What is the evidence that sound travels as a wave:zu:f hra;vvbp w k5q)(nwr:-?

What is the evidence that sound is a form of energc-a8o u9/qbj8nma 2tyy?

Children sometimes plazt 6sdf6zd/xjt- xiff 3j5,m/y 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 heardji /,m6 6ffd x/z-5stj tzx3df at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave pas3e 6oceta3d: sses from air into water, do you expect the frequency or wavelength to3 este6ac3d: o change?

What evidence can you give tc1 j lv r5thpeni46u9 rl*j:s/hat the speed of sound in air does not depend significantly on frel p 6eri:s9n*u/h v4t 1rc5jjlquency?

The voice of a persof;)2 gg01up c,krjm3gt g+d gnn who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect tjk(hqe9kx8qx- nd+5rs 4a- hmhe pitch of organ pipes?

Explain how a tube migh7u tp 62j9rwh l7vvz)jt be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muffler.)lv7jt)vru7 92pj z6 hw

Why are the frets on a guitar (Fig. 12–30) spaced closer toge.cer2+ okq.xa*6aomk o er:m )ther as you move up *m)a2o ec:k6.+mxa . rqorke othe fingerboard toward the bridge?

A noisy truck approaches youjee 6zafox59iy:n0m)n ;ku )b from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly e:z0;)iuno )6 fy9ne5bx kam j“brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be sa 4ffacuefb7dkajlayn1m*w 2 (s0 4+ /jid to be due to “interference in space,” whereas beats can be said to be due to “interfjf41ff2lsj4mn (+y d/ *0k buaacea7w erence in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would ted u 2t9(vk-68p w0 p:wzllge)lxk5b r5.n jaahe points D and C (where destructive and constructive interference occur) move farthernkp80 wja p( lzlxk:td ge26.lrw9 5eub )5av- apart or closer together?

Traditional methods of protecting the hes.y.knz a-l34*,7nqcv ousimaring of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead,o*z,.-u 7qcksms .y3v4nnail 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 wagh7xl. knd8o b.lxo5 1ve can be thought of as a superposition of two sound waves with slightly different frequencies, as in ho ndbk7l18lxo5 xg..Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler swt4tpyk05b b0hift if the source and observer move in the same direction, with the same velocit tk 04ptbwy50by? Explain.

If a wind is blowing, will this alter,.o)lsqk15uvb aw -)sa3y iir the frequency of the sound heard by a person at resriu s.b)5ya ),13owvakis - qlt with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swi7 egi uc;drfx5/gxe56 ng. 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 highest6rgueg ; 5cf7xidxe5/ frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines th,o,nda52doey) d rup8e length of a lake by listening for the echo 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 the lakd2)yop, 8erd, a5nodue. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterlim:t*zf7 bmxj: 2 :lqqrcj.0zd ne. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How dee*lbzxm.trjc :j : zmf2q:0qd7p 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 airoyt.tn y *s/yeu4 o/d4 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 tunaz f24dl fmr 5iom:vh7;j3g r5s on a foggy day. Without warning, an engine backfire occurs on another bmfzmg2;hrr4 l5s3 j dvi 7o:f5oat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it make um ) ase30+nhkcdlpw p,kb77px519me6 t2akes when striking the water below is heard 3.5 s later. How high is the clifp6eak27 d7u+ epa1mcnswlt0hb9 ) mp exk ,k35f?    m

  A person, with his ear to the ground, see*6kdzb i8t: ecs 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? 68tik z*cb :deSee Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-seconu,5+swovzngz2xv7 )u *jb g 0wd rule” for estimating the distance from a lightning strike if the zg+,gbs) uw 72uv zvnx* w5jo0temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pcwn*wvb 1 ,kr3*s3,c z;ok lyoain 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 levrkjej0/x)a(ewe7 9 hriu0z 8lel of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when f98w6jv t5 p8euroz i2 ;t9sb2c,rpum tired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: tou6zj8 tec, isu;b9trwvp 2 p825 9mrAdd intensities, not dB’s.]    dB

  A person standing a certain distance fne2tuen +xw /w) aiv33rom an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would thiu+t /eni23w3axw )n ves person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to havoip d53 d7rc w-5b:veje a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the baid7w re3c d-b:vo55 pjckground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a pei4e1gnjs nyyq4 11x w,rson speaking in normal conversation. Use Table 12–2. Assume th ygexnjq1,w1 nis4 y14e 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 sjad.wssm4v j) c:53h vtrikes 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 q) gh80b/wkes o 2( mkjkh)moaqj*o4+A is rated at 250 W, while 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 loudspeaker connected in turne+kjb ah oo8oqgm*(2qk)kj40ws )hm/ 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 a yrg* em+uq.c5 jw (nl5loudspeaker on the stage.*y( erqumw+nl5j. 5 gc
(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, ers6m wr4w-o difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Secti-rm4wsr 6,ow eon 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the ic)k:5q/xgpzm9l1l .w* acmim ntensity incmz.m*5 p)a 1cligx /:c9qmwkl rease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displaq v5ozrqhvd-2n o07v )cement amplitudes, but one has twice the frequency of the other. What is the ratio of their5q)- 0oozvv hvrndq2 7 intensities?   

  What would be the sound leve1hn wb-. )0v gltbowi;l (in dB) of a sound wave in air that corresponds to ao tv 1wg)b hb-;lw0.ni displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seeigm izpv 8fo506qd(/ b*k/kk nm as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.) z/*bk5nko 6fq ki0v(m/dgip8    dB

What are the lowest and highest frequencies that an ear can detect whenkq0; d zeh;e*t the sound level is 30 dB? (See Fig h;ze0 et*;qkd. 12–6.)

  Your auditory system can accommodate a huge rangoxz4gc)ap/l2 6gcl 23f llx97szuqr z zd*.:x e of sound levels. What is the ratio olcpfcldzos g7z r62a x x /gu *93zl)z:xlq42.f highest 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 hazrl wxb;zyw xv,l3vn/.9 zz./s a fundamental frequency of 440 Hz. The length of the vibratiwn.r .3lz zw/v9 bxvx;y/zl ,zng 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 fundapvqae:bh(wivj+.e; 6ky )tuf/t 0 i3gmental and first three audible overtones if the pipe iw3 6(e:ikbe;)vfty g0vi + /jhp.tua qs
(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 gm/rj49 gqyr(an empty soda bottle that is 18 cm deep, if you assumed it was a /(r9y4j rmggqclosed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a 9 w io7, ulox 8(uj9+yjj:mhev/wsaw4pipe organ with open-tube pipes spanning the range of human hearing (2 ,jx w9/iaow:ojuv+uwmy7s89leh4j( 0 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has 94 ro 5eyb/ db4+ni)09e. mcq5wy nvdodpsek3a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it qwonyen5 kdp4re o.d+c)db m/9ys5 e3 9 ib4v0is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long a. z7jdvbn.yj:nd is tuned to play E above middle C (330 Hz)n .v. ydb7jj:z.
(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 emits middle C e8 3hmpo of5hozz7r 1.(262 Hz) when the temperoh ofz31h o78rp5z e.mature 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 20 piw4ip 0wzop 40io/ 1h$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the doa8b9q-nh* l hole be thatbodh8ln* a-9 q must be uncovered 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, ak jkzf :+3z3vsnd 616 Hz, but not at any other frequencies in between. (a) Show why thiszk 3:sfvz3+kj 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 rp d6isno 7+9t2km*m gis open at both ends. It resonates at two succeo9prkm 67+ t2gnmds *issive harmonics 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 ja :jn8y/w9ut+hz:qkk ;ru4gb(,okq 1 gz e1 a$^{\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 mcqu4 +q1tvz0--aw 15rub bbxpresent within the audible range for a 2.14-m-long organ pipe atxutab4b+5 -c 1wqu v0mrz -b1q 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatelt ).n5pe2inxqz3 qs v1y 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. What is the relationship of your answer 12z53q qevs.nnx tpi)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 ts/kq1i /* hvpby tl3r/o adjust two strings, one of w*l 1v/ /tyqbrskpi 3h/hich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz)q7p-bne x us lucz+/1gm* pv;9 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 23hg *t *o1i(civ.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 simultaneously, estimate ogv1*c tihi*(the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning for 8z(k pzo:p7dz23dk .rsd 1qfkk and 9 beats/s when sounded with a 3z .k3d(zs 1:p2dqkdfp7 o8zkr55-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz87h5cc3j*a6sb)gbzdd) px et . The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played tocdd z837xh*pa tgcb5)b6 )jesgether? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if twj (n;prz*w4xzo identical flutes each try to play middle C (262 Hz),w(xjz;*4n z rp but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 4kmhf9;i nwn lydq *,d*i8,a w)41 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 possibl,ldw)* 9*d i8,k wq;hnyaifn me when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m f-- w0ddmraob(rom one speaker and 3.50 m from thad-w(d 0ob -mre 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 ar -1p -ife-ikkne supposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vk ei-pf 1k-ni-ibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 9sdt()0y+r wiz:vdz m2.64 m and 2.76 m in air. How many beats per second will be heard? ( )0t+(dvy:wd zzsmri9Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freque; .xpnwhvie33 ncy of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move witpwve.x 3;n ih3h a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still..wgvkmxw5cw1 +r + 1s ;emtwl4 What frequency do you detect if a fire engine whose siren emits at 1550 Hz4w.t 5m;1 v+kc+m e xlwrgws1w 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 200 ab6gji- x5r/l(wkn 0s0-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactl k-ba(r0w/s xn6 i5gljy 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 single frequeiidt1q,5a7c9b 3j cpx ncy 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, j53qcb x i1c97pdtia 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)i 4xra -nr nnj00mda6w4u ua) at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound dnj 4iu 0xaa6 uw)rn-)m0ar 4nfrequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies/mi 6) ebiyt8fm(9suy , the bat emits an ultrasonic sound wave with frequency 3 i869s(ye) mi/utmfyb0.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimen4ppk0 uk.hq5xlk 2;vl:k f5jus5jb5lts, a tuba was played on a moving flat train car at a frequency of 75.5pulvkkqjjlk 5u p:s5xkb;fh5 420l Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bl.6nh l nl+51 voebdz19iqn, jlood-flow speeds. Suppose the device emits sound at 3.55bh.jv1n ie ln l9,zd+nq 16lo 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 f /x;2j1uaa yqyrequency $2.25 \times10^{ 6}$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 souwdfqrbwmjp,.(56 z,r nd of frequency 570 Hz. When the wind velocity is 12 m/s from the north, fmj 5 ,qb wr.wd,(p6zrwhat frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if ijn+g7 gvwfv 0y8 s9fc,71st dnts 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) Wiopo ;eyn3 cvlv (y 5jnorj2dm0;4o)*hat is tv*m 4olcn;235dopro ye0 j (y v;o)nijhe angle the 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 whix iy426t*fhg(q beulc)i;( rere the speed of sound is only *ylr 2fg)46ihicb( (xitq ;ue 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 strikes thh)i nkxlfzb s9d6o,i 6u)c.l2e ocean. Determine the shock wave angle i))l islbd xnhifu6kzc.o2 , 96t 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 h54m :knxc:fn 88ir.d+jdry x$/theta$ 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 abobkp aimq1h2 ;e9tz d7 k,po*7mve 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*tb7qa m,mpeo21izdp;7hk9k km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulselc46i uzqi0vrup-53 yz;5 2wexigqh2 s downward from the bottom of thei6 0 q xpu ;2cu42qg5yi5ivr-w3z zelh boat, 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 j+x, q k *o1:9f uf09dqzufd)cnn;lyuare there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called 5oxj/:v9)i, l k qyojfa sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both endk: vx yof9j,j oi/)ql5s.
(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 mxn( b w1e.kc3mtx p5z2akes a sound close to the threshold of human hearing (0 dB). What will be the so3 ( m21nwxcz tpb5ek.xund level of 1000 such mosquitoes?    dB

  What is the resultant sound level when 0og,buuc z/3u an 82-dB sound and an 87-dB sound are heau,3u /0og bcuzrd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 10y7.fqy s) )qg .dk2r )b1uyfdb5 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all direction) )qy q2bfrug7s)fkb1.yddy .s?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. bn q5 .xhtty6:The power output drops by 10t xq5: t6byh.n dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically w4f: f93 -k3hdh(athp j)u7pv qzpi2pcear 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 bet3h:z79hpcppkq3)avfd4( uj f- i2ph the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communi wnu6p8p(o6 ti0t nhp; rrz)l7cations 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 bc8/y-isy /gtgvx1v0y lu /t0 is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long betwe*ecvg5 ar ut21en fixed points with a fundamental frequency of 440 Hz and a mass per r g 51ve2atcu*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 vertbm4-i)( w/w o1gvqjvfp 4v vp3ical 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 4b3jvf)pv / wi1vvpq m(owg4-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 is5t9(r9h+r ji 7c cylnc 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 fundamey cc+nl(r9t j59irc7hntal mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obmri,kx:hce gzs:oojc3 4 l(:- served to 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 pures e-y*rv lvfncx/1qb j i-m6)3qfx3t4 tone in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and fim y1-xeq/b3)*fsj3qntv ix rl64v f-cnds 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-oc4c 2(, yw r.aere*d5uejy l-Hz whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other traw 5d- y(ue*c,ycj.la oeer 42rin approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as evzi sg 0cgi-bh;3 j ip-vh72jj0 c8(zit approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fastez2 sc ji7hvcb z0i g-08j3pjh-i;( vg was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the d v.p) psjbe/7gifference 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 psp./evg) 7 bjis it going?    m/s

  Two open organ pipes nd;)sns41/ffujb;bmy;p4jc, sounding together, produce a beat frequency of 11 Hz. The shortmbfb 1ujcs;;s/y p4 4j)nfdn;er one is 2.40 m long. How long is the other?    m

Two loudspeakers are at m9 gfn5b o66wx u-(n)) jywkfuopposite 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 g6w)wbufno m)nf( uy x6-9k5jhears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.3gs fn ja+4ae-vdh0d+8 5dwup/2 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flvad5j0ngew ad 8++hpf s- 4d/uow 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 zw: ow(7 4y/mzlddvm1while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the fre 4m7odymw:(dz v/lz1wquency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequencyt8 g;wwcfd fu9(l4 +nt sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3. gffc+8 (9;tn4tduw lw0 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 Alpiihic)w5d4yism5iz+48 4ikj4nsv p g 0 ne 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 blownyh4i+ z84dn5iji )mskwgv 0ii4 s4p 5c 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 presencehd(ix;lhgax8cu:1j)ei-k w v c0.c .l of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamen1gxiej -vdulci0w):c l;8.ck( ax.hh tal frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “sing 1o0rbsd6kmwp5g 3)szing rods,” involves a long, slender aluminum rod held in th1sw3bg s6pzmr0od k)5e hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of 0 qnv6,utz kbl /v/gm2hearing for the human ear at a frequency of about 100lvvg 6//tkzu 0q2bn,m0 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 gr6y mw sb,kms r8a 19o0j)gv :daql:t7tound hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude?rgo9,la v) 6kwa:0bm7 y18smtd:qtj s    $ \times10^{4 }$ m

  The wake of a speedboat isjrh 6 0py)c j1x6gng2d 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