What is the evidence that sound travelm*+i 7p 75dxj /bxgpxjs as a wave?

What is the evidence that sound is a fge8rv:se v bvk7,m(u) orm of energy?

Children sometimes play with5ls gen+m 6hy6 a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound che56l g+ms y6nan 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 wt(y*-r 1pix*0+1i w)ggw,uev.i sl5a qnljqwater, do you expect the frequency or wavelvy0* gsij5a1 -lult)*(p, wgriiweqx+ 1n wq .ength to change?

What evidence can you givojrxbs.t-vkj + r7+ y8e that the speed of sound in air does not depend significantly on frequencr7 .st +k+bo8j-yxrvjy?

The voice of a person who has inhaled helium sounds very high-pitched. /zxeqy4 i0cy 0.kx4g dzczs-+Why?

How will the air temperature in a room affect the pitch:/* hrvlqh+ hv of organ pipes?

Explain how a tube might be used as axh 4cl-y mt8.a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a c-t 8 xm.alh4ycar muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togekqg1/0)uxeycgldnik hn78 9l)l v15rther as you move up the fingerboard toward the bri9gglr7 ni5vxu8kly c) )0q1/h ek 1ndldge?

A noisy truck approaches you from behind a building. In wck2gl(ori6 x,4fnc f7a*lg 9itially you hear it but cannot see it. ,cogc 67*l42 (9ixfagrlfwn k 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 space,” where gda+yt , xk4+ap*ti:zwl+prin(p9g6 as beats can be said to be due to “interference in ti9t, *nigw+g +x6aa pydp(p t: 4rizkl+me.” Explain.

In Fig. 12–16, if the frequency of97nk6j1 fu dzajdd+)d the speakers were lowered, would the points D and C (where destructive and constructive interferenc619k anj)zf7d judd+de occur) move farther apart or closer together?

Traditional methods of protectien2zq9etl.2 4v8qse wng 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 could2e8 nt.eqsvq ew42 l9z adding more noise reduce the sound levels reaching the ears?

Consider the two waves shou2 -+ze ij*svawn in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves -u2e s *jzvia+with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move iv75b hxtslhm. +r;o07cp zi*bn the same direction, with the same velocic7 x0h ib.s+7zvmlo*pbh5rt ; ty? Explain.

If a wind is blowing, will this alter the frequency of tsx l8 mbu(y 817bw8v1(selrd dhe sound heard by a person at rest with respect to the source? Is1((s88m yx7wl ubrl8d1e sdvb the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. Ashz2wf4 )1k 1q/xrtbt monitor is blowing a whistle in 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 whistzqw142xb/ sr1thf k )tle? Explain your reasoning.

  A hiker determines t. x jijn0*k /naqxc34;h j+gnqhe length of 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 2.04/.gqq ja *j ;nn3 i+x0chjnxk s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his; v .xr, rze,glfro*8 y2(ykkv ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s lvr yofg.8r k xke*vr,z(, ;2ylater. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wave p*/6xz2l o flve6-scilengths 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 +c+ li f5w0rvr m.e8ouabove a school of tuna on a foggy day. Without warning, an engine backfire oc u0mvwir8c +feo.r+ l5curs 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 to1 vl 1lgm3e r1dds(eo1* ck6vpp of a cliff. The splash it makes when striking the water below is p *sgc1ovd e1vk1l36(mlr1d eheard 3.5 s later. How high is the cliff?    m

  A person, with his ear to t jgbk,etn//cou70*kj )ds: gthe ground, sees a huge stone strike the concrete pavement. A moment later two su/t/),jjk:7gbs kg0cn* otdeounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent 2/y5tjsioty. error made over one mile of distance by the “5-second rule” fotoyjs.y 2t/i5r 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 paingvwd;6vh/ b9ab du5 a+ 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 of a sound whose intensitmrm a t wxnr 3p4kld*1q**9dz9y is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 9 l*(l6 a-ihh xkdgs,)k5 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hi kihl hd-,laksg x*6)(nt: Add intensities, not dB’s.]    dB

  A person standing a certain d,um ronw w67k1istance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 mwkuo7nr 16w, 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 of5 e 2v53quoz;wjk du/m 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the s/ ov5 e2wjdm5 ku;3uzqignal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the pow9i4z m:(*nadg u .fgeeer output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centand9fuzm4: g( .ei e*gered 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 eardrn/p42* eq8ezk c b-mlkum 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, wmkreep14xij 6 xc-2i.p7+ skjhile the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you wo+4-x m2ecpji1ek6j rs.px 7kiuld 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 13:hfx z(z8f7u *bbohm *0 dB when placed 2.8 m in front of a loudspeaker on the stz* h*h7:bfmfo zxb8u(age.
(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 differentwuwa)h u8z/3ce in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this awh3) /wu8tazu mount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the icbs*r y f:l-o)t i-b,wntensity increase? Increase by a factf-sywr,)ti locbb-*:or of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement ampli-;*ux :jpeq1 r/l*nxonx ym8o4 4 mtietudes, but one has twice the frequency of the other. What is the ratio of their inten/xp ex 1*xiytjrn ;o4m 8oum4l* q-:nesities?   

  What would be the sound level (in dB) of a sound wave mg bqx/8b/:-j cu5i;hvn9t kh(io w 8cin air that corresponds to a displacemi twbvgi knh-9hqc/ ob8/m5 (u;: x8jcent amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem asrghftma: d;8m7 k xwf5b-/2e l6 mb-wp loud as a 100-Hz tone that has a 50-dB/rlf26at8m- -bdmbwxe7mw5 ; g:pf h k sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect n/,x2jxav+ j awhen the sound leveajj n/v2+x,a xl is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of soumsa;+rk(ac y; vgii;8nd levels. What is the ratio +amr(8iys;g;i v;kc a of 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 6 )stfs oz s;43bob33zxp d,bsa fundamental frequency of 440 Hz. The length of the vibratings;obp6,zs34o3)txz f3 s bbsd portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm loipa) (sp kolg6yeu*(dn19 /n ung. What are the fundamental and first three audible overtones if yikps l1(pg du *onu/ 9)ea6(nthe 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 fr7dxa (qy3aop (equency would you expect from blowing across the top of an empty soda bottle that is 18 (3dqx ao(pa7ycm 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 wityyi0,dl(t 3 b:rgdjw+h open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be ttg(dlr3:j y,+w b0yidhe 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 third harmonic. What will lo53fa+va4qn be its fundament5qavf no43+l aal frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and isqodp(jt(xm11jja k8k ,-b n4g tuned to play E above middle C (bjdjo j(xq p g4 a-n,k1t8km(1330 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 pzma 2q4 np q)g;w7obhx2s 2w/mipe that emits middle C (262 Hz) when the temperatur/q7snh22p)mbwq w oxa g2m4z ;e 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 )px;,j vvq*o w5stv)vjg fb,.b r0fe 520 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of th8xd: n )8ur0ld 0mgrag/tko r *ej)jn6e flute in Example 12–10 should the hole be that must be uncovered to play D above middle0ju / n*nd 8rga)0 e:djkr8t)6mrlxg o 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 ca:,wv0c9s xkb v)upv a,n resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pipb,spuvcka,x0) w 9: vve. ----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 resonhg+a6 .j a;kllates at two successive harmonics of frequencies 275 Hz+lalkj 6;ah. g 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 1rejii o )2* yu b5qk5,6krdzv$^{\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 pk1az);ohd .5 qi b+rzrresent within the audible range for a 2.14-m-long organ pipe 1a;)hkiorqz zdr5+b .at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm ls1 s2x:zhq/;g o )j ac4lz-kveong. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is t e)o1gzszj:c/4vh2;x-s ql kahe 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 w7zz,o(ew7zp50ar x mvhen trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the0(o ez rzvzw7,75xpam other string? ±    Hz

  What is the beat freo74kf; cimf,s quency 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 (brk22rvu:,g evhand 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 occurs when they are played si u:h,vge2r k2vmultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz 5.e mpdy ,g09bjsd6og, orm x9tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequgsd 0,oxgbo5mj9p,6 dm . yr9eency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension- p8y*)milaw sxljb) 5 pfdju80m0 wk( in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings ab (kj ml0)js85 p*-8uw0miafpldyx )wre played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flut ;y1a59y pnyd*hvda m0es each try to play middle C (262 Hz), but one is aa;*n1dy50 phd9vymy at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has uvk+g*kk op v fgk,ab -748b)xa frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are )kbvgkk4b fg,k p7*oavx +8u- sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 mpn sb/7bq5 n-mdc4pke73 fbg1 apart. A person stands 3.00 m from one speaker and 3.50 m from the c-mdb3/bq fkg 1 74sp7ne5nbpother.
(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 tunt0vk3by *bpk* er hears three beats every 2.0 s when they are played together. (ky3ktpv0bb* * a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many b-)b 4r8cspj3z0 k x 9jogh5boaeats per second will be hear 5akz9br xpbj4so3h0-)8gj cod? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire.0h2 kd q dgqc(6kw9mrk+p(jn engine’s siren is 1550 Hz when at rest. What ( w(0g6jd r.n mcd+ pk9k2hkqqfrequency 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 fire8 /a9aj+i hayczn ha)jp on-66 engine whose siren emih-n6+ j 86jyahco )/na9aazip ts 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 movz( xsy0m*d 7quing toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are theyy*uq (szm7d0x 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 equ5ue:llf 5uc *i;qzrugyr;;6 kr4tiq:wq us *0 ipped 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 hear6ilr*;:;ui *5tqrqk lyf;50cuu4qru:e gsw zs a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz a /g3sy vu1v:,a;3hli r bv;tacnd receives them returned from an object moving directly away from it at 25 m/s Whciatu s:, 3 ;ayvvh1l grb3/v;at is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat eu9 f .n8mve)htmits an ultrasonic sound wave with frequency f8e) mhu9n t.v30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuh3-bi *nybm .fz3 inw7ba 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 frequency7 .bi3 -yn3zwfmnih* b 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 measure blood-flow speeds. Supfkc6kig2 z p;wtv*1) spose the device emits sound at 3.5 MHz, and the speed of sound 6ki;f k2 zpvs*1c wg)tin 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 /+qt6wdax 33, oufaqu$2.25 \times10^{ 6}$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 emitsyddog dyn9+,5 sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest9d,gon +d5yyd ,
(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 movintzw+o vqvsfa4klm0cd56:i1 + g on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where beglsj+ 8hn.8 the speed of sound is 310 m/s (a) What is the angle the shock wavs+8 lhbn.g8jee 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 planet wherck5xcbt* - (ewe the speed of sound is only about 35 m x5tcbcew -*(k/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(wvqysr3( ,kp . Determine the shock wave angle it p rw(y k(3qp,vsroduces
(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 nw1c(gge,m)v $/theta$ 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 exactly 1.5 km above the groundk c,/ovyv1v4hseivfx:ih (33 flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. Seexy ikc3h/3sv 41evo, (i:hvfv 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 de 33s,e.y .v3q hqwhrq4 v+b wog/xawm4vice that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth f3qq v.,wo3.xbv4qrw/4 a shh 3+y gmweor which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves arekgv 4/j:hzctpa0 v 82r there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a8zioe,l aem :9(djg- v display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both ends. mvj- id:9e,og8(ae zl
(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 thresh*n8nn /fz hp c2l0cz+yold of human hearing (0 dB). What2hy fnz/l c0zp 8*n+nc will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level anz1903w7m / ,w8 u8f ri.,bx zrw-ssx ewufnjwhen an 82-dB sound and an 87-dB sound are heard simultaneouslx3bemfu/ nz0 -i x,19ju8,7z wwn w.8rsswfray?    dB

  The sound level 12.0 m from a loudspeakercl+,a()lw -9ecp b,sdg,0iqyjb ikb( 3 l5k yi, placed in the open, is 105 dB. What is the 0kdl-w5p,)i c ci9jy(i,ys(e g3bkqbl +b l,aacoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 y(a3 * ingmx1k2ef7czW output at 1000 Hz. The power output drops by 10 d(f igz e 3ykmnxa*1c27B at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their eal jel-3saas688x1 fqxrs. Assume that the sound level olxsxs -3aal 8ej6 q1f8f a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sgoy zv p-4t*q5ystems, 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 tuneeutuy g6er5u1-clk0og67 r) hd to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fum3p:o1e(/e g :c e5cbf/ pitawndamental frequency of 440 Hz and a mass pegc(coeemtp p :3/:i/1 w fb5aer 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 tube filled with waterwqv,*i/ .ly5n69svd i::2swh*zp yum b+h vam (Fig. 12–35). The water level is allowed to drop slowly. As it does sosh*+q b i*wyw,dvslv: :26yi5mapz./nuh9 v m, 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 afj;i s(i8z8zsat aq1w us 8:i9t one end and also 75 cm long. How much tension should bez;j asz(tfw: 91qis8ua8i8 si 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 on2 feg2bpk8/lla9 -gngd 0c;lbe full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz ranga wvzd/xn51xg-qxv0 i *,dhs- e 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 qxg0, nx*s - /vxadwiv51z-dhlevel is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductzst 1su1c:a3ys7a9 /h0lod wvor on the stationary train hears a 3.0-oy1us 7a01 wd v:hss3t9 lz/acHz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After *zc8i9 6 yy 1fe,ucgpi1zi.mpit pappu,.mi ici8 f1e961z* yzgc ysses you, 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 card,r30gtsy+6io s *vnas just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. 30 vod*n rti,s6yas +gHow fast is it going?    m/s

  Two open organ pipes, sounding togetherj+,w.e ye mjicg.qet t10 30kn, produce a beat frequency of 11 Hz. The shorter one iq jt+0gm0ke ywn ce1.3.,je tis 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it jk9vi9(co) hm wn ,sq-moves past a stationary observer at 10 m/s as shown in Fig. 12–37.sn(,9w c) 9j homqvi-k 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 ao wy9vvq4z0 rdo4c jd7,rta is normally about 0.32 m/s what beat frequency would ,zv 0d9j y4roqcv7w 4dyou expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward2w4mz9oz ps /j 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 by the bat after thaz9j4s2/mw pzo t wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound prx:saxq x154 tulses as it approaches a moth. The pulses are approximately 70.0 x5xqstrx:14 ams apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one A6nwh;zat)nuxq8tpy1(ok u( 4lpine 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 calann(t1yxutkz pw)4q ou8;6 h( led 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 c;ap1blfe7v7ee xc 88can be compromised 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 foe7ebclvp7;1 ace88xf r 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 alumina3 -mort 7vv)lum rod held in the hand near the rod’s midpoint. The rod is strtv-7mvr a3 o)loked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing 2uesig2 c 1l7lfor the human ear at a frequency of about 100glle721u2 sic0 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mzsg68n:.kyd a;ipwg lk4 wt.*b0m; vbach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What i68bz:g .;4svl*gkn i;pwtyb .k0w mdas the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat oxor)s4 k2dg .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