What is the evidencezo. :i0g exslh z-y.f/ that sound travels as a wave?

What is the evidence that sound is a foj );rjykwe;9mdua2r. rm of energy?

Children sometimes play with a homemaraavqe6*v3x 0fu*cj5y m8 -qbde “telephone” by attaching a string to the bottoms of two paper cups. When the string is str0fvvc5qux* a -b*6 my8qja3 eretched 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 - oigwm8 ii.g.j6g(yi from air into water, do you expect the frequency or wavelengthj8i g- y6w o(ii.g.img to change?

What evidence can you give that the speed of sound in air does not depe*;4jrdff,rf dwy-;glo2, pc hnd significantly on frequer rf4p,-y; d;*clof,j gd w2fhncy?

The voice of a person who h w0 7.fkwhf,qhas inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch ofl/*4erwm,2g3ajh wzql k 7r t8 organ pipes?

Explain how a tube might be used 4)orc/(gryfnxiu q,1lm :.jv as a filter to reduce the amplitude of sounds in various /n,o.) v(u xjqiy1r4fcrg:mlfrequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced c k/4idk qs21fq4fcv -dloser together as you move up the 4 -ksf2dvfq c1k d/4iqfingerboard toward the bridge?

A noisy truck approaches you from 3h-q /e; ewfcebehind a building. Initially you hear it but cannot see it. When it emerges and you d f/-eche3 w;eqo 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 injoar1v nyb/p lr;m*-. space,” whereas beats canvy1 rom. /-;nplr*b aj be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequeg;ve*s31 vpsyx6b w; vncy of the speakers were lowered, would the points D and C (where destructiv3*wp sb;vgv e v6yxs1;e and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with - tlz70u8;1t wpv2fv*lc lhf kb6c;zf1btt(w 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. Instwt0v l8ltff 1hc6 l;-ztv; 7pw*zu21b(ktcfb ead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thougg5nz0 h chm7(pn5t/ ziht 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 a( nhzitmghz n7c505p/ part? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source akln;a ym 96bu/nd observer move in the same direction, with the same ve u9l;yna6b/km locity? Explain.

If a wind is blowing, will this alter the frequency of the soukj ,4p m1s6)hir jdm+bnd heard by a person at rest with resm,4 d kjb1i)sjh+ prm6pect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a cj dmd9nl8j)v0m0i gf:hild in motion on a swing. A monitor is blowing a whistle in front of jv8)d0f mngi:0dm9lj 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 oby.gxn:w. f) kf a lake by listening for the echo 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 of th. gby.kwf):x ne lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hea879bo+np c7+c c ygingrs 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 the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with dc 8cb++7yc7nn g9goipepth.    $ \times10^{ 3}$m

  (a) Calculate the wavelenlnw6qdr- 3o/m gths 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 driftingkk0e 0l36i nev just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses befok0e3ev0in k 6lre 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 make 7)biclux3 *wc-q,sdt dnk2al*/one9+pnva ,s when striking the water below is heard 3.5 s l*tn,d+dlpeb3x c * 9ukvan)7-aw qi2 s,l/conater. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the conok0f+ow zj8 d.crete 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 apart. How far away did the impact occur? 8kzdfow+ 0j.oSee Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent erry,v qna ce+;7 aa)iri.or made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temper, .ae7n;yiiqvra+ac )ature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dBe8 9cobc19+ais d ckpq(m2jhagq1 r *+?    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 9p ro2lvr9ik57 o2u gssound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level hwb( 3tz5ij)mof 95 dB when fired simultaneously at a certain place, what will be the sound level if only onej53i)tbmh(w z is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance f83q0f wyxjb6*nh8rvel /g ojku/p .c8rom an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the 6vg8k / 8 j*lyw 3o/unpb8xj.0hrcefqcaptain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said t./o*vsm )vmg +vs;l mzug35 dmo have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise fosd m*lgv/o mm3 +v)uv g.5smz;r each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal cwdovmp h i:wg7(4 (4xsonversation. Use Table 12–2. Assume the sound spreads roughly uniformly ow m 4 (io47pgvdw:s(xhver a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area uwbzea;.82 rc/*t rdj 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 more modest amplifier B fxqh3v+5 e:ei0o2clj 81yz id is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in e xceh32l 8 y+51i0 vqi:jdzofturn 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 whe7m7kk nhk ;-ven placed 2.8 m in front of a loudspeaker on the stagee nhk 7vmkk-7;.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level8hda k;h8 x07x4wj.e)pcw lvm of 2.0 dB. What is the ratio of the amplitudes of two s7ehjkw0dxv c8)w8ap h xl4.;mounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) *ccvyi1c i58 bev8x 4 5qv:trh/, wcmeby what factor will the intensity incevb rity vc1:cc q55ci/ hmx8 w,*8v4erease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice th h+ fbhenrw ;p5t+-q(:3mzlh xe frequency of the other. What is the ratio o-mqbp+e(f h;zl+:5hrhtn3x wf their intensities?   

  What would be the sound level (in dBj/vaq u26:olwo g(ypg2vp +w *) of a sound wave in air that corresponds to a displacement amplitude of vibrating a v w/gw2ujopaov6 2q*+lygp(:ir molecules 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 tonh *+ayq3tlxg 6e that has a 50-t*gyx6lq a +3hdB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest 3zu/v 1hpmq8g frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–3vhp1g 8qz/mu 6.)

  Your auditory system can accommodate a huge range of sound lo g v;n+fvh3af ;))shhevels. What is the ratio of o ;h3agvfhv)+nf;h) s highest 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 freq)brc y cep0z1(uency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed? cb) (e1z y0pcr   N

  An organ pipe is 112 cm long. What are the fundamental and fwg*+oh)wov 8r*(oga1 vi 9c jpirst three audible overtones if the pipe is()o iv8*vgw *ocpho1r+ 9jwa g
(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 blo lhecq b7,3e)a :ii(iuwing across the top of an empty soda botti,)e i l:7i(qeuh3cable that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes 4f 9-dzeh5b qhspanning the range of human hearing (20 Hz to 20 kHz), what would bee4-bhz9q5 hfd the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its thir:z 8sp;nshi4np8vog ;z1a ;rc d harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lenc v8in1 hgo;apz 8s; 4rszn;:pgth?   Hz

  An unfingered guitar string is 0.k+)8 fkhunb+y rwr m-473 m long and is tuned to play E above middle C (33h48m- w++r)bryf uknk 0 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 ):pxrtwxu1j g lsa86a6.uh y/Hz) when the tempera 8l:a/uaxs616 tx)h .ujrpwy gture 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,gy2mxd xp /p( 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece o dre;m5y49ew61vg:cvhb4t t lf the flute in Example 12–10 should the hole be that must be uncoh4v95le1:eb6;dy 4tvwgr tm cvered 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 resonate at 264 Hz, 440-y+g8vep z*8bwkl o4xl 6:gni:k0i xo Hz, and 616 Hz, but not at any other frequencies in between0x nv *68xow pi+kykbgl-o ze:lg:8i4. (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 gdo0 wc8bl0n: 1.80 m long is open at both ends. It resonates at two successive harmonics80:nbodcgwl0 of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 h v9iwn ,yfslijia6m;-p)e3k4s-w ;q$^{\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 av 5atc6 7u2aix84k gjzudible range for a 2.14-m-long organ pipe at 207v4tx8 2 zuc65kjgaai $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. Ijsf 1 7erqbb1g)om)/ ndh hv/;t is open to the outside and is closed at the other end by the eardrum. Estimate the frequ1)r gm1h;/hjnf7/eo)vbd s q bencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat- ofv 71csxdx7 every 2.0 s when trying to adjust two strings, one of which is sounvs7fc 1x d7-oxding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequencw ti;;* wn/lcby if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operatdkya en vw.+u* 6xc2bh1yut 89es at an unknown frequency. If neither whistle can be hear8dutxy9ab6k ehn y*u+cw 2.1v d by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork an7qjjr ( 3 akk:dpy1ku0d 9 beats/s when sounded with a 355q aky dj u71k0k:3r(jp-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the samebd(u5h .vp z2k frequency, 294 Hz. The tension in one string is then de 5kvhb 2pdu(.zcreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle 6n2gk8q(e jxm2n+h yjC (262 Hz), but one is at 5.0°C and the o en6m8kjg2jqh+ y2x(nther at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B .4eqvf)i83w svwh *vzhas 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 to) f34v sqweh* .vviwz8gether, 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 i4l wisyb5w;kps x4 *(from one speaker and 3.50 m fr (4x*wkwil5y i4s;bpsom 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, but a piano tuner hea)6xbvp6 j2gw b ofr(.ars three beats every 2.0 s when they are pl2rabbx6 j.6f) ( gvpowayed 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.-ovk6 txb .v ;fc8 zz6hqb*r/y How many beats perfrz68kb- yh.t o6/qbzcvv ;*x second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sir2p)emlxp 9n,r en is 1550 Hz when at restxl2)9 ep,rpmn. What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose sirek3q2 yyks,bz+n emits at 1550 Hz mov,3qy2zky s+ bkes at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in fre4dj)/, j4ile2wlef.3 jlyipj) lh, dfquency 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 exactly the same? Are t fw/,ihyjpil ld,e ljj fl.j3 ))e442dhey close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency hor:8tu6sjjk zyjwcl)*(swj 43 8joh5zmn. 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 the frequency the horns emit? Assume T = 6ums(cj5k8* 3zz8)j tj:jlw wos 4hjy20 $^{\circ} $C    Hz

  A bat at rest sends out ulxh s ) s+,k33oczy (z;ma5wlcftrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What 5lyzszf ax soc3ch;3k()w,m+ is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it fliess5 omq7b1fe ea2z7y g3xgn*y6, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear i2o ey13y7s zg* f6ebg5 7qaxmnn the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler ex.dt,*dt :d avh jh8ah7/f-tgnperiments, 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 station at a spenfhaj ,/vt.t :dd8gda7*h- t hed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow r/asxcn9szvh wckx 01o*2s2 ad u/l4- 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 away fr a/osz has22 4s-cl kd01r xx*wvnu9/com the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequecgq6h):i- xh ency $2.25 \times10^{ 6}$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 s *wk3qsjqnl-3 n jy7g)ound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observernyks37*-j nj)l qg qw3s 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 lan(21d6u17 kkp b5, i5rail xva7nha oyxrr3n: vd 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 Mk/b w-a+4lst kach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes witha+/k4 -stbklw 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 atmosphekm2 4x)w 4rtgzre of a planet where the speed of sound is only about 3 w4x)kz t2r4mg5 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 8500mk ,fqgosw6bn7o 0 m), m/s strikes the ocean. Determine the shock wave angle it produc)w 7q gmokb,osfm n,06es
(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 todxndlp;4,:rzz z 4:fv -5la$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead acduc: 4ih tgr3h290ay nd see a plane exactly 1.5 km above the ground flying faster than thgi 0:chay h 2u3d9rtc4e 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 dev yjyizin52.s.f+ -fcoice 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 desioc.. inj5fzifsy-2y + gned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the humab cq1k7qi, r5vd;p b;zn audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of mtlflsj:1upx(1ajs-)pv 8 .iqt i-h0gany plastic pipes of8.)qi jt-1av gtxsf p0j:p lui-h( 1ls various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person m4ffh2kvl2g f s;e( 4brakes a sound close to the threshold of human hearing (0 dB2vebffksrh 2l f;(4g 4). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level vexa r*4f1 7rrme 1mfz(dm(d1when an 82-dB sound and an 87-dB sound are heard simultaneouslxd (frz1r4 (d*1 mmve1mafer7 y?    dB

  The sound level 12.0 m from a loudspea1 nv h9j fin 7l2i5;gxpo(l 4)aaj.yicker, placed in the open, is 105 dB. What is the acoustic power output (W) of th v;1ioc j f y.i)apjhi(n952anx4llg7e speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops brf hki80 dk5d kk-y i+ucli7(1y 10 dB at 15 kHz. What is the power ou1- 58chkidkdifk k lyur(07i+tput in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears8b2 smbzttf)zh x0+ x/ome62r. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 14tofrzb 62 mzhmb/s+8xxe t20) 0 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 qo 6)wqvu.r (kv)dv-b, 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 a5eea-ygx2bj) -xe ly 8 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 between fixed points with a fundamels,/,dhf jc6t ntal frequenctcd6s ,/, jhfly 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 into vibration above a vertical open t ts0t;i*ldha2ube filled with water (Fig. 12–35)0d htil2* sa;t. 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 fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open n fcywj3(;xl(at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mod(n( f;jwcyxl3e) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonatek6f,zzy7 7etb( *wr(i;vtfn h 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 t+ux:/zp wfruy5w 0*bbone in the 500–1000-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 farther from one brwxyuw z0:puf+/b 5*source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whln+ jc 3l4kb2z*ha/ alistles. 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 tk n+l ah/jzcb 3*4l2lahe moving train?   m/s

  The frequency of a steam train whistle as nuaap 0 wfuv0,56nuk9it approaches you is 538 Hz. After it passes yk95 a ,w0un0uv ua6npfou, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to theb5edo4c*y5;2)gcj a eg l9ddy difference in pitch of the engine noise between approae4cdde by 9 5oa52d)gljg;yc*ching 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 5zrd;ztt7e ;wse; gybz ;0fr 2beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the other?gwsre;e;d7t y;frbz5; 0 zzt 2    m

Two loudspeakers are at opposite tpuwm/bv.k9* ends of a railroad car as it moves past a stationary observer at 10 m/s as shown ink u /m*tbv.pw9 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, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what be9 x8d f3x tt1p9(2q2ucbonrpwat frequency(29x8b1 2f9n3pwxdtcoq t pur would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moish:f o9 b2tro74tz1a th at speed 6.5 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. What is the frequency of the wave detected th:4ib217so a9zorft by the bat after that wave reflects off the moth?    kHz

  A bat emits a series o 8gdwtmh7;yp6nmn q0k+za bhi,e7 2r(f high 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 one chirp rztdr87h na0g nb;7 (eim,m hqp6w2ky+eturns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once uy74zwg,n klc r dmmjc1fy;; )5 p9eij/sed 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 )w1;jjn ky m pdy lmcrzi5f7c,e/;g4 9horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listedl s e.0w9gq7jzko g91ning can be compromised by the presence of standing waves, which k9dqe7.w9j gogz0 l s1can 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 room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,”t7 zv6.z xsy*fnxat-e70t srjuv* r2: 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 made to “sing,” or emit a clear, loud, ringing sound. For u 76*-azvft v*nsjt2x0e rs.xy r 7zt: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 hear (2z ixcdgmod : ,ska9ec+ kipya.7a-+ing for the human ear at a frequency of about 1000 Hz z m7ydc9psei:.i k , ao+dxg+( -k2aacis $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears th 7ja )hwwje.gc(ycn *9e sonic boom 1.5wc)(hw yjaj*g9ce n. 7 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1c34qmq+ pt1je 00x5 rhdt/xhseot.u55 $^{\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