What is the evidence thay7 e9f6 td3km+x *xit+o6nt;tf; jzact sound travels as a wave?

What is the evidence that sound is a form nez; .c4pnk;q of energy?

Children sometimes play with a homemade “telephone” by attacivx i +z6bj+4roree*a8 ,mk ri0kr5v7hing a string to the bottoms of+, kr4rbizv6e7 vmirri5oj ke8a *x0+ two paper cups. When the 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, dorl a -r5laeh6dw;1i3j you expect the frequency or waveia6 llhrj-;wreda 531length to change?

What evidence can youfjwyq22)tvm1 jzw1p + give that the speed of sound in air does not depend significa12qmv y) 1jp f+jzw2wtntly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Whaxf:j,/*zg dwq,i3uz 5 asn* ry?

How will the air temperature in a room affect the pitch of orga kx:w 7f6w0jscn pipes?

Explain how a tube might be used as a fiycqm1*+n8k n olter to reduce the amplitude of sounds in various frequency ranges. (An example is a ca8*+nq c y1moknr muffler.)

Why are the frets on a guitar (Fig. 12–30) spa-xu3ht-2v3q vkc6wleced closer together as you move up the fingerboard toward theqh63v3xut- l k2w-vce bridge?

A noisy truck approaches you from behind a building. Initib:68kmblt)9srq tj e xsm0 07wally you hear it but cannot see it. When bt0l:eqmr m0k t 9 68s)x7bswjit 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 “interference in space,” whx o -u* wsxfbrpy,s6(x/g m8i+ereas beats can be said to be 8f,su-w(gp yxs/xor*m+6 b ix due to “interference in time.” Explain.

In Fig. 12–16, if the frequency ol*4le me44naxge3- sof the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apa*lexsn3a-4 e e log4m4rt or closer together?

Traditional methods of protecting the hearing of people who work in ari13- s-py ,5lo;jxm h.lmvhj eeas 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 nxiom y - jle,3s1p 5h-;hl.mjvot 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 in Fig. 12–31. Each c(okl )id9x tr :u55q zh7x1wqwave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–cx tk or5ulxq h 1):w9qi5d(z718. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shiftmh )t 7zx i. c:+sahm;sn4vxg: if the source and observer move in the same direction, with the samhzmvs cgs4hi )tnx;:7:x m+a.e velocity? Explain.

If a wind is blowing, will :pwyl6edzry,k8xpv/1 j hq5 + this alter the frequency of the sound heard by a person at rest with respect to the source? Is the qyrx +ekp/1 6v hlzpyw:d85, jwavelength or velocity changed?

Figure 12–32 shows variozy6r/keqxs9 p+( pd:wus positions of a child in motion on a swing. A monitor is blowing a whistle ink:(rz9e/+ wxs 6qppdy 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 3 i0 yb4j9badha lake by listening for the echo of her shout reflected by a clia9hi30dj 4 bybff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just bjxi8 kfmvuwymb( (.85xq g12 telow 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 pov .q u5(y ij82xb(xtk 1mf8gmwint? 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 airkxii7bt bqt9 *0+: iwg 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 ju,n f.9tm karer/ i*v m3bkt5s8st 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).sa38m59n/ *ke tm bkrv .itfr, 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 owf )u 5hxym:qfmc0f56h xti; r1./aoc f a cliff. The splash it makes when striking the water below ix0 .oc5 1tqrfh 6:;y5ixmm/ahf) fuw cs heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees3ultc 9idgeog lu*pt:d3cf +; f(-6yt a huge stone strike the concrete pavement. -lt9tf3 +t(6 pefu;*c dic:odg3y ulgA moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance*cv;,w nmt 6ok+9fz4leh e n;e by the “5-second rule” for estimating the distance from a lightning strike if t + ke;4tom9 ;lch*eeznn,f wv6he temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain lev gu,1nrkec:tla m1/ g8el 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*q.:ivt*+aq7g 1l utaf8 btlp n9-obpuqb)n9 intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce ; 1k*ry;boniya sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intey;yo ;nb*i1kr nsities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noiszn85p ss1quu9y -h +:ht)qbhb y jet engines is experiencing a sound level bordering on pain, 120 dB. What sound +ub n hzq9 sh 1-uy:t5)pqshb8level 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 hih (rjv06ib z.yyc*8;y0 aatzxf qete(;, 7kuave a signal-to-noise ratio of 58 dB, whereas for a Cbey 68 a;0 yk(.,thyxacj0iqt* rev(z7 u;izfD player it is 95 dB. What 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 out-jzxs2ul u;6-e5z hh,z ol:jpput of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound sp5slu-xh h jo6ez-jzu,; 2:l zpreads 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 strg:e0se 2ie gd(bg0hd.ikes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the morw b*ksx:wzh/ .n0kw ail:iv;7e modest amplifier B is rated aki7kwa.isnzvxwb0 ;/wh:* :lt 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in hok*0nq5he3q .wl4w gfront of a loudspeaker on the st*w30hoqe5 l .gqkwn4h age.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of4*i0xd: 7cl x xq5kdvb m*+idv 2.0 dB. What is the ratio of the amplitudes of two sounds whose leve:xvd4xc vdqi *+k7i5b m*0lxd ls differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a so l4nsxf6)(yy;l+fe26ixo nz ound wave is tripled, (a) by what factor will the intensity incr )snlfolxo2z6x(e y4n6+ if; yease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes,yaudyr f0 qeh6dm6.h.*f4 q f0 but one has twice the frequency h.0 0yf*dfyfa h6m6uqeq .4dr of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresps z.k9j8o6 -gzro le-jonds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300zegs-8z o.6k o-lj9rj Hz?    dB

  A 6000-Hz tone must have what sound level to seem )bl3 n4wxfe6nooi2+: m t(nle as loud as a 100-Hz tone that has a 50-dB sound level? (See F+e4b: fl(wmno e t2)no3 6nlixig. 12–6.)    dB

What are the lowest and highem+b /k5ioz1 7km aut+rst frequencies that an ear can detect when the sound level is 30 dB? (See Fmzaou/1r +mi7+k5tbkig. 12–6.)

  Your auditory systemo*b2 c ft3/hu3ywnc7p can accommodate a huge range of sound levels. What is the ratio of highest to lowest inte*3/t 7cn f2wcpo u3hybnsity 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 levfvgqw o)wh -n6e(/5q3u u 6psngth of the vibrating portion is 32 cm, and it has a mass of 0.35 g5/v6f3qs)vhg u( wqnw u- eo6p. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamentdxg 2.f33ddgsal and first three audible overtoness32g. dddxf 3g 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 -p/ oogv:4x/4ddng6-t ay)tkb8 7di1j bqfk vacross the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closedx p167 tatdvi:/8ndgob4- fjodv/4 bgyk-k q) 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 op t(tl)i, bg68xijo x8jen-tube pipes spanning the range of human hearing 8xo bjiit ),tgj86x (l(20 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 a frequency u-0ih5/i,o )oanej suof 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a l/0 o 5ia)eo,jui-u nhsength of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abovi9 v3ua3thg,j frax5 7e middle C (330 Hz).a ,tiuxg9h 3fv53a7jr
(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 oaji7o.7d z4 c vk)mpy0pen organ pipe that emits middle C (262 Hz) when the7ivma4o)yc zdk.pj7 0 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 20 id(m2qxx7 egus3)a: m*l7aku $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the moubm jb3s)m 58ilthpiece of the flute in Example 12–10 should the hole be that must be uncovered to play D above m5libmbj) ms8 3iddle 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 61k+,ga)gf 0 cyp6 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed +paf)y0ckgg, 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 uec aalcgu,*a8jlv g6r b)qz85dq4 /0 both ends. It resonates at two successive harmonics of f 8lba a *,j/vz4g608)lu a5dquqcrg ecrequencies 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 qdtszu2nh69 le gx9 :-wbko(2$^{\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 r0-dpd z/ovyo:g-rb5 fange for a 2.14-m-long organ pipe at pgd/bo-05yd-fz :vo r20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It mvk( *;xfz).gf2el va is open to the outside and is 2 gvf;)*k f la(mx.evzclosed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s wh4-;; x:zw4pull ab xhyen trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string;lbhz aul;y-4 :pxw x4? ±    Hz

  What is the beat frequency 3i re3.lq0kcn if 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 opelnrs c3 evh914rates 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 frequency 5000 Hz occurs when they are pla lh4s v91en3rcyed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with )( i-qkjmii*f a 350-Hz tuning fork and 9 beats/s when sounded with a 355*fmiiqij ()-k-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 Hz6 ,d f1:p76iu6e c fd9despuia;h-fcj. The tension in one string is then decreased by 2.0eda 7fif66,- 6s:je9c cdi1pdu u p;fh%. 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 play middle vvps*f 1k:jq-C (262 Hz), but one is at 5.0°C and the otheq:kp1vs- fv* jr at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has c5xk h* )ixf56uc - hcuibd(x5a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz i-5i 5u h bdc5*6 x)cc(xhifxuks heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person sta8kj3xrai3,y l,2qia mnds 3.00 m from one speaker and 3.50 m from the other.33 2 ,mariqx,yjali8k
(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 suppo z ,klwohcu 661woq36j-stc .ssed 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 vibrating at 132 Hz, whw-cjlc3h 66qw1so. 6o,uzkt s at must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many bex/lx( axcct95h:+ 9t-nz mtgeats pernetmt x(h c9zg5:ac-xt9x + l/ second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engidc y vqal(;4y;ne’s siren is 1550 Hz when at rest. What frv;(a4 qlycdy ;equency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency dou3nmuv;z kfz9w. e6g r*clu-l.p -kb : you detect if a fire engine whose sirenuu; 3f9z6km *.g ek:.rlc vpl-wzub- n emits 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 source is moving toward )p8soghm .w9k you at 15 m/s versus you moving toward it at 15 m/s Are the two fr8hpgkw m.so 9)equencies 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 bk y0.,,gntpp/mokk0 same single frequency horn. When one is at rest and the other is moving toward the first,my bp ,on/0gkpk0t .k at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and rece7yci r a/ppph+ *0h1q ,vb0qrq:rx;zj ives them returned from an object moving directlj*ricp1hh/;:qa0pz b +r07 qxpr,q vyy away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward av0lch-f1+ hl8c8xfz n35o- i hdoomll;(p(c l wall at a speed of 5 m/s As it flies, the bat emits an ultrasonic f8;l-mh0nfl+o -(l ilzocch3lx v1c oh85 ( pdsound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the origina7*z1mj)p3wm dor+;u ikhkzy2 vh kb).l Doppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station73zu;h bwk .hmv)*o2jk1+k )drizmpy . 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 tk: udc t9hhd;0o measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2cuh:90dk dt; h cm/s directly away from the sound source?   Hz

  The Doppler effect u3pyg28o1yf fgsing 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 w4iev hrz) 0/tg1wp0g m/s from the north, what frequency will observers h4hzw0g )1gpt0ivwe /rear 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 landi mx88n-y/h9jf,vsqf if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) 5os-hd*u t0oi;o/ra r What is the angle the shock war-ot;h0disro5uo/* ave 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 o 1c-zl4 se.luhr8 +) uxlort-of sound is olcthr4rlzl )o+ex-1uus.-o 8 nly 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 the ocean. Determine the shock wart+ 0fvi 5b2;vgy bky7ve anglei;2gfv0b5+ r by yt7kv it produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle r(-9gg(zs n2eg7 tfwq $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the grouqpmdo/-.w kt-nd flying faster than the speed of sound. By od --.qpwtm/k the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-ermw:v36 lx+w 1,zi qxHz sound pulses downward from the bottom of the boat, and then detects echoes. I :xwvi36zwq1xr+ ,lem f 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 occo+( 7o fp a8 tnm:(u8mgdf6 tv-nf,tutaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displazje qtkhq i9(z 58c:b,rg;+juy called a sewer pipe symphony. It consists of many plastic pipes of variou5q;(,e+9 jz8r c :btz jqigkhus lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sou u5fnq v*uhs; v -35ww(nmq ksy5e.*hrnd close to the threshold of human hearing (0 dBm wy5-3sn** 5e;ukhqq5 unw vhfsr(.v). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultan6l tq qwksyl7).sa;c :t sound level when an 82-dB sound and an 87-dB sound are heard simultan;slqwl)6 cy:kas tq.7eously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, i()p60pfy czxwve3d u/c9. hu bs 105 dB. What is the acoustic pou c9yphpcv (/ .few3zbd)u60 xwer output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 +twg* )exn86ph, :ic4snmotkHz. The power output drops by 10 dB at 15 kHz. What is the power output in wat 8 4 p)nwshc6to+:itkn*gme,xts at 15 kHz?    dB

  Workers around jet aideji*+jq 8xb.)9 a 0u8irxxjc rcraft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of bc8idqrj0jx)j xxe 8.i +9a*u 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, thxfcwchot x,xtv*07;/ e 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 frjk1 ..wb7m / uu u4zn3aqcser7 9xzh2wkfte9.equency 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 fundamental x / ra *(jwwk,8/ ogema6yzhs2frequency of 440 Hz an,axk*g/aesz/ 8jwr2m(oh6 wy d 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)bmndy 6l; b2cwo7ek-j 5yp1 j with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m.76y5 ;)j c omyp-bd1j2ebwlnk What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar stringu7hcx wnm6.n: of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to prwnm xn7:h. c6uoduce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed 0o( tx kodx0g1h 35ydeto resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–d t9io*6norqy.1k*l 2 d ja7fl1000-Hz range coming from two sources. The sound is loudest at points equ1 konfiq*da7d2 jo*tly l9r. 6idistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One :.i l:pxiow b0train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency whex.li b::0wpi on the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches jzn78gd:; ,wim ns4fsyou is 538 Hz. After it passes you, its frw ;:n s gs8,im4dfj7znequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listex jsw,;r od3nmua, 5f(xgb,q*ning to the difference in pit(*x,m; j3gw bd,rxf 5son uq,ach of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sot,e ht jt3c ao.u-8te;unding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is tt -te; h8,u3 .ettjocahe other?    m

Two loudspeakers are at opposite ends of a railroad 2fk;rzjp id/*4p3qt-rdu6 y 9 w 6oviscar as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passe/qjtd- 3y 9up6si dpfov26rzkri4 ;w*d him, at C?

  If the velocity of blood flow in the adc1vv7 vnx a/+)*ockj )yq if4orta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along y)7 d/joci av f+1)n4 v*vcxqkthe flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward the940+oo fx mxnh/et+delz76u w bat at speed 5 m/s The bat emitz6u/two o+ndf7x 4m+ 9eh 0exls 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 a9knm (0a9u lx/j,cn i p9ex)jhs it approaches a moth. The pulses are approximately 09k i/ acexj9 p n)jx(n,umhl970.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38b y46/b nyhyr;gmw4 j3) was once 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 4yh/m;6yjbg wb4n3 yrcreate 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) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence ocy-q 3x-h-vb5;bk ks 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 fundamenv-b sx qho;k3-bk-y5ctal frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves9kv+c, ;1uh:uolma,a1ez6 ou stmvjxw8 36dz a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice,zeu6:c; o3j9zm ao,uh1sdv 8a+tx1v6,lmu kw 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 earky r,/m2 4fpqs at a frequency of about 1000ysq2k p/4mf, r 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 g) xq m0wnz7qxe3 wrzcnen.811round hears the sonic boom 1.5 min after the plane pan 1e cr qw)10xw37 qznenmx8.zsses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboag-o: 0kr3 h0vv.*ozwps q9 oi)hxiyr0t is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h