What is the evidence thz)zel1lmfixn xhxz2,g +t) ::at sound travels as a wave?

What is the evidence that sound is a form owqncq*o2 g 0z a-y7:-lwlum)(s 5om amf energy?

Children sometimes play with a homemade “telephone” by attaching a string 1m ii-tu0 pn/ito the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–/ tiiu-mpi0 1n29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequenc+ohfir25 1 tpjy or wavelength to changet+pr2oj fh 1i5?

What evidence can you give that the speed of sxaxwxho2 68q9:zo .7l h1jvxy ound in air does not depend significantly 6q1ajx8lxyho7v:o .hx2z9w x on frequency?

The voice of a person who has i 1q5pt jlye-j5nhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipe eux14y 1 5wwvxqv2a7fs?

Explain how a tube migd w(ope(sp .bhm-rg ;0ht be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muffle-he0( pbp;.r o(mgswdr.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togethez2, 8ab16co jv ibc;mnr as you move up the fingerboar cc;jb a,1bonm 6izv82d toward the bridge?

A noisy truck approaches you from behind a building. Initia1w v7ia7 tqtw 1y-p,ntlly you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” —wp yati71 n-t7w,v1qt 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,b)33q gu oht+rvkt;g bl,:qr “interference in space,” whereas beats can be said to be due to “interference in tbrt bgkl3o;,:+u )h gt qq,3vrime.” Explain.

In Fig. 12–16, if the frequency of the speakers znhz ecy37e54 were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer toge3zyhzecn e547ther?

Traditional methods of protectingc57k wz 1*mtvs 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 devices t 5wkc1m7*vz 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 cauebhxm4 lv2z4 6 mlu73n 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 t2lvbuuz374m4 x 6lehmwo component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift ifm5ygm1w *r1 pu the source and observer move in the same direction, with the same veu1 ymg5wmr1*plocity? Explain.

If a wind is blowing, will this alt4 w )d3ry.93o2 eo4cdhkglp smer the frequency of the sound heard by a personrgedcwmlosd 4 39)o3 p4y. hk2 at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of ah 8t.kdvus5dg x*42f y child in 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 highest frequency for the sound of the whistle? Explh42x* .5t uskdd y8gfvain your reasoning.

  A hiker determines the length of a lake by listening for the echo of helhz8: w9j :j:im l:q/ prjx5ibr 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 the lake. qjx5/ j :lpwhi9rz 8ml bij:::$\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterl4qrtugtm*6 ,del h0*2aewy z(ine. 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 the speed of sound imduyet 6hl4 g0a ze*,2*(qtrwn seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveln+ q*r 07sxru42rk7jjg. nmvwengths 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 ():wx ver:gqnr4qk07 a*wj ola school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig.j*k )x qrq47(w:ge:or0wl a nv 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 m6 fncf.1u q0x1 6o:bw9qgwnikakes when striking the water below is heard 3.5 s later. How 0 xnukon. ffi6w1 9g6:c1bqwqhigh is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pt5 k*8q0qj,(* rlbm2vez coir avement. A moment later two sounds are heard from*qrrek lm8(5cqi2bv o,j t0* z the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made ove gwl5)ek+c o-mr one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperatuw)l 5e- gk+comre is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound atethv8d h/7m7 ksjr5q/ the pain 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 leveod61 2ni1,4ybo. er2tnzd umt1 :t*yfpl lew(l of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a pse5 o13alcpv l sp;;8sound level of 95 dB when fired simultaneously at a ceras1l ;5 ;cp 8p3vopesltain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with fourowo0 fs.g9,wirgfj+jn6ywd ,2 h czzg)le6 ,8 equally noisy jet engines is experiencing a sound levelfg,6zyicn,j)d fjgo r,2+ww sh8w .0g e9zo6l 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 signkslk t +xue1/1al-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 for each 1+u /ts lkxe1kdevice? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person spes1c f *mt+dck2zl vjs 7npi;1 -dm3.vjaking in normal conversation. Use Table 12–2. Assus-dsk +j3v17vi1* jd f ctmlmp. ;n2zcme 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 strikes an eardr3am5f8l 4yobp 7o+mrjkv5 / nkum 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 more modesg .jnktqw0 ,k4t amplifier B is rated at 40 W. (a) Estimate the sound lw,nkk0 tjg.4q evel 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 me3c8 5huo trl;l la(e-jter registered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. lo tc-j8aul53 ;relh (
(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 l1*zlin71a prh froja3-:a4xt/8 hq auevel of 2.0 dB. What is the ratio of the amplitudes of tnrqh 8 ah/ 3jla4*fpua17 iz-tx a:or1wo 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 factor will tb e*vb 7rv6b-the intensity increase? Increase by a factor ofb7 tv-v*bb e6r    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displau.ul ffxk1.8 ucement amplitudes, but one has twice the frequency of t.1.luuuxfk8 fhe other. What is the ratio of their intensities?   

  What would be the sound level (in od v1huu49q/odB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 d1u4h oou9q/v Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud:ir.bpd8(+ ,tj 4i ylxqe, saw as a 100-Hz tone that has a 50-dB sound level? (yrdal.te q j,b 8p +ws4ii,(:xSee Fig. 12–6.)    dB

What are the lowest ) zrw4qa-8og t9zza7i j7ctk6at23r ww+k *fland highest frequencies that an ear can detect when the sound level is 30 dB? (S 3fta-qakct7 z ir*z9wr2z+ alo wj4)k8wt7g6 ee Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound oa +zx +qfubt .7)a0i/embi c3levels. What is the ratio of highest to lowest intensity 7ao/ ta e+. + qfbxzmiu0)cb3iat
(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 zbl3vnk7* q a)of 440 Hz. The length of the vibrating pobvkn*3l) a7q zrtion 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 long. Whahe jm07 y4ys),en7y( 2wn potct are the fundamental and first three audible overtones ife2en c 77)sm 0yo (4tpjy,hnyw the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequen0 y6 nxt0/ ;ufn+aaeqacy would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumnu;fx+na/ teqa60ya0 ed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of huzvf)ulp+. 7jv g 6ukg*man hearing (20 Hz to 20 kHz), what would be the range of the lengths o)*6g g.p+vukzvful7jf pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz a ;xnsegl; ;u:;k8lu pds its third harmonic. What will be its fundamental frequency if it is fingered at a length ofugd;8;e l;nxkp:;u sl only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to plao.)iuaw:wj61pwl2b;bmr2 t1bpz 3v vy E above middle C ( wu3zti) j a221rpbwbmwo. 6p; vbl:1v330 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 08 -ps6kvhiwoC (262 Hz) when the temperature is 6-hk 0iwsp 8ov21 $^{\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 eda,t,wxed. u..)qcl at 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 thyz*w-pa:ejx: s4*k hv+ssd* jk 3diz,at k ds:ik,pv+ssejx-dwhzaz *j4**y 3 :must be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, a;i1(h, ib wjqb6qt8qznd 616 Hz, but not at any other frequencies in betw btqh6qq, (1bi8z w;jieen. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both endac j -+r6o;yq)txxlyxz. 4pm 5s. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. 6 tzplx5- mq+axr;y)j xo.y4 cWhat 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 rpor8o9l 6gvjd2 h+j5$^{\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 prese *sb*vf3q evbc-wim t .rke9ng /b;;s-nt within the audible range for a 2.14-m-long organ pipe at 20kgw/btv3 .i--vm fn* ebb ;rsqc9* se; $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside and n)scde+xzn1/ o: dfx8is c)+:f /18esxoxcn ndd zlosed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the 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 whenlbuizz *7j ( 5ave8d5l trying to adjust two strings, one of which is sounding 440 Hz. How far off in d5bize7a(8zj5ul v l*frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) 5ks klr s5,c1pand $C^＃$ (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 ope.sq c5p migpcd8lo:ka 86m /k,g,qtb7rates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans whecbomiaps/5 ,8 .,qg7k6 8 :ktq plcgdmn 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 tu(ocw8kze,.i ihv5mt viq n3;/ning fork and 9 beats/s when sounded w,hwv/o(;kvqzi3.t ii men 8c5 ith a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension i wy:t-zv- jv,kn one string is then decreased by 2.0%. What will be the beat -wtk :vyjzv,-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 . cwc/k y;flimi.xi(xk:i)/o each try to play middle C (262 Hwi o:/;lxcf c(xk ii /..y)kmiz), but one is 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 a frequency op u0atp( k7v:af 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 sounded togeth av(p0k p:uta7er?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. r6o hml(ovhu*kd+0u w zp8usbf 60n+3A person stands 3.00 m from one speaker and 3.50 m from n3zf+6uo0 m6+ov d8 0shk (p*l uwuhbrthe 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 hear,hrde/ itg;q2p/4fmhk)8 rn j s three beats every 2.0 s when they h mj/ed/f n qkr, i24)r;gp8thare 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 2.76 m in air. How many beatfho4n . acc64ys per s .cy 44ac6fnohecond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at r 6 pog -hit/h* tw*b4ezlw0h(jest. What frequency do you detect if you move with a spee*-(zwto *jb ewt6 i0h4/lgphhd of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you devvb-x )ff57jerqhb-mjwn6p 5e9 k2 e; tect if a fire engine whose siren emits at 1550 Hz moves at a speed o 9w7beej;xpv-v)e-fb6rj q55fnmkh 2 f 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving towa7ygdgr7q*m0 .it -r xrrd you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they closeqm7g xd 7r-r* ry.gt0i? $f'_{source\,movine}$    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 hornn,v)ptn i;:d gf--ac h. 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 fret ;in a:pnv-cd,h-)g fquency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them rn k-ow)r72uneg9j.s p+an)b* 9emyoceturned from an object moving directly away from it at 25 m/s What .*))aw-m2nsy 9n7 eprg9un jebk +ooc is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wp o2tgbb 2h x;-gx/k9tall at a speed of 5 m/s As it flies, the bat emits an ultraotk/hbb9 g2p xgt2 ;x-sonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler2r zk35:tqkyg experiments, a tuba was played on a moving flat train yk kg2 :r53tzqcar 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 speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrd*pgb e:h fg+v5jb,8 easound waves to measure blood-flow speeds. Suppose the deve je+d,p5:gfg*vhb8 b ice 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 from the sound source?   Hz

  The Doppler effect using ultrasonic waves of fsehl 9lq9,4o rn0an)orequency $2.25 \times10^{ 6}$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 emit0x0+yqb4gso 1r8 bgxo s sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are loca0ys4b+xgrox b1oqg08 ted, 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 ipj3d8fm, u-opts 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 q5z vrjj+s.ie2n+o a 3tl9xi7of sound is 310 m/s (a) What is the angle thee5.vtnsa qi9j 3+i7r zl+x2jo 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 az5.crp:k -ih btmosphere of a planet where the speed of sound is only about 35 m/s z:. kc ph-r5bi
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock waveh1ec:,+l g/tgu7bk4hhe i8 wf:;prn g angle it produceug+wh,e:c/n4b8r 1th k7g; feighp :l s
(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 fz4z((4 a3 d t/zlvpjx$/theta$ 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 gro 3ub4+yy-ybtr und flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distan y3by- t4ybru+ce 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 device that sends 20,000-Hz sound pulses downward ;7fz(5mcy7cr :r4vveo z0mujfrom 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 bv7m zvro7:4c;y0z u mfc rej5(etween pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audibv2 77 +kbpdygule range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sympvd+tgn ,u26 fthony. It consists of many plastic pipes of varitu2 dg v+,6ntfous 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 makes a sound close to the threshol 8rwmmy;j j-oi:;ab2 od of human hearing (0 dB). What will bmr8jm2o ;yo;i-ajb : we the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB so/;gaai3;m h(+f:pwcyt9 x cfound and an 87-dB sound are heard simul;ictf+apw of cyha:/(; g3 xm9taneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 nnhjed.f f)+ id*-ic 0dB. What is the acoustic power output (W) of the speaker, assuming itc) hfden-j0 n+*fdii. radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power xz ;us6nmox/3 output drops by 10 dB at 15 kHz. What is the power output in wxo/s36xum;nz atts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their sqw9((bi5*, ygm;rwnxnzx w 1 ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human 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 5x *gm,1ixq zyn 9 r(bs;wwn(wfrom a jet airplane engine?    W

  In audio and communications systems, the /ox85rfvdwu/69 lv dkgain, $\beta$ 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 freqz( -;1 k osru6-5(utzmxk 8cxdpcy.y euency 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 wqo-f 6igu , 37iosl4ioith a fundamental frequen i3s-q7o io,ouglf4i6cy 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 tube filled(q/ha,hlr* az with water (Fig. 12–35). The water level is allo, qrz*hala (h/wed 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 agc914vo l,xq c91w z rlzt3d2i tube that is open at one end awi 4gcx9l1v1d2, tcqzro 9z l3nd also 75 cm long. How much tension 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 om c5rw2r0 thib,okf a9.o 2hu(bserved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tq o ;d)6t4mlhvta6ancos8 puf0 :8f1 done in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To deter)p 4fdo 18nudt o:ta 8vs;6 q0falhm6cmine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on tg9wkxg y/nh )+he stationary train hears a 3.0-Hz beat frequency when the /gw+yx9k )nghother 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. ybb2vuy wviwk::-y0,v6 ssp,After it p:vv-:kw 2s, 6b,w y0bup yysviasses 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 spe4glq88x+3brag 8m +lcct0us h ed of cars 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. How fastqm+ +8u4th3 xabcg88cgll rs0 is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. Tuyaely 24(utm atpis +6+7,r jhe shortey +t4pu6( am+tr,lyu 72aji esr one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it csn3o.bba2o 5 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 positi.2 cb53baonoson 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 mg a9.i i55i4dbfm5te*g i sm)d/s what beat frequency would you expect if . igiaf4e 5m9s)d*mtgi d55bi5.50-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 b.v6a9h yu/d 5cuiz 6gwhile 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 by the bat after that wave rc u .yi z/hb9d566guaveflects off the moth?    kHz

  A bat emits a series ofw6 bia -6nkz6su+zq0n 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 returns before the niz+ bkwazq6 6s6un- 0next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals fq g6i 2k7;xffnrom 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 tn6kqf2fi;x g7 he fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of st 8 pss: y3d2*:xraxjrp2)mn k0pykej.anding waves, which can cause acoustic “dead spots” at the locations of thex2 .0 mk)rp:y2*pprsjes dxkn:3ya8j 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, calxk zqx6)g/zz+8 19aj yceq4z.dqk sk*led “singing rods,” involves a long, slender aluminum rod held in the hand near t xz/xz a.8946e qy cq*q1kzsk+kgdjz)he rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a freque x,(mtn gwpr-5ncy of abowt( -5m,npxrg ut 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2sg fs,9vzq;dwt u36-r.0. An observer on the ground hears the sonic boom 1.5 min after the planeu z;3rs6qv,fgw-t d9s passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is jli+ ;fvb6lsx/4;*7uj, lu, q ymbip s15 $^{\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