What is the evidence that sound t kgb2w)5aa.a bw-a3ou ravels as a wave?

What is the evidence that sound is a form of enkobrtsuk d)2 t4w5y6 .ergy?

Children sometimes play with a homemade “telephone”z5s w6j2 j3lkk by attaching a string to the bottoms of two paper cups. When the string is stretched and a chij lk3j52wks6zld 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 eap1t +sr-*0d8 c0.ksi sn yic0ie mn u.yer6:jxpect the frequency or wavelength to chang.:*60eer8a+uit 0cdpynksrn- 1i miysc0 . jse?

What evidence can you give that the speed of sound in air does qnb kxh z7u08w;:on6q not depend significantly on frequencyhon0q6x7;nz k 8 u:bwq?

The voice of a person who has inhaledj p /vp ;w7yqa my31acvvtzf2)9 m8qr3 helium sounds very high-pitched. Why?

How will the air temperature in a room affect the piaong78 g+ufo f.2c ;urtch of organ pipes?

Explain how a tube might bb4 /txecn6 b9rpr+x8* j of8bbe used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example +cpxo*6 texbjnbf9 r84b/8br is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spac*xib ob uxfuui +9.*0red closer together as you move up the fingerboar 0b.*o i9xfbi*ruu ux+d toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear e ij2gpswp5f4 soua9l1n,ok03 y8s1i it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more onk11yao 3s 8pl0jws, p i594us2gfei of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be s kni uwpmfd v7i-d-o+l4q7*f) aid to be due to “interference in space,” whereas beats can be said fi7p i-4lk 7*fquv-dd )+wnom to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were loweredyu :nx8obkpdj :zz)ug)g0)-. zydhw 1, would the points D and C (where destructive and z:)wp :0xny)dk8zguj g)1-z duyb.oh constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in area6m2 e1hs ts+ets 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 thet16+2ms stehe 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 wavexltr l9qw4 :40:uftkhs shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 10xq49uw::rt l t klh4f2–18. 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 m e17xc/v7pav -.1gyxy s+m hftove in the same direction, with 7 f1set+xm-a1p vx.vgcy/7hy the same velocity? Explain.

If a wind is blowing, will thisevp ez8b)q ;p0 alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity p0)pze8bq ev;changed?

Figure 12–32 shows various positions of a child in motionu.f/u2 l7 hgggip4zq)t8 g(p yxqr1 /a on a swing. A monitor is blowing a whistle ig u2r4/q71y8 igfgh ta. (lu/gqppx)zn front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the e3lp5uo yc88f ucho of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length ou8uof p3l y5c8f the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the +.gnyq1ehh9 s9xbyo: echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep 9b:1neyy9x+hq os hg. 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 wavelengm+s /q7mjcr 9-gje;x aths 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 foggy day. Wiuruh/ y(,b;-1u.qdi*i mbmeh thout warning, an engine backfire occurs on another boat 1.0 km away (Fig. 1i.y*ur hq1mu;b bu-i/m h,de(2–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from t1on w q0gbwk::he top of a cliff. The splash it makes when striking the wa n::g1kw0wqboter below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone s+/ro; pr+e5/ f sil+ k-pwupujdj(;ua trike the concrete pavement. A moment late p(/uu s+;wjpurr+ ifpkd-la5o/+; jer 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 by the “5-seconpt26ri: -s1u yjuqwm55j 1tbmd rule” for estimating thewjq u m65ty1mbuj: t5 1i2-rsp distance from a lightning 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 level of 120)zhrcljzx5:cs/o7 +s0vzx 9 u 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 e 1n l4jbucvcuw e p5s0zqyt80g-:1p5whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers producw+o tffwj73:pe a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound3fwt f:pj7o w+ level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally ,sy;1dq ,yi 3pshafo8noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down aloas;8 ps,yy13hq,id f l but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-nsr+9x + cuw(qm+ezg9q oise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the+mx+c(grz qsqw9u+e 9 ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output3,gqpe,xnhwq a :h z7 p+d9:bo of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mqwp qdphn, o ez:3 bhg7,x+9a:outh. $\approx$    $ \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 strikev t7mrrl-:qzm6:hmj01o r z/bs 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 2i.wezp u4y 7bW, 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.b724y peu izwoudspeaker 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 b/ twvh+s ,u0bjf(9mx/ s.mdkregistered 130 dB when placed 2.8 m in front of a loudspeaker ons(xvh fubm+d09. kswbtm/j/ , 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 soundys2;5: 0 jii9q chs7be;ua kzm level of 2.0 dB. What is the ratio of the amplitudes of two sounds whoseq7;;m:yu2 zs05c ekb hjisia9 levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what faedw r+28tl. x(eco ngmg+j7 m2ctor will the intensity increasendt 7gce( mjg .w+22xm+oer8l? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displaceme7*e6cy k;yme u adi1nf1)amf 3nt amplitudes, but one has twice the frequency of the other. What is the ratio daa f6 fycm)7;e1u13im*ye nkof their intensities?   

  What would be the sound level (in dB)g3fio42 svcm, of a sound wave in air that corresponds to a displacement am4,2i3sco gvf mplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what souns6e9o (gjyd0t d level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–gey (jt s096do6.)    dB

What are the lowest and highest frequencies tz+duhv n-x ndrje4q9*a 0,bz9hat an ear can detect when the sound level jz,n-9 hd u9ne+04vra qdb *xzis 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sow :t5iierkqtb, / +9 ks-lbu9xund levels. What is the ratio of hig9+5ktt /i9s lqb-ux,eb ik :wrhest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. Th,22aegqqha *zr -2 ej0wg5yy(+ xd nnhe length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the stri+heqa2 qg5 ,(xnywz20*neh-ayg2 d jr ng be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and firr:j : fdi/0arx.x6tcist three audible overtones if the6jrc/:xd xaitf0.: ri 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 the top of an8x66x3x8sayrc*19 p art h khs empty soda bottle that is 18 cm deepxyx93tkpas8 6 ch a *rxr6hs18, 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 spanning the range n(a8,e t l8yw6 :brh)3goxc.8sgov vmof human hearing (20 Hz to 20 kHz), what would be the rang6cv8wy. garsgl,nhv3:mtx (o ) 88 eobe of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency ofwo(;onc0w,tokks - k*-hq;zw 540 Hz as its third harmonic. What will be its fundamental frequewnt -wk,q;koho*k0(o c s zw;-ncy if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long u*zdo-y04.k) y2 dfkkk yelq8 and is tuned to play E above middle C (330 Hz)ue kk2olk d0 -.)dzq fy4yk*y8.
(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 thap+n2h yx ib2 n vqeu7(yq2-4obt emits middle C (262 Hz) when the temperature is4bq 2xh-byoiq2+n2e( pu nyv7 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 r+b o)w0zyb 6 b0oru0)m dvnw: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 b9eozy- n* n* phj63 pezmm)-poe that must be uncovered to play D above middle C at *o-ep)6pno * 9pmmynzj eh3- z294 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 reyhvg 5j :wq2xm d-8qz4sonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in betwe-v8 gqj dzmh4y5:x2q wen. (a) Show 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 end/-y6i mtdfm2 wm)u+z ws. It resonates at two successive harmonics of frequencies 275im) /y6u wtz+2mwdmf- 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 :4sqaarek w9u04nx.;m k ( ri jbsk*;e$^{\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 audiblvps j9nd8w;i (*vkey7e range for a 2.14-m-long organ pipe at i9yk*esvp (8nv dw; 7j20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is appr 7 ruse:nby dywy+*s8(oximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the informatioy 8uys +de:w7ynrs b(*n 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 ad,yvga*b .bl(mlu,64 gzh 7swd just two strings, one of which is sounding 440 Hz. How far off in frequency is the 4d(wb6g*.,7syuglv ,z mbhl a other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) anzdgr( 7mm z8l4d $C^＃$ (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 8ij61ht*nftp 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when playt*pfn 8ih t16jed separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning9do1qbdt f;c7e0eze8 fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrationa0t zoqd 9ec87f e1e;bdl frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in 2j oszcn, l7- a*aw+maone string is then decreased by 2.0%. What will be the beat frea+-*o, lwan27mcz sjaquency 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 xbku rmlu.+: *4 u1fy:fr6vg)ml6m im play middle C (262 Hz), but one is at 5.0°C and the other ruu mgm m* )lb6fx.+4irm61:yf:vlukat 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forksfxlh-nsj +a:vz,v y2d9 1;g bn:6:n)xm uae jf, A, B, and 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 sounded together, the beat frequency is 4 Hz. What are tz)bsl1a v:-,fn6myunh xd;jg f :+je v:xa n29he 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 stands 3.00 m(wn*j ):k w;g:og ktkf from one speaker and 3g:kf)k;(tgk:w*n o wj.50 m from 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 arfq so-st.qd(w t;dg+* *m 6rmee supposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are plf .s 6me+o;wt- q(dd t*qg*msrayed together. (a) If one 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 wavelengths 2.64 m and 2.76 m in air. How mazh*e 9+wvwd bu.+ 4xbtfo6g ) onvm37hny beats per second obgvo.3w e+9z*xdn4hbv7h+)f 6u wm t will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequn*ayim c s ;yo(n6a4c*ency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detemnn*ay 6ica* ; (cs4yoct 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. Wap bg*mwk96 vuahqcu0 o (a(6;;e.hs what frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/s .s*c ;(6oqaga0e;hp(kb awmu9vhu6 w
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequek jbr 84ldr/v;/ir 2nhq+qj6 uncy if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactlybqkr+i/ jqj4;/du2nrh6lvr 8 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 -wip.:swvj ,2mt-)d l igs(g dsingle frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at restl)(pwg-t-w im,s.gsv d:ijd 2 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 andihlfa;a(e9 s gc)kj 6* receives them returned from an object moving directly away from it at 25 m/s What is the rehis 9;a)j(6f* kcaeglceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flieg lt-o lu8 8 u/l;q2uo2;dboe;uklmi( s, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?2;-(8oou2ulodgi ;k uml8 bl tu;e/ql    $ \times10^{4}$ Hz

  In one of the origin m949rmmc6ua lal 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 station. What beat frequency was heard if the train car approached the statum4a96mml9 rcion at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measurb 7i) m4hpr,m8bw u5vwe 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 li,5mbm)w v7ub4hr8 pwarge leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of felze 7tlm.1tn++n g9p u7go9uv9 x7utrequency $2.25 \times10^{ 6}$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 5bge 1( l(9yweh70 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are bwh (yl 1gee9(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 lar b xv;1r-arctj.pt2t ; z5,nlnd 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 souow9.-rmh.sn k.u ( uxand is 310 m/s (a) What is the angle the shock wave makes 9au-k(s..woh u. xmrn 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 thinvjcrp ,r9j.y6;am+vx atmosphere of a planet where the speed of sound is only about 35 m/s 9c;v,y a.mrp +6vxjjr
(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 travelinghu s61 +nxxa4;x uwjp4 8500 m/s strikes the ocean. Determine the shock wave angle;64jn1x h uasux4x p+w 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 h.4ciipz u4 v8$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plan: 5og2i 3owyj+12z 1bd hdiubye exactly 1.5 km above the ground flying faste: oi13 d21odwuj g25byyhb +zir than 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 devic3 g-; wq:nmschy1t.( bd 2mewhe that sends 20,000-Hz sound pulses downward from the bo hyw3dmbhqsem- 1. w(cg 2;:tnttom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the awnr6 g vh;4 )j.om4usgxop/2human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists y:ey4q+/.evuga h3bb3fi;w tof many plastic pipes of various lengt tq b.33ua yigbyfewvh4/ e;+:hs, 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 to the tex/a0/n7n j up.hy 8anhreshold of human hearing (0 dB). What will be the sound level of 1000 such mospah/78/ nu.x0 najny equitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are w ;39mzl5sv sb+m.xhtz3l+un8.t c8c luphi) heard simultaneo5hx8luz+8+ tccw m ms;vulp.l)in b9. 3sz3thusly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 1n)6hu.z1 dip 8jpdyrlas98i:05 dB. What is the acoustic power output (.pr ai)dpizlu68s9 :h8ydn1 j W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 1h.f6tk0(uxi v(-m 2yc tud;rq50 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at60uyhcr2tkvxf m-.dtu( ( ;qi 15 kHz?    dB

  Workers around jet aircraft typically wear protective deve,n7exdpov: 5 )brka:ices 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 :an,eod7rxbe)5: vpkear 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, the e990dx,:fd b(e gps5qqf uuh.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 tjl.wkl9,cx,p*l 1e c kuned 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 betwma)jvg)7,,, frp.w*gonj fxd een fixed points with a fundamental frequenf,)m.agxw, ,g 7 v*ndprjfo)j cy of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set intdoh,t r j:gpl2;/kwfv)1r 0vi o vibration 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 t/l h wdpj);vt 2g,0vf:orik1rhe tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open ),v ozb h:t fy sb/r6ig0uc)f.at one end and also 75 cm long. How much tension should be in the string if it is to produce resona hbufcs/ ri),o)tg:6 v0.fz bynce (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fulx .6n0 kx+-j 1he-x+mlmquba7lil; abl loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sources. Tt8q74l a+arbg he sound is loudest at points equidistant from the two sources. To determine ex7gaa8qr b4+ltactly 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 train is stationary.3 gd5kasp o.j 7m8y5r;ic*mum The conductor on the stationary train hears a 3.0-Hz beat frequency when the otheg s racd5.538;p7kij mou*mmyr train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it 8kp)b)/lkoj 0d t.ued x5dq6vapproaches you is 538 Hz. After it passes you, its freque6 . kdqko )8xt /vb5upeddl0j)ncy is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you canx /h-k/. tmo)csp/kc x d(xa,c estimate the speed of cars just by listening to the difference in pitch of the engine noise between ockd(a h k/sc)tm,c x/ .-pxx/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, produce a beat frequency of 11 Hz. p0jv;kc syvf dm8j3kb3kb(j k( *gj )1The shorter one is 2.40 m s(3k0 3 gmjkkjdcky) *pb;(f8jbvjv1long. How long is the other?    m

Two loudspeakers are at opposite ends z-*fgsmcx msg55 o ,4cof a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, atgmm, scz5o x 4-sg*c5f C?

  If the velocity of blood flow in the aormqk +ctgc2p+,p.cll . ta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz +.,g ctmck+.2cppllqultrasound 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.fr o3gcp4n8zme lm( eyc2 1(7z5 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. Whao7c gecn1el pf 2ry4z (83mz(mt is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of h+1ggm m;s*xs:ltqw1 cigh frequency sound pulses as it approaches 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 that the echo from sl;q:x w+ c11 mg*stmgone chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals p x;u 0)odowd6dh59(m7fg pmbfrom one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, longdp7fdm);p96o5 xdhmg(u0bo w 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 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 o9r0 ng1edj.yif 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 fundamental frequenciesy e.ir9d1n 0gj for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing .fb.tdj8w)p :wa02mvsd y q.kal 23usrods,” involves a long, slender aluminu.:0 2ykvudwa a slf) mts3p.82dqb.wjm 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. 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 thaaks;4 5l.bwc8 fk zqxl;6e6umjdz(-e human ear at a frequency of aboutd 5 ;s-lcu; bzmfk8eqlaaj.6x6z(k4w 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the grou;wv* o4+ ,uxewwc)xchnd hears the sonic boom 1.5 min after the plane passes direevcx4whw;+co)ux,w * ctly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is )f:oei 6qd y2r15 $^{\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