7 zfe9xlnt:rc7u d):of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled wwx6) rg 4zucii0hr sm9ap,( x;ith 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 w69;, rri zsx4g (imc)wxpuha0hen the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is .y,xdh9uyc 9w 6 sy7vdd(w*jy open at one end and also 75 cm long. How much tension shouldy y(9x7.yhwduydjd6s 9 *cv, w be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fl6e ,w6a:k himull loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sources. Theh3mvm5 v q4an0 sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is 03h45 avmn vqmthe frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. Oned) .65htzh**tavkgt n train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train5 khdvh ).6*ttt *gazn approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After 23y-;kr0cvus3 fk gkwit passes you, its frequency is measured as 486 Hz. How fast was the tra krfv y3 c;gk3us-02kwin moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listeneaj u 3t::+.1yfxo tnning 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) any3jnef: u. 1+:txto as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding toge5l)n cqpavm08/:a q mfther, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the othep :cfvma nm)aqlq0/58r?    m

Two loudspeakers are at oo8j )/9pc mws) fqt5ohpposite ends of a railroad 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 acwmo8sf5)o9p/)h j t qfter they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/snj*r6co4;a7e ( yy8tl0yjrmlb27i di what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow ani mteiy 2 8;y0jrd6b lj7(rcno4*ay l7d 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 moth is flyigzgvhk1. om5 uc7z,,xz .3 lucng toward the bat at speed 5 ml3gx5kg cmz7h, zzvuoc,. u.1/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaic(5c4-di 9 kqq;ahpkches a moth. The pulses are approximately 70.0 ms apart, and each isa-kq pqcdiih;4 9(5k c 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 owy5 -am8*fwxnnce used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) ho*8 wf5xn- awmyrn. 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 t db( utp6 9fv3l+mys7ahe presence of standing waves, which can cause acoustic f6m l3yv+9tas7 (bupd“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 demonstration, calleddbw)j52fk96qu k 7w(ei x1pkd “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. Witp7w2kb f jke1 w k95u)iqd6(xdh 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 hearing for the human ear at a frequency of abofx8 g-o 5.xgfdj /5pgou.g5o j8o g/gxpxf-df5 t 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 g f5i:uvj g,u-observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitud-,5uvf giuj:ge?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 uhyrks 9,o;y5o; gzb 8$^{\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