What is the evidence that so 2asjawjd+; 0fund travels as a wave?

What is the evidence that sound is a form oe4a11 +/;u o4 bod9mpffvcvsxf energy?

Children sometimes play with a homemadlbtc yv-(eq7 8e “telephone” by attaching a string to the bottoms of two paper cups. When thcv8 q-yl (7tbee string is stretched and a child speaks 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 frequency or3m+5toli a3 -u.txdg b wavele3 li- +o.da bm3gxut5tngth to change?

What evidence can you give t 1rtqfgeku. x 30pygchxc qk37v.g8,/hat the speed of sound in air does not depend significau.8x3qcykq7c v0gp3 , fe. r/1htg gxkntly on frequency?

The voice of a person who has inhaled mmibs7 pnid s*+z/x1*helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipe6zm(n xtiq*ie . )/wfhs?

Explain how a tube might be used as a filter to reduce the amp m4(j 8my7 e)vfh+8grbj1wisqlitude of sounds in various frequency ranges. (An example is a car mufflr7 h4b 1f8vj+jsmi)qg8y w (emer.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together a5qw(0jps vt ,4hdtn 5ns you move up the fingerboard toward n5t5wnqhd,4vj p0t s( the bridge?

A noisy truck approaches you from b23 ky0gtgq64r5 vnf+ nnp ;inuehind a building. Initially you hear it but cannot see f gryg6iqnp t43v un;nk0+52 nit. 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 diffraction.]

Standing waves can be said to be due to “interfer2 )irwmhy* /gj,6y5a jp5k gfcence in space,” whereas beats can be said to be due to “5gjp/g k6h afrj)wym,* 5cyi2interference in time.” Explain.

In Fig. 12–16, if the frequency of the speake0owp(v lg/f*r; lyup+ty / o 5,n1gpejrs were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer t// pwfyeo jyg +;(0prpg,lt15lnuvo *ogether?

Traditional methods of prv ;g )zdls+is+v/cok8otecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, o+vcgkz)ss8+d v l/i ;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 sho jj0 51ud6vh (g5smwpzwn in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, ash m60 v5sp 5(jzud1wjg in 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 shift if the source and observer move iburs9(1-21u,x n / +eofpeq5sro joxzn the same direction, with the same velocity?o 5 1 preob2e1rfo-u/sq+xxnj9 (usz, Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a pero *wxb otpx-n73ys02n cy 9mt+son at rest with respect to the source? Is the wavelength or velocitb2 wyptoxm*9y t+ oxc-0 73snny changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monito0j)3u dsn-bfbnfo3( br is blowing a whistle in 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 reasoninbju( n ff3 0n)d-3sbobg.

  A hiker determines the length of a lake by listening for the er64zmmd -.n2uqbw oa, 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 lengtb m uad r,on46qm2-z.wh of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just belowgspnf/6 5o0im ;/mwt p the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/0wifm;m 5to ps 6/png/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveln.*v 3jmobr vo 219ihxengths 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 d u x/a9ih6p:;hl3f1eij6e jdlrifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the back6i ;idje3j9au/p61h:hx e l lffire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. They6 d( un),isfk splash it makes when striking the water below is heard 3.5 s latyis()u 6ndk, fer. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone ,aynpegy sc,7e1hi rpdn nwv:6f/789 strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concreteywy7i ,8s6g:/ne1f hvar cp,ne9p 7nd, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of7x ojw: m,rr-kyk 2*uh distance by the “5-second rule” for estimating the distance from a lightn u2m: oyk-hwj xk7r,r*ing 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 rc6.eus2 b,x i) 3 ljtvft9tx7level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensimze*r: r+f9 iu1y*w bcty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired u 4x fzp)2g2 uvv6sf)vsimultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensitx)vf pv vs42)z2 u6fugies, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noihu(m8z-6q csqjjdg + 9sy jet engines is ex6jhm +(dj9q -c qs8ugzperiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio o17+yzq hf8r xzf 58 dB, whereas for a CD player it is 95 dB. f+zry hx71q8 zWhat 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 frtrbwub(+q6 z *om a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a6* z+brubq(t w 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 gy9u gdas20qcj)0a7hy -z f9seardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest sl2ffk9n/akb f.v 7 .b en(pt+amplifier B is rated at 40 W. (a) Estimaktfb pe /7.9asbnn k 2(l+f.vfte 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 regis,hunirrm y0/1tered 130 dB when placed 2.8 m in front of a loudspeaker on ,uy1r0r ihmn/the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound l:n0( vek2n2cai -pmlcevel of 2.0 dB. What is the ratio of t2l:ve (n- m2cnkc0pai he amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a soundc)9ez7n5d0qfmj.t7fi z yc 8w wave is tripled, (a) by what factor will the intensity increase? Iqnd7 yf.ctf c0z)w57m9 j8izencrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the freqm3 )j ;u9 7ed hobdn h6ud8 l;wtast2qqm68t:puency of the other. What is the ratio of their intens;qa:2t wj p38htut d6 76hq8ns;bmm lu9ode d)ities?   

  What would be the sound level (in dB) of a so /end*ac(jcrbr0j8v,und wave in air that corresponds to a displacement amplitude of vibrating air molecules or/ *ae8 b,drcjjn v(0cf 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound lgrn.6f)3sax8 kg 3xp lk .-gmaevel to seem as loud as a 100-Hz tone that hask ngf.x83xs)m klr -agap3g.6 a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest andqteyu rgy i55d)23pt , highest frequencies that an ear can detect when the soundt,uytr )epq3i2d 5yg5 level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What (cx c,aqnuo/ *,f p9pwis the ratio of highest to lowest intenw, fqou p(,c/c*xap9nsity 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 fufg xz2 n.70xjzndamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it hasfx0xz g. zjn72 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 fundamental and firs hh 9o x i9qs(pr*:cu(ujzno./t three audible ovr .hzp o*/hi9xu (u:nosc( 9qjertones 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 you expect from blowing across th1db*d t24dc wje top of an empty soda botdjt wdd42b1 c*tle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning2str7 / acgb 8ltxn 9r1f i*a+mh-aj7t the range of human hearing (20 Hz to 20 kHz), what would be the range of the leag hlrt2t/s1aa*rn 8 +9bji mxcf7t7-ngths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonubwq e:l3uxr- y8/l 8q- fad9hic. What will be its fundamentau89elu8l: qyr3h b-xa q w/-fdl 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 tuned to play E abovq;-3 0 jnxoffce middle C (330 Hz).c-;fnfq3jo0 x
(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 th5dkwlgc r/ z ,-lf6qi7at emits middle C (262 Hz) when the temperaturekz,5-flq7 rdwc6g/li 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 atmo zn6vao ,yj7tb63 e1 20 $^{\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 hole 67:tk.yu qurc/pacc( s xnm5 zv(l7;w be that mus .clx6ruy7av 5c uks wp nt/7(m;:(zcqt 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, and 67( y+--eiz oz0 vp ,jbztvngc+16 Hz, but not at any other frequencies in between. (a) She b0-j + tv7 yzo(cg,pi+z-vnzow why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at two tvtg2xz b8u1:5ixg; 6bl lx8lsuccessive harmonics of 6ub8;z51tb8 lt x:x gliv2lxgfrequencies 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 r2;;c hzqny ufiz+82l$^{\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 :c z+ck1 mjoi,within the audible range for a 2.14-m-long organ pipe at 2 1z,:+m kccoij0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outsu4v x17wg sm;zg/*fylide 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 relationshi/zfsg4lmw7u; x1yg*v p 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 tr okld()j 5bdk1ying to adjust two strings, one of whlj1o()bdkd k 5ich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz19i a(p9ujja0zm a6mxo u+7qb) 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 opn1;-h;yz y yjserates at 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 f;-nzy;jhy 1sy requency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beamw yuhzv c9;hcc6r,d n::0qh)4paot 2ts/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning forh)z:h946udt y hmo:a p20c vw;r ,ccqnk. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the syz,ug7 j fpu. b-a-6exame frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two str6ju gby,z.-x a-7 upefings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes eacjop +9:h ofs-.b seb;hh try to play middle C (26eh;s:b -joo+sb 9h.pf2 Hz), 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 gykq p/p(s: yb*2hm65n obf3tof 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 okb bm q23ph npysg5of :6/*y(tf A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1-k( xqry a0wj9l0zj8o.80 m apart. A person stands 3.00 m from one speaker and 3.50 m fromo0rj9w0qaxlj8 k-y z ( the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuneyd( abkz- a5r)r hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequencyy brd(- 5ak)za of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 mlbgx5b2-ttxq;g7 / evz 8p) ix in air. How many beats per second wil-)bgx 5t7 g ep b8zvxitqx;/l2l be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequencyxc*kz-8) xj fb of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with f8*-zxcb) jkx a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fiz 4:ru-/dqrn vre engine whose siren emits vr:z -d4/n qruat 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 ixiviko:(:kt ( -b o3ntf a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Aro-:(t3k(i:kt oxib vn e 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 single frequency horn. When one is atic.+ ;ncsro*/.8ti4bi v 7dme hwl 2aj 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 +* b8 idhacc tiev4rj/ 2.o7lsiw;nm.horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves;(. h+fud: cz o/ ct:ylnhba8s at 50.0 kHz and receives them returned from an object moving directly away from it at as(fhtlhu:z;c + 8d c /no:by.25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a spe(csfw) l-kbbeuoy c ,u:,3dm)ed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wamb:c uw-boycd)kfs, le ,u3()ve?    $ \times10^{4}$ Hz

  In one of the original Doppler experi h3(b+xwy/7;fy 3z lfem)svddt p2x-pments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played tbdmpxpe 33)y2-hlwsdz +ftyvf(7 x/;he 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 blood-fh 6lzbw a90p-glow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 z0g6h-al 9wbp 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 usiwnq)a*jsyeu1u./f-vemvq 1 2a ld /8tng 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 tkm25+m18 4litrgwy qphe wind velocity is 12 m/s from the north, what fre tm l 2qkiy84+w1rmpg5quency 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 its speed at 2rb+ddm 5n;mk70 $^{\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 where5*tp q:oyxr; v*jith k* 2z(un the speed of sound is 310 m/s (a) What is the angle the shock wave makes with vh* p yr:5; zkxo2tj( *utnqi*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 so (8wr7a1u zgqp*ufq 2gund is only aboutu1 (z7fq*rga guwq8p2 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 8j tz85irtd3n /obtw/the ocean. Determine the shock wave angle it pro/i3j5bwt o zttd/88rn duces
(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 )me oj w2xedc :(og+m.$/theta$ 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 1kx j6 8dq0t)ih.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 horizontal distance of 2.0 kmi 8)q0xhjk6dt . 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 pulses downwkr k) cyjz3 d-l6jl**0 li:tgoard from the bottom of the boat, and then detects echoes. If the maximum depth for which i6)-0* tj*lykzdkjr3l oic:g lt is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are theredadeww w1c**n+) ei4n7 lhez8 /e f5jr in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists lzem7gduu s s7eo0 i5+213uzvof many plastic pipes of various lengths, which are open on 7su 12ze mueu3g lisvo 0+7d5zboth ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the th0a. ym ah3:w;2yulw ewreshold of human hearing (0 dB). What will be the sound level of 1hwuwyy;3 :l 0m2ewaa. 000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and a6z uzie/p k).sd2 vmg-e0m0iwn 87-dB sound are heard s -id /2.gi0z ve0skpe)zm 6wumimultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, dk)(sx2v+nz e is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally i) d(zn+ 2ksxevn all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drop,yi(*s4 y (ut. amfzd4 1ie8:khrjc eus by 10 dB at 15 kHz. What is thuh a4e*4ky ( :,se1uz(yirti.d8 fm cje power output in watts at 15 kHz?    dB

  Workers around jet ai n4e+nu+)c d8lfr(jp2al m **;dcf7j m h4ajlircraft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engin (+j e f 4uci*h7lmln*cl4fra ;nd+a)d28jjmpe, 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,)r;47sq f jp8)zw krux 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 violiss6lb 6m/ - vjjx+ck9nn 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 between fixed points with a fundamentgc n1.nvnve4.4l 6 abyal frequency of 440 Hz and a mass pen n1.n 6byae.v4g4l vcr 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 verth)+2xwv.l /tpcw4 hjb/ o5 y: xzxz1yzical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tzh+x4vo zxt1w 5l w /hpx2zyc by)j/:.ube 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?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a s foy(avnx:r5cajc.t7g 2 :u4 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 gjs4a(: r5: fnoy.avxtc c7u2mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full ln ihdpl6i2 1bze/r22loop ($\frac{1}{2}\lambda$) 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 the8;+agi5d lx +9j jyejz 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 finds that the sound level is minimal at a point 0.34 m farther from one source thj+le jjda+ zyg9;85ixan the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The condwpei/b y586tv uctor on the stationary train hears a 3.0-Hz beat freqevt i6bw/ 8y5puency 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 is 538 Hz. After k;*0 x.*yut;ywo t yjoit passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume y 0y*wx;ty.t ku;o*j oconstant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by lis ur j*y8f;bu7t72vbyitening to the difference in pitch of the j*87; iutfv2yyub7b r 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 going?    m/s

  Two open organ pipes, sounding together, pro6/vy66 no uy9 wwsj4p du)joc(duce a beat frequency of 11 Hz. The shorter one 9u/v)n 6oyw dyjjsw(6 p 4uoc6is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a st+xwen. rwza u3fi* 0-mationary observer at 10 m/s as shown in Fig. 12–37. If the speake3fr w-nie a*+mx.0 uwzrs 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 him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s w o+.w9mjvhk (hq35lg what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow kg jw(m3.q5+ ovwhh9land 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 mw9czl+4/m )ovbunoq *+h5jb mfc.m/noth at speed 6.5 m/s while 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 frequency ob.chbfv)5*uzj o /mm9w+ n l/onc4m+q f 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 approache jlc :*3jz s)5zcv-yscnrm-c oe)b 96ks a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so tzkvze--) lc5 rbmj9 c6noc3s )ys*: cjhat the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send sioj0n qtu*1;b24 pdo dq++pm cegnals 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 alpen te 2mpp b;o+d cq+0*ndjq4uo1horn 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 2v+oozo xjyc 607h-jethe presence of standing waves, which can cause acoustic “dead spots” at the locatio-vz 62o 0jjex7+hcyoons of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a lo7 ke/voeug:5 u4 5wqkvng, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. Fo/75voqku 4gwu :eekv5r 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 ozsq*h -1q+v kvf hearing for the human ear at a frequency of about 1000 Hzk1v -v*hq+z qs 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 Machj1*srgmgr1k0p ey9f+ycexib 3 ,6+ ur 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. Whatyp r rb0 +e1rxfj9gis6*k,3+ce m1 gyu is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 gw39g(da/ wzb$^{\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