What is the evidence that sound travel 0h(frxs rgb 7.)o0bqbs as a wave?

What is the evidence that sound jcgrm1askh/t ) j )gy1(6 sf(eis a form of energy?

Children sometimes play with a homemade “telephone” by attachin:,egyuf.aj ,ws+u 3qh g a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from onejuhu3g .qf +:,ey,ws a cup to the other.

When a sound wave passes from air into water, do you expemz ok3lt-b) r)ct the frequency or wavelength tok-zbo3)rlt m) change?

What evidence can you give that the speed of sound +b4 ved ap5vt7in air does not depend significantly on freve td4b5v 7+paquency?

The voice of a person w9p9yt lw1frz( ho has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the piq mfvj pw nhcy)s7zr umzf,1*13z12i6tch of organ pipes?

Explain how a tube might be used as a filter to;-m3ghp g hn-h4gv,sf reduce the amplitude of sounds in various freque g,g4ng v hfsphh-m;-3ncy ranges. (An example is a car muffler.)

Why are the frets on jad jq2bl: ,q3a guitar (Fig. 12–30) spaced closer together as you move up the lqq,2 j3:dabj fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear i39k2/vvky9g vh1yfd)jpk qc; t but cannot see it.kc)khv p93j;1 f9yy kd vq2gv/ When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spacethd qne4 xee., g,v66x,” whereas beats can b,e ,tx6evx dg.6eh4 nqe said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequ;py,zc lbt+ d +qvrt57ency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or vqz+tyc+ tr bp5;7,dl closer together?

Traditional methods of protecting the hearing of people who work in n6) *g4y, deddeqwc2d7(r tmiareas 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 electronically, tidwyg4) q*drd2( 7endmec6t,hen 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 can be thoughwco2rj1uy8 i ;hpjc 4jfd 5/4ct of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are theu4pojh; jjcwrfy1d/i8 c2 c54 two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shiftd0:x ocal z65e9:lobgy 2ak*b if the source and observer move in the same direction, wi6yd 5: aeal*lkxz9oo g0cb: 2bth the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heartf hj0zfym.uflo. k9y)uo -8rl-v 2e5d by a person at rest with respectz fvrftyo k- u 0jyh )l.59u2fe-8lo.m to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a chiz xrnzp,o0q3,7 e rlv3ld in motion on a swing. A monitor is blowing a whistle inr7e0o ,xplrzq,n 33 zv 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 echo of her shijvg(-co exe3lc;g 7efj4zn/ k)( -adout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s a( cg(-/n jkf cea4 7je-il);3 vzdegoxfter shouting. Estimate the length of the lake. $\approx$    $\times {10}^2$m

  A sailor strikes the side of his ship just below the waterline. He hefmas 7likbz6a +)+vh6ars the echo of the sound reflected frm6iavb+6la zsfk 7+h )om the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $\times {10}^3$m

  (a) Calculate the wavelengths in: y,0usgna9k j air at 20 ${}^{\circ }$ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. ${\lambda }_{20Hz}$ =    m ${\lambda }_{20kHz}$ =    $\times {10}^{-2}$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $\times {10}^{-5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy day. Wxk)lry qk0 b5id:k+/fithout warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How: byd)0k5krlqfxi+/k much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliffb1mkc6su6o, ez6j q; o. The splash it makes when striking the water below is heqk1 s,jozo 6e;6m6cb uard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concr )kedt8adis p8(,zr/f ete pavement. A moment later two sounds are heard from the impact: one 8dedpa,/ rsk 8tfiz )(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.$\approx$    $\times {10}^2$m

  Calculate the percent error made over one mile of distxy,eu( sxpn3+kq+ v,n ance by the “5-second rule” for estimating thq ep3v(,nxy+ +xukn,se 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 saniksraqb* u68w )k(x+7yrq ( ound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $\times {10}^{-10}$W/$m^2$

  What is the sound level of ahuiv :.0rngg8xz, y 9- satxi.r2ero: sound whose intensity is $2\times {10}^{-6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when firedrxq 4pi8h6*h.l1yz6pojdu.j t-n6 l x simultaneously at a certain place, what will be tl6q1 y6 dxzriox. 8 hp*4uhjltn6.pj -he sound 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 noisy jei3j 1kl9mg:2rj vnq*dy ,lz,hn f s)*bt engines is e* ry i9q)1ml,sk: nfg32z jldhbnj,*vxperiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, ewzgmu u589ozwa*1decj h616lcda 29whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise ew z5ma2a*jl6zc1d6edg9u8uwo1 c h9for each device? 58 dB =    $\times {10}^5$ dB =    $\times {10}^9$

  (a) Estimate the power output of sound from a person speaking 1-dod;f4y ;xvf4erauin normal conversation. Use T; 1-oyad u4xrfefd; v4able 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $\times {10}^{-6}$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.]$\approx$    $\times {10}^7$people

  A 50-dB sound wave strikes an egj3telko2n;zou-i + )buz 31 xardrum whose area is $5\times {10}^{-5}{m}^2$ (a) How much energy is absorbed by the eardrum per second?    $\times {10}^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $\times {10}^3$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B is ra, /ik9 wn+fr-jvxwgp,at;j y :ted at 40 W. (a) Estimate the sound leve k/wr wxyi j:,tj,pag9fnv +;-l 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 pldlo,*r 46reyf u5a9 bjaced 2.8 m in front of a lor, 94 oryfd jle*5au6budspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $\times {10}^2$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $\times {10}^2$m

  Human beings can typically detectji1*f d;xh0fob;7ag t a difference in sound level of 2.0 dB. What is the ratio of the f;0ia;bftd7h*g 1jox amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, u jt: b+rst8t;(a) by what factor will the intensity increase? Increase bysj:u;8rt t t+b a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twicy;kjxbe :q* 1me the frequency of the other. What is the ratio of their intensities?y;: *ek1xjmqb   

  What would be the sound level (in dB) of a sound wave in air that correspoe73 -s-ogg mjrnds to a displacement amplitude of vibrating air molecules of 0.13 mm at s-mgr3g-7 oje300 Hz?    dB

  A 6000-Hz tone must haveo78 yext +fm ;ad;n8vs what sound level to seem as loud as a 100-Hz tone that has oaf8xeym+ 78 n; t;svda 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detec56opnq l9// vba rhrq*jg fy+;t when the sound level is 30 dB?/*6j/ yql oqb9f+rapnr ;h vg5 (See Fig. 12–6.)

  Your auditory system can d0w n2hiv1ui4 accommodate a huge range of sound levels. What is the ratio of highest to lowest intensity 4v2u0hid i1nw at
(a) 100 Hz,$\times {10}^a$ a =   
(b) 5000 Hz? $\times {10}^a$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frkms x vwhl,p,e0w* p0ys-z. c hb/,t )vdg/qj5equency of 440 Hz. The length of the vibrating portion is 32 cm, and it has aqk)y ,vjwxsv0 /*lct ps de5/.0m -zp,hhwg,b mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 6dhvit6pppj/o2. 1o jcm long. What are the fundamental and first three audible overtones ivtopo.2/1ih p6 j pdj6f 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 yw0/5fn8+wuxz iy ot6vou expect from blowing across the top of an empty soda bottle that is 18 cm deep, ify0fv/itwn8x oz +65uw 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 orsr)k x h(ph .yx*e3p(rgan with open-tube pipes spanning the range of human hearing (20 Hz to 2y sx)(h.xr pr* e(k3ph0 kHz), what would be the range of the lengths of pipes required? $L_{20Hz}$ =    m $L_{20kHz}$ =    $\times {10}^{-3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. What wc9mcwg-(nf*jbb b7i,x* k9uyill be its fundamental frequency if it is fingered at a length of only 60% of its originalbgywn*(m,xf i9jc9u bb*-c k7 length?   Hz

  An unfingered guitar string is 0.73 mm1oiu a1at82dzbw20 k long and is tuned to play E above middle C (330 Hz).k u2daw1m 1iaz b8o20t
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) when;wp-5 r 1n4lc6b :huiqf s,zou the tem5qu: nwu1r l;-4hczob,if6s pperature 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 ,7xtw)o1cdg i0e twl:20 ${}^{\circ }$ C. By what percent will the frequency be off at 5.0 ${}^{\circ }$ C?    %

  How far from the mouthpiece of th4pq):ln qlkwo k::cl4 e flute in Example 12–10 should the hole be that mustpq l o)k4:l:w :4cqknl be uncovered to play D above middle C at 294 Hz?    m

  (a) At T = 20 ${}^{\circ }$C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resoni,q)f 1dxolvm3 23fhpmlb 3x/ate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show l/mixvf33 o ),lm3hbd2xp fq 1why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at twu6( lp+r sdlt/2 nu)ufo successive hau(6ulr/lt s+ 2n)dpufrmonics 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?$\approx$    $\times {10}^2$ m/s

  A pipe in air at 20 a gd qkcd- g58u92bc/r${}^{\circ }$ 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 wb p,p7h4k1*v w;( lj20k8saxca eoeb the audible range for a 2.14-m-long organ psw ova bkbjw,7 e;lh4x81p0c * pek(2aipe at 20 ${}^{\circ }$ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.d;9mn ct mg6u6 kv9jo,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 stnmkm 6 vjtudo6 9c,g9;anding 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 when trying to .lu2s0g2q ufm3x3 dg aadjust two strings, one of which is sounding 440 Hz. How far off in frequency is 2g3 f 0uxg dsmqla3.u2the other string? ±    Hz

  What is the beat frequency if middle C (26 lj+udadmo6cg 1 7b+y22 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) opera)10(p 9hyflvzd.ioms tes at an unknown frequency. If neither whistle can be heard by humans when played separately, but voisz. 9pdfm) 0h1ly(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 tiilq*14j /izmuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the/mj1* li4i zqi vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same freo: e+: nxlziic);pi6cquency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are ple;x6ci: co )zilp+in: ayed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle Cx50qw rf-vel)4 j0ba v42g wym (262 Hz), but one is at 5.0°C and the ot0rvy4bgm)jq v0fe5 a2 w-l4wx her at 25.0 ${}^{\circ }$ C?    beats/sec

  You have three tuning forkswqyq ,ucrx)5e6;n u)smu (*uw , 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.6u (uq uw5 x)wyu;,mscr *)enq 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 stands 3oe0.hvex s/soe-e.k(w7 is7g.00 m from one speaker and 3.50 m f/ vwxs.o0i(e.ss -7 eo eeh7kgrom the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 ${}^{\circ }$C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz,1)ahj8;jpl8 nmwd 7oy;m fw,s but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating da1mlnp h ,)mwo;js;wf87jy8 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 wavelenguhp7)a 3nud lnnzk21 2q2c(av ths 2.64 m and 2.76 m in air. How many beats per second will be heard? d) 7uu2aapl nv2k1q (hncnz32 (Assume T = 20 ${}^{\circ }$C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is uw5b2o-j68)oycp m dc*q zd sikk3)0i1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 c)p dsyjco2 i-0k k mb*8u5iwoq z)d36m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire en;lu.vc ys+1 t cir6p,fgine whose siren emy 6.s pt,vcli1fc+ur;its 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 g)2 xjsud)jv b;/zba w( -:bgrpzg)mpnh,)2hyou at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Ar)d pw2gphbnm) gbg,(v/ r 2h))xzubsz- a:j;je they close? $f_{sourcemovine}^{\prime }$    Hz
$f_{observemovine}^{\prime }$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f_{sourcemovine}^{\prime }$    $\times {10}^3$Hz
$f_{observermovine}^{\prime }$    $\times {10}^3$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f_{sourcemovine}^{\prime }$    $\times {10}^3$Hz
$f_{observermovine}^{\prime }$    $\times {10}^3$Hz

  Two automobiles are equipp2)ixbgem8 9 i6 f sgbnvr)7;xhed with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is mnbe; h 6s2vf) xix7 rb8gig)9the frequency the horns emit? Assume T = 20 ${}^{\circ }$C    Hz

  A bat at rest sends out ultrasonic sound waves at iier:uh(tvi-c2 , dh ;50.0 kHz and receives them returned from an object moving d(t ivehi-u:c2; ,i drhirectly away from it at 25 m/s What is the received sound frequency?    $\times {10}^4$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it fli-pp , e+vxwjk2es, the bat emits an ultrasonic sound wave with frequency 3xepj ,p2+ wkv-0.0 kHz. What frequency does the bat hear in the reflected wave?    $\times {10}^4$ Hz

  In one of the original Doppler experiments, a tuba was played sf; wau4s8c33qkv bj0on 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 frua b3 c03qjfv;kwss 84equency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measyw-tlax3--e kx6,oj1)j hyvuure blood-flow speeds. Suppose the device emits sound at 3.5 y t3jja6,y-)lo vwuh-xk e -1xMHz, 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 frequency v- cg6.hp.sh6 bn wmz2$2.25\times {10}^6$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 $1.54\times {10}^3$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle em du*ud:iw )oo3its sound of frequency 570 Hz. When the wind velocity is 12 m/so*3)iodw :duu from the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 ${}^{\circ }$C

  How fast is an object moving on land if its dfwy gy7*e ;mur2we1+zmklo )+ bw;2bspeed 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 (kgq ;(ifdl7mis 310 m/s (a) What is the angle the shock wave makes wi;l((7fqkmig dth the direction of the airplane’s motion?    ${}^{\circ }$
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of.j v axbra o98urlu xzcx383zmn(;8 w7 sound is on98n.;8cjuzx uor3b r37wzxax vlm( 8aly 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 tgprjs yb 1cb(2h0sg./he shock wave angle it producess c.ybp/g s(2b1g0jh r
(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 fgpvc04w (/6cgqce kia8 j2/j$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see akkflqz4g,6pxb5)3)qqy h wj 9 plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the soni) 6qq34hk9,wxg )yzjf 5lqpkbc 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 n-b5a mqhz- +pf4tz;fsonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to wf5+abqz pm4t-hz- ;fn ork is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in 44pta e8zqt1 g14gmqothe human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dis -9p;0y imjmw0mo/wep k6:tgg play called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both ends. /pig9:wy -k06wgo;m emm0t pj
(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 makesqlvbo uh1b+7bl0ek4 +zo8b0j a sound close to the threshold of human hearing (0 dB). What will be the sound level ol 0oub+hov+e8q1kjz b47lbb0 f 1000 such mosquitoes?    dB

  What is the resultant sound level when ans;ick j(wm 4xabh, c-gs;b*4 r 82-dB sound and an 87-dB sound are heard simultaneously* b4gas-c,mx4;swhb ;i rcjk(?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. koj 02i nbfpj:00o,v2lw7d*iwv vcd)What is the acoustic power output (W) of the speaker, assuming it radiates equally ink dbd jv22*,0fj:)0i0iwcovwpnvo 7l all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dx xir; v1+4rvzrops by 10 dB at 15 kHz. Wiv +r v;4rz1xxhat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically w+wq:r t ;pt2yl*o g-ncear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, c ntl;: oqy*r +-pwt2gand that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicationshxag:,;je. r0 e7 pwxk dei g5;zq*)ul systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequ k 49dyvt3bn*qency 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 a b, :zx;j-e*o:+p apjcey.wbwith a fundamental frequency of 440 Hz and a mass per unit length of ;* b.eoa+jpw jb,x:cp -ayez: $6.1\times {10}^{-4}$ kg/m
(a) What are the wave speed and tension in the string?    $\times {10}^2$ 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 tubxa0ohf oduudv (hv h5.e8/-z; e 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 at 0.395 m. What is the frequency of the tuning f hd.u8xo( /0ev5d-uvhhafo;z ork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube th2h3.c+-gx dxv2 *mgdv4voyjy6 t tm0 rat is open at one end and also 75 cm long. How much tension should be in the string if it is to producemd2 2-th. v xc4ryvvg3tmo06*x+jd gy resonance (in its fundamental mode) with the third harmonic in the tube?    $\times {10}^2$ N

A highway overpass was observed to3*x(ejoany a4 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 500–1000-Hh0tz 3m4ap5je 6eb(f i* 6ixttz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine b56 6e0ip4h*tie jt3(aztxmf 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 whis o m+ unjd4dw+zln6c5xj l61c+tles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the+c46zoj 6n1+nl d+duw j 5xlmc moving train?   m/s

  The frequency of a steam train whistle as it approaches you is u 0(tr aliji.,538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume .riu(liat0, jconstant velocity)?    m/s

  At a race track, youi / 0g3cb*dbknbu /hqn0tc)4t can estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and recedingk q/c 3h*tgc)/b b00ndt nuib4 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 togeth yggc80 86tnafer, produce a beat frequency of 11 Hz. The shorter one is 2.40 m l8cgfay8tn 60gong. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a ,f-;a hg3:+jmunnan c 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 th njuhfm:3- ag;, n+ncae observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normall;ju0owwq0/pf ni3c8. uhewu ur9 u) d9u6) yizy about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were d 8nwf;69)/ zp09ywu ujiu3o )0euqcudi uhr.wirected along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54\times {10}^3$ m/s   $\times {10}^3$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward the :0 nd) ;d1kuqloqmiei;8,kpz bat at speed 5 m/s The bat emits a s1)d; u8zlpeoik;kqq d0m,i :nound 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 appriygmrwxx7(s to.2i3pdew 53 -oaches a moth. The pulses are approximately 70.0 ms apart, and each is abow3rx32ti i -(pdye mgw57sox.ut 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. 12–38) was once usedh vl0n1es/-p u-bqh.b 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 overtonhq0bsl nu.-ev1 -hb/pes 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 na*e da* hbn01be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodesdn0a a*nh1*eb. 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 a s)o7lbs6rmby2c 7zd3 q5 2croxrz4 x3luminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hax2o sbrzd3qs 2mc cl74y6z7 o) r35bxrnd. 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?    $\times {10}^3$ 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 ear at u5* 0sei 3hoaba frequency of about 3aouhe50 b*is 1000 Hz is $I_0$ = $1\times {10}^{12}W/m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1W/m^2$ corresponding to an increase of intensity by a factor of ${10}^{12}$ By what factor does the displacement amplitude, A, vary? 10${}^a$ a =