What is the evidence that sound travels asp0 *g64ibdvgve7(oz0l r:2fax s ( x1 g:uuvhc a wave?

What is the evidence thasf7 ae-e odqfw2/it1( 0xcd d+t sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to/+kv jbrkw 22kyzb8.h the bottoms of 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 thkv 82k+bkb 2yhz/rj.we sound wave travels from one cup to the other.

When a sound wave passes from air into water, dod8sc w)jig *o0 you expect the frequency or wave8jois*w0cd g)length to change?

What evidence can you give that the speed of sound in air does not depend signif vl us*ky 5(-knmpm8b 9pu9i.oicantly on freq-skkbo(m vpyu 9l*ni8um 59.puency?

The voice of a person who has inhaled heliui kzn z4x-+*nvm sounds very high-pitched. Why?

How will the air temperature in a room affect the pitchobkhrt8a r+**4 o ml)vijhb1 lzk7u:mw4 d(l8 of organ pipes?

Explain how a tube might be used as a filter to reducedh:ug /f+on ld u dg5isk*g--2 the amplitude of sounds in various frequency ranges. (An example is a car mufffug-l:g2 5+n gsio d*h d-ud/kler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togethery qr;.6q(k mka as you move up the fingerboard toward 6kq ;qya .(rkmthe bridge?

A noisy truck approaches you from behind a building. Initially you hear i lkmpa+xt*i5* t but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter”x pl mt5**+iak — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said touco pa1kmpu+iq (* v(hvap3t f51 a2;m be due to “interference in space,” whereas beats can be said to be due to “interference in time.” Explainv;(+m11 a c3kqfpu(u *pamtha52p ivo.

In Fig. 12–16, if the m.f1: )rwjbo r9ifgu8 frequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or f.jif 1r9 :ubmw8 o)rgcloser together?

Traditional methods of protecting the hearing of peoplek/n6;wpw1gijw:noui nb ; x 5+ 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, inverts it electronicallypuo w: w+; bx5;wgniin1/j6kn, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave caojp7.g , cu8srn be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In u,sc7gjr.8 o pwhich 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 movei ubonco.y, d kvc842zghk(s 1ojx188 in the same direction, with the same velocity? Ecny xog2 8 oudb,j1kho1(c.4skvz8 i8xplain.

If a wind is blowing, will this alter the frequency of the sound heard byn7 qb k9uo1wtu57k-0q xza k8vxaz94e a person at rest with respect to the source? Is the wavelength or v9awk q 8xt1vuo47z57 k-qeukz0bx a n9elocity changed?

Figure 12–32 shows various positions of a 7ulb)k n x 42cw99vvwrfjlj 6.child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will th7jl6 .k4bn lvc) 2xfu9rj v9wwe child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a -fl33kxyd ic0lake by listening for the echo of her shout reflected by a cliff at the k 3li-xdyfc03far 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 below the waterline. He hears the e4on0k.qm6ciwpg*a d wc.8 s/ bcho of the sound reflected from sgno .*ma8p 6k./c4qwi 0bdwcthe 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/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelx;jj:jt6mz5afw ma ae 6u 4,gsle7z,*engths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a frs 88 igod-tc-eqpj+y;/p0 :;j fj nzxoggy day. Without warning, an engine backfire occurs on another boat 1.0 km a- f/itr8n-o+zpjej; xc;j:ysd 0p 8gqway (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 topl5s4ks 813 jqi xn9xoohg4ln. of a cliff. The splash it makes when striking the water below is heard 3.5 xsqnjogho19 4n5 i 3lk.84sxl s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a hzv9r:bbp :pwa 7+voa9 uge stone strike the concrete pavement.+ bv9z :9:rwaovpbp 7a A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent uxeiv z1jc:i jr9o2 bvst: 80,error made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperatur1,0 bj xjz:i ceu82vs9: tviore is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at tyf6 k 9yr rrhk*:m/ro.he pain 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 level of44ga12qm4 f5hpvq evj a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers eo iu,hc3l-cn;.4ei eproduce a sound level of 95 dB when fired simultaneously at a certain pl.l-ce3,cno;ihe e u 4iace, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with fouhp(2 sw z8*xyur equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What souh8(xuwz2*pys nd 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 s--k8/zp c 02 a (ziediduoi6wxignal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio do dzw0(pxa/-2iciu ze8i6 -kof intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conve4lc:m 6 ak)lb3j+wp owrsa3k64+pll:) c oawwjm btion. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum wtv)9d8apck:y hose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rattzu +ld :8;duaed 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 l: autud+ d;8lzoudspeaker 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 registv0p+ m+k vuzr)ered 130 dB when placed 2.8 m in front of a loudspeaker on the+vuzm v )+kp0r 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 level of 2.0 dB. h 6-(,qarkxih12d wjxWhat is the ratio of the amplitudes of two soundswki,-2xhxj rq(d1ah 6 whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sou2.ppty q r ft0lx091-gmc+ tznnd wave is tripled, (a) by what factor will the intensity increase? Incr 02zptpy0q+ xft tr9m.1lng c-ease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but u 7b7u c2gekwnh g)nsx(j2h4toy p,9.one has twice the frequency of the other. What is the ratio of their inte7b,s2n2.) hy (7h pn cuu 9okj4getwgxnsities?   

  What would be the sound l.i5phc1t(j a kevel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air mol (hpj1 .t5iakcecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound levetzk,othyeytv 1p(8 u6/ a.57;zka swa d7t9j wl to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.,/ap s ad .u96t1w8 yvh j;7tzkyt7wk(5eaot z)    dB

What are the lowest and highest frequencies that an ear can detect when the sounq yyph0 55j l z3cxy-p/xt8.)e dvu:s7eye0 dgd l-557s0v uthc.x 8yx qp3d:d yy/yj)ez0egep l evel is 30 dB? (See Fig. 12–6.)

  Your auditory system ca i(aojydn pu+x 09/-man accommodate a huge range of sound levels. What is the ratio of highest to lowest intensityip n xo0jy(/mua +da-9 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 fun9sganvf r.7,antx9+ adamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has aasr g,.fnx979t nva+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 first thakib8 i7 uvvn.cc2z*1wo):w t ree audible overtones if w i azu8t 7cwv):cn *ibv.1k2othe 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 fkjs h x:6 ;f9ul:wp9zqyw7d. from blowing across the top of an empty soda bottle that isu k;wy:qlwz69 s97p j:fhfxd. 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 ppjk3lv;qy *ifz+jx6 i 7.bhg/ k*en6lipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requiredyi kheg67n+i/xvl.f; pq*6jkz *jlb 3? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz aiet; onsdh. /-c*wg z3s its third harmonic. What will be its fundamental frequency if it is tn*;sd.eoz wc3hi/g-fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0m/h* h8n erb7g.5fszkcl1s 9lcel;5l wf59w i.73 m long and is tuned to play E above middle C (3n lw/ w9cc g f5l9ieh5ks78f1;l.rms*zh5l eb30 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that vb-q *ak ns7,cemits middle C (262 Hz) when the temperskq*7-cnbv a, ature 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 awr : rkx( lg-a.rm1 p/t/ imlz-.ftvs.t 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 19 em+3u 3 .lf/pyqbcxk2–10 should the hole be that must be uncovered to play D above middle C at 294 Hz9lcbyeq. fp3 m k+3/xu?    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 p*rav ax)8 *ttq3o4kelipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or r 4xtv3t l *8qa)a*oeka 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. Itny mik)p-iq3y z3 +dj4 resonates at two succesynmjp-zq id 3i3)k+ 4ysive 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 x*fjgw:+ o4sgax w-s3 $^{\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 prs-;dhx,1u xw yesent within the audible range for a 2.14-m-long organ pipe at s- ud,w1 ;xhxy20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 c1 0 /a x1ro3findb,2ykplwjvu)x4 gj+m 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 rk,a4pv n) d ox+ 1jiuf21wb 0yg3jx/lthe ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust tmv ( m- wc(/9z8ns)hn8jfh mgpwo strings, one of which is sounding 440 Hz. How far off in frequency is the other string? ±9 c njs m(m v)8-wh8pzgf/mhn(    Hz

  What is the beat frequenc5w1e j(b cwdx6y 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 operates at 23.5 kHz, while another (brand X) operates at l4e9kl4 ypi cfp;iv8,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 the operating frequency of brand X. vpei94y,4 p ;fli8clk    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and 9 :kyh0.x+7ej s+ jzwg q) 3x2ozqsqu8nbeats/s when sounded0ho 7q3z :s+2j ynwuq+x k szqe)g8xj. with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the sast0qbl*wr 2v a/o74zame frequency, 294 Hz. The tension in one string is the*4z/0v2oaatq 7rlw s bn decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middl.lqn7b9+wg opz2 mrhwpl 17 y:e C (262 Hz), but one is at 5.0°C and the othe1p9l qz m7. wp7:gh+nyrolw2b r at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, andd xn qcu ck:gx(jh6*2/d-stn, C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sou s,:tdjux6- (n/2hnk*x gcqcdnded 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 0:ziut8 m.3a r m,ogakstands 3.00 m from one speaker and 3.50 m from the other. uzm :g am ika8r3.,t0o
(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, , 5zc3l7ropf5hohor (but a piano tuner hears three beats every 2.0 s when they are played together. (a) If oz3ohrlfo(o5phc, 5 r7ne is vibrating 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 wave uc fvjx47g7(olengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Ass uf4(j7 xov7cgume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s s).tvugdrg2-1ha)w m6fza )rt iren is 1550 Hz when at rest. What frequency do you detect if you move with a speed ofa) -w u1r)ztatm r .62dgfh)vg 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you det0mpjax3f-lekl6 (. obaz-hgc +h(y6 u( gdg5qect if a fire engine whose siren emits at 1550 Hzyq(5c0ga lg6zg xf+bp.h dj-(el h6 u mko(-3a 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 towa,8 5s ufsqao6bb9j.tx rd you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they 5 fja89.osbtbq6us,x 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. Whenpoo,xhu5-j vb g: jtq8bxy00 ; one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the hog-ptou05bx y;:j b0 vo, 8xqjhrns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrason7j 4+z 6qelu49mneh 8jmwuef e0u6o q3ic sound waves at 50.0 kHz and receives them returneml qmq3+u8j uj 6eeo0964n74wzf uhe ed from an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flietd 7*c wnmu.nvipntfd (984g* s, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the rvf*pmd8(4nw g7 icd.n ntu9*t eflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was plag7u+x1ndg5c)to 8ovk yed on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequencyo 7u n8c )dxg5+1tkvog was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves uk 9vj.p6zty3to measure blood-flow speeds. Suppose the dvu3z pj.kty96evice 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 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequencym y/. r-2bygd4 ijq vcn8ye0gkm.6s.b $2.25 \times10^{ 6}$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 thcz1vlgei h 5./e wind velocity is 12 m/s from the north, what frequency will observers hear who l.h /evcz 51igare 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 agr* )whp7 qt jym n.055uc1wa13a qljlt 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What iv;6 uf(*:gxtqqrnw7b3th3 izs the angle the shock wave makes with thtb7vhz (i*q6tqg 3fnu;3:xrw e 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 ofk )wn*x hc)b3d a planet where the speed of sound is only about d* kxnc)3wbh)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 oc8, yuudrtj c:(ean. Determine the shock wave angle it produces8(u dct,juyr:
(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 sp n.tg/u ,75ocd -sbe+1tiudv)gf9h$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see ;c8rioz qe- f*sv 6er4a plane exactly 1.5 km above the ground flying faster thef4r-re qc8*;z vs 6oian the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device tha z o/6 nsueqtp(.9k7 qw/awe11ilp+f it sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If p w. af(/ie kq t7le+u16sio/1qp9wznthe 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 are there in the human autgfqc:6er9qx7rk+4fq7fb fio 6 67iqdible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a di9v7r:vp+k z )kcb)xj9+pfp -qc4ep q tsplay called a sewer pipe symphony. It consists of many plastic pipes of various len )k4ptk c:e b-qp7vpp +zfv+9rj c9x)qgths, 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 sound close tojesuq y yt6 /ngs.p09fw 57w,a the threshold of human hearing (0 dB). What wiq59j 7ue af0 tn/pgwy. s,s6ywll be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-d uygqn i h.5p4l2gl-1o4 co-;udzjnq-B sound are heard simultaneously? u-y-hp i lc4; j.o-gnouq g5zln142qd   dB

  The sound level 12.0 m from a loudspeaker, placed in the op5y pjxtz. , s+2ch9pzodhk/ r1en, is 105 dB. What is the acoustic tz /x2kds1o,.p hz 5cjph9+ yrpower output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rj idp*2a 7rwv5num:g 0ated at 150 W output at 1000 Hz. The power output drops byw5m7ga2n p ij*vr: d0u 10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically weari)go( :sbu)1l os:yai57 f tbe protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engin7i:)uf 5gby:t( )osboseli1 ae?    W

  In audio and communications systems, the gain, q;nn dfi;tr+9an-:4jv x ,jo k$\beta$ 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 tunedgc.icp zt 55cq 7cz,w.cg c3m1 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 oks h;z*dni/0is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit length ofs;zkn i hod/0* $6.1 \times10^{-4 }$ 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 madwisyn.e sf8yr; /z +(e cbff;5q)6 above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again/a8;b; eyf.eyf6 zm )c+ifdr (w5nsqs at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one b iq,/ drsg0887 ph;+ ozrxulh3zr1cuend an3b/+0 z8scp8olu7ghz ix ;qdur1rhr,d also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to reson;w(jxqrvm 2+rrj *n*oate 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 500–1000-Hz (4isr s-t0wk;sxmhf) i yn1z.*d) agmrange 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 lev-m s)(mrn1* xifkwt)asyh4. d; 0sgzi el 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 whdh + s.p.wcz,mistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What + pdcs zwm.,.his the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you xzd4*a qlmnz5yu44)y is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the tr y4nld4z y5m*4 qzua)xain moving (assume constant velocity)?    m/s

  At a race track, you can estimate the xkx.2k(i; f)kgfh0 o ispeed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by )k 0k xf i2if.;xkhog(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, produjdwmva y vxh852:y (sb/1 wkj7ce a beat frequency of 11 Hz. The shorter ok hws5/v(yj8ja1 d:wx2 7bmvyne is 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 sm2mx xvtnfub n-)t1q8 gwn2s5*) k) ystationary 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 observeg 5 2ybfsmxv-kx)t*snn2u1n ) qwm )t8r 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 0.3c5- vt8glbs. ok9 4ctg2 m/s what beat frequksl5v ottb9.-c 4cgg8ency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while thejl:d f d,4mr-u n7g8vz moth is flying toward the bat at speed 5 m/4rd-8 7lf ujgnmdv,z: s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a jv(poc :xgk89 moth. The puls(vokxc9g 8j :pes 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 that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. d 7/0g0 1f xycpjxe+ad12–38) 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 create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is th1+ gx/edcy70j axf0pd e 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 of ch lprne+. 8c:standing waves, which can cause acoun:cl hr8p+e. cstic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender aln1 +zk d2ln9z d7juvs;uminum rod held in the hand near the rod’s midpoint. The rod is stroked with the otherjd71z svu +2n;zknd9l 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 hearing for thuhx;k:bxbo+2 4u1 x5s ,mcdfee human ear at a frequency of about 1000 Hz+51xx xoms d:hue2bbfku;c,4 is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hear 23.vokne0rtts the sonic boom 1.5 min after the planete0kt vn.2or3 passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 6hd 4 4eqsn*ecymi - 2mvj51jz$^{\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