What is the evidence that sound trave n8 :xtkgst97mls as a wave?

What is the evidence that sound is a formi1i z:*-qhh vbg go w)v1 ex;ro2;j3dk of energy?

Children sometimes plhmn. +dz1rc 0ec1 4waxay with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is streh a01x edzn1cc.w4+mrtched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do youoi8cgdijtsal)+u63 / u h-/aprj0cy3q)i;lj expect the frequency or wavelength to cgl + /pd0 trus)o/ u6;jca-j3 aj3liq8i)yhci hange?

What evidence can you give that tjl 6u:.t xrl2qhe speed of sound in air does not depend significantly on freque2 .6xr ltqlu:jncy?

The voice of a person who has inhaled helium sounds very high-pitched. yp1 v-zy()fhm Why?

How will the air temperature in a room affect the pitch of organ pipe 7xp9bd,siq7ndz8p 5 gld/3qhs?

Explain how a tube migrd1hgpmtq 5buv;8j-2 0wc hy /e4g u/ght be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example isej p bt2 qr gu1/-dw8m4u/5 0hvyghc;g a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move l.:/zof0fhop-1gxfsg5h 8fm( dr +uk up the fingerboard toward the brx - 0d8o. uf(5fsrl1g: +/kzoh hfmfgpidge?

A noisy truck approaches you from behind a buildi-squpqtl(6w(/j u/y sng. Initially you hear it but cannot see it. When it emerges ant psys lq(6q( wj/uu/-d you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas u,dy,r c e +1g6pjdp,kbeats can be said to be due to “interfer+cud6,pdre, j kg ,1pyence in time.” Explain.

In Fig. 12–16, if the frequency of the spea5yuiyy5posw .xz)j9 2kers were lowered, would the points D andiysx jw59.ouy25zp) y C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protectinjp k);t1bm6z8b.fwco g the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, 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 thotjmbc;68p1b kz .wf)e ears?

Consider the two waves shown in Fig. 12–31. Ea7 gcthm bo5y:2keo3 bt4-/a foch wave can be thought 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 the two component frequencies farther apart? Ex bk7b 2ocgat h:y-to45fem3o/plain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observel 4d od;v/u ofl(p, u.hrz- dv5kp6s/xr move in the same direction, with the same ve, ol(l khrp5x d/.dv-du6;z/vof pus4locity? Explain.

If a wind is blowing, will this alter the freque; v1k3oiol)z ,g wx o+pi37i can)a3rlncy of the sound heard by a personi1o3kaiol7+ 3ivl)cp) z3 rnow,ga;x at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child i -+j)8a rcsk 5favilsav.4 )qhn 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 the child hear the highes r lsa jsvhf)+8.)4iqaacvk5- t frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening fc 1l1u.i fbwdv-;4c suor the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s afterclb1siu- .c4 w;f uvd1 shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just bel1 1lurpg (ylr))0 ejs2sr*3mo)atkufow the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume theraypll juu)rt(1omr) *02fs1e)3sgk 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 wavelengthsv2m0a huu2bu* g 9uwui0t 7p4k 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 sc4g f 0:uen2cbg/0tqbsy9pinhj ;:5p nhool of tuna on a foggy day. Without warning, an engine backfire o ;5 : spnu49i/b0cjeygtqf n02:pnhbgccurs on another boat 1.0 km away (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 top of a cliff. The splash it makes when striking umehj (w9) vi.dx+ly f(/q p7p8xvkn 0the water below is )q+y8vi0xjdx. /mpk hw(u lenv97(pfheard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees aojsao rguiey,. 16k+9 huge stone strike the concrete pavement. 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 apar1k+u.s igoro je,y69a t. 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 vrb48hrw , nv(by the “5-second rule” fo 8( ,n4hbwvrrvr estimating the 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 6nnxi+; v9c1qpufg6u ,zf.jxpain 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 ;xig ve)97kqp of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers pro9zx5cvoql-iuq mr7g6jgb 2: 2 duce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’u29j : g-z6xqrol im cg5q7b2vs.]    dB

  A person standing a certj wy/,g8im4h 4udml0h qk0xr5ain distance from an airplane with four equally noisy jet engines is experiencing a soundukgh5 h m4my/0 qx4 j8w0r,idl 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 ojm4shyo- : j1.qmg4mgf 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for eac g smg1jom4j :hymq4-.h device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speakingp n q 4am2/q-o9nt7io8mwx r-cr4ezm* in normal conversatiotio4wmrq 9rq p --nc nem7m z*/4o8ax2n. 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 strikexxw-9r4tz0 zrs an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the mo3 *mwvy3g1hys26 imu r4e8fvzre modest amplifier B is rated at 40 W. (a) Estimate t 3v6yzu42hgi3evrfy81wmm *she sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registksn7g ;,;xr5bhtg;1 p*eywqeered 130 dB when placed 2.8 m in front of a loudspeakb;gq,kh;; e1 g5t wxp*er7 snyer 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?$\approx$    $ \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 differp6) xfcme p)8v/ fjty:7kva0ience in sound level of 2.0 dB. What is the rapyf:c7e8vjkmv)p a 06f/)ixttio of the 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, (a) by what factorgl;jn fm)j i63, u7 zvi+,lo2j+h oltp will the intensity increase? Inh t+o;i flm)i6 , ljgv7+jz3pn,jl ou2crease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement ,7it p f h:jl9iyxb..tamplitudes, but one has twice the frequency of the other. What is the ratio of their .,x.hyt:tjiip9l7 f b intensities?   

  What would be the sound l sqyemg(e) (0qqdx3o (evel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecumge()3(( y qosq0 qxdeles of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone g37mw//aetrgzvp,x(et bk4 :.d 7 dfm that d(k7e fedm./ 7 t 4wva3z/gtbrpgm,:xhas a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can d)s,2 /j ahuwkcetect when the sound level is 30 dB? (See Fig. 2, scujw/ak)h 12–6.)

  Your auditory system can accommodate kq a,plmenk;44d7qeks)81qm a huge range of sound levels. What is the ratio of highest to lowest intensity atpq,eks; en4 1mkmq ka74)lq8d
(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 aowd7*1f2 zxs Hz. The length of the vibrating portion is 32 cm, and it has 2af1* xo7wz sda 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 three audin;7a-c: an4ildf *o;qc2eh aqkop3(jble overtones if the pipe is fa hel:4nia;o;n3 27j*o( d-kaccp qq
(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 bluya 0m5f,c1l: , c/6kholqgjd3moee) owing across the top of an empty soda bottle that is 18 /0 3l6jou hyq 1 )5fm ,laedkg,cemo:ccm 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 pipgzp/jqy a9vto (,b7,ppd 9lm6e 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 pd(,g pzymv69j7/ppt 9 b,loqaipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency c k 3,c:1c5 u(unmrxkhof 540 Hz as its third harmonic. What will be its fundamental frequency if it is fi,5c1uh(r: kkuc mnxc3 ngered at a length of only 60% of its original length?   Hz

  An unfingered guitar bbu ytl xg8*:0o 1znt:yi+ho(string is 0.73 m long and is tuned to play E above middle C ((i8gnz+yxht:lb 1o0 :ytub*o 330 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 emits middle C (262 H/i;oad v+ 40 w ky/h)molxlf4ybnzy2-z) when the temperature/zhy 24 dnm ob+/a)vikwlo y04;-l fyx 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 a:s (lx.6 x8yupjnqaf: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 12–10 should the hole be thca6ws- sw/0f hat must be uncovered tws-a/0csf 6 hwo play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 6-vt *) u*cdeuigj0 i8q16 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closei*vqi -u jedgcu0*8) td 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 sz8hl2e-q i0oends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz-0shl o8q2iez. 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 g /0s:oh b .hg bfzx2qs;u*zw-$^{\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 th bj3bhdn/5086 zptvsv e audible range for a 2.14-m-long organ pipe at 25vnz0 d3bsbhpj 6/8tv0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is ( ;(glx c bjl,/;hgnib 4lb:qvapproximately 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 cc(g 4lb vj,/ing ;qlh(lbb: x;anal. 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 g ziu8n9 j7+9nsui6p z2.0 s when trying to adjust two strings, one of which is sounding j+uz8 uzni 7pi6g9ns9440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle )q n3eb3a/q reC (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 1cv i:;9la -uqh3 bf4ghbrp4s X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occ1bf 44qapi:rl-v3ub hg9hc;surs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 3xtkwv /)y)9iyh3mx:m2 lsj )d50-Hz tuning fork and 9 beats/s when sounded with a 355-Hz :jtml xy)s/yx3 )h)vw9mk2idtuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the sam.y0xo3xq*kj70xv 1grca lk1fo ue 65qe frequency, 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 plafr uqvxgaqk0.167x5ex klc* 0j3o o 1yyed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical c (2bjdr6c1welst: :fflutes each try to play middle C (262 Hz), but one is at 5.0°C and the o edcbcrf1 2:l6swt:j(ther at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B hpo) 6la;v(vl)cnl9 kld5a )rn as a frequency of 441 Hz; when A and B are sounded together, a beat frrv5l kn v;pn a)a )od(cll9l6)equency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m fromlt0z hem 8f4ni(0bvp9:r ;ede one speaker and 3.b 8te0(e 4riflzmvhn0e pd:;9 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 are supposed to be vibrating at 132w k(;xbu5c; +ofd pgj. Hz, but a piano tuner hears three beats every 2.0 s when thgduo(5 p +j;.fcwb; xkey are played 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 h*y336hy+15vy o nc ha(fwq4a cyntn02.76 m in air. How many beats per second h1n fco+ 3y c0 wvayyy4*5tnh(6an3h qwill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engj dzox qhi n 1:54lia9-1nfpy6ine’s siren is 1550 Hz when at rest. What frequency do you detect if you 6 nx5a:qi9zp1yl fno4jd-hi 1move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do yb j0g*9o;r( w ev1ld 2dwe0ynyou detect if a fire engine whose siren emits at 1550 Hz moves at a speedrw (lowen*1b9ydgdje 0; 02vy of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-H*:;c grv-r-mx*:lxyfejai gf7+a/ z qz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the sameq - :; *far-fagyvm:e+*lrcxji xz g7/? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single fc3 r+) h g+bkalx5zai.requency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hear.)b azg3lr+i +kachx5 s 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 ultra0io2 7psk k+0w3qxllb sonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequencb+23okw0p i0sk ll7 xqy?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall atcnsyq0z 0tx5 gc;u(n: a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 gxzt n(cu:;sqn00c5 y kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a mogkoptbaiiev -x f -s(x8:,1k81sxz3 rving 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 station a8 zk e(oigk 3bx8xp-assi1rt:f-1,xvt a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-f ;zuv .;ccj /hds37qetlow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly awaytqse j;./h3d7c;v cz u from the sound source?   Hz

  The Doppler effect uskn .ewl79,r) c5s3weo .vknuas,w tq 0ing ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound rm6;wjbb 0o8tof frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hwm8o r0jb6t;b ear 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 rf v;,; z ml3n+r hktuah6:4azits speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound za,vq7 p/h,pw* psud-un7,ujis 310 m/s (a) What is the u-,p h, p7/adsnuqw7,zjp* vuangle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a plard57 ,t otxtj,net where the speed of sound is onox,7,tdt trj5ly 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. 9/u4vplh-o,w5v4jamb g0f ghDetermine the shock wave angle it produces9-,4/ gg 4vupaohfmj5bl 0w vh
(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 .sq)8jpn3 bcs3 hw ;fm$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exaceic; g5l8v-c+j u6g)mdjt-mctly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2gmt v)jj85ci ;egu c6 lc+-md-.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 d bw fxbxm0: tq4(*8ysdevice 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 work is 200 m, what is the minimum time betweensdy m:*tq 84(bwbx0xf pulses (in fresh water)?    s

  Approximately how many octaves are there in the hr ;5 vi3pm98g/ztwqta t ac,;numan audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It c0 l fadndusvkzg: s9 0us(;q25onsists of many plastic pipes of various lengu05v 9uazss0 g;s(:n 2ldfdkq ths, 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 threshold of wv,e5v-- q4qa;rq7vvc;s3n. d xtwp shumvsw eqq3dsc,wt7p4v n x5v;aqr -.v;-an hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sounigbld+ cq-3* y28zxsk k:zn1 qd and an 87-dB sound are heardx:l3g-i 8z2qk +1kn*cyd qzbs simultaneously?    dB

  The sound level 12.0 m from a loudsnn:8,hx)lpes7 re vy pq c/c9.fhu51mpeaker, placed in the open, is 105 dB. What is .lucev/pner :8y)1,f 9 pxq5 hmc7nhsthe acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outpy7 vcen acl1dp03(+ya ut at 1000 Hz. The power output drops by 10 dB at 15 eydv a0c7(apyl31+ cn kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devilqud+ kv+nuh9/a7f) eces over their ears. Assume that the sound level of a jet airpd+u+/h l)qea9 k7fvunlane 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 engine?    W

  In audio and communications systems, the gainm2xh ;uzq1jdgmq7v/ki3)91uoeoqs7 , $\beta$ 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 fr 3h)* +f/uwbwzbrgsh6 equency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long beta8yuj+rw53x4n /jo9/g bdpycween fixed points with a fundamental frequency of 440 j9u4y/d rgap/b3xj +c wny8o5Hz 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 into vibration abfczfm cz(xq)-1n.of;(vfge4 ove 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 opzz-f mn 4 f.x1fc()f (goc;qveening 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 nz7ianj,ldp g ibf0vf.**,8bg is near a tube that is open at one end and also 75 cm long. How much *na ii7b* f.,0nfvjz,8bldpgtension 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 resonate as one full loopac yp0*upj,2i ($\frac{1}{2}\lambda$) 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 500–1e- -5 yjcrh1rhzuatl+ )7xa5x 000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m faruz5c e1-hjrr7) -ytx+x lha5ather from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. v -mkhd0 c5i:eOne train is stationary. The conductor on the stationa:h 50cem -vkdiry train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a s7 b.cjh2urid/drerpq; x7k .hb662gwteam train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocityh772 .rbrqd66h b kc/;uwpjegdr2ix.)?    m/s

  At a race track, you can estimate the speed of cars juxxxbd34k0iq lph+ q r+1baeb6-4 d 5ycst by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops b53 6a di -+lbhberbx xkqcd0pq+14yx4y a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, soundiyzypr/ nr.so7z vn*4 -ng together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the other rz./zps-4nvnoy * 7yr?    m

Two loudspeakers are at opposite ends of a rabvf-lv kpfxxr0, c(6*ilroad 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 s(xvb*,fvp cfrl0k-x6 peakers after they have passed him, at C?

  If the velocity of blood flowtpgql,kl6 1vq8y4l 3 (cei v(v in the aorta is normally about 0.32 m/s what beat frequency would you expect iegl34,8( 1vvklqtv( yp6lcqif 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 the moth is flying z64p9mwlukx;9 jn q 2jtoward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. Whaw2j 9lkxupj;46 m9zqn t is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series ofr p)gpup judq4 53(l:r high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 msr34 (:pdqppru ) gulj5 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 oncehu6i uo as;s)l b 0m/n+f;-uno 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 the fundamental frequency of this horn, and whic) luh6 snon+-oa m0ub ;f/s;uih overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be comprekf7wn 8qcco2n0 jsi z1 h2(0womised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this rooc(sqkhezin7n 210jwo w8c 02fm.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods*m5 2f.eh -o8axaz.jencru9 s,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made5.9 8cerexs* huafo2 ma.znj- to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequency of ntwhjakgyiec /s,1gu88 1f/x: k ib1 0about 1000 Hz skbj kce 1x:1g// 8u8 htgin01fa yiw,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 observznzp *b+qt(ntsi /hf*ezl3f v 3cb6*4er on the ground hears the sonic boom 1.5 min after the plane psqe*6c*n3bttf4i3*/b z hz zpn f l+v(asses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboa0zfahoz*bbmpu(i nx*t55 4f3 6 o6x ugt is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h