What is the evidence thahvrfo(w86 *) k3c kgxut sound travels as a wave?

What is the evidence that sound is a form of energu7; y*ipd(bg;;o k olz,wxv-ly?

Children sometimes play with a homemade “telephonqv+y7k 40aiy ce” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the soua7y cyiv+0 4kqnd 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 fd 6g pml 1+x8uje8+fworom air into water, do you expect the frequency or wavelengt+u 8el1dj go 8+fpmxw6h to change?

What evidence can you + v,/x var8 hqq,dg.kcsfj k6/give that the speed of sound in air does not depend significantly on frequen.kvs h,6qk 8fvx/ d,carg/ +qjcy?

The voice of a person who has inhaled heliul07ib mbkpa /:m sounds very high-pitched. Why?

How will the air temperature in a room affect the pitchf+f (eyt v6f7j of organ pipes?

Explain how a tube might be used p vapr hib::ss)// f9jas a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muffler. j srp)9s/:afip /b:vh)

Why are the frets on a gu, hpbx4i*l9t eitar (Fig. 12–30) spaced closer together as you move upebp4*l9h x ,it the fingerboard toward the bridge?

A noisy truck approaches you from behy.ib /x9aj qnqy/9 r1fz7,mkc ind a building. Initially you hear it but cannot see it. 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 o9qyczfya1j9 q,//r 7nik.bx m n diffraction.]

Standing waves can be said n;u fm n(l-g1pto be due to “interference in space,” whereas beats can be said to be due to “interference in til1n-p n f;(umgme.” Explain.

In Fig. 12–16, if the frequency of the speakers wer:e771d cmosmcu1a z(c e lowered, would the points D and C (where destructive and constructive interference occur) move farthedc7cmazmu cse1(1o7:r apart or closer together?

Traditional methods of protecting the hea,48avxb5r+ n icd un)gring 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. Instc4ud8 +gxnbrva) n,5i 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 th 4jvz )8w4f-wmi3/c7 tt6rvh o b6sghlought 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)3jw6wm/4 io-4tfl) vv7c zht r8ghsb6, are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move ig -y98 q6s ,ukjwis6je:4ajbilj:oeo /em d* (n the same direction, with the same velocity? Explwj-:8es6:9e j* ylkjq ij(me,oa idg4b/o 6us ain.

If a wind is blowing, will this alter the frequency of the sound hear ry(rf)eh*b,wx 7 ou+zd by a person at rest uxo,( hzbw+ )feryr*7with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitoiw(g2pvis w/qu ;z2 e;r is blowing a whistle in front of the child on the ground. At which positi i2;evu (wqsig;2w /pzon, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her sn abl.jj2-si 25g+ -wz:vti6x x:w, omvrep+ahout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the lenb: wo. g -rsx-6pnvl xa22jm:v+i ,ez+tj5 iawgth of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just belowa)s: h/uvb ;kb+xrz 1f the waterline. He hears the echo of the sound reflectr )fx: hb+zsb1a; vk/ued 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 depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths*6ws7gug s4 -ynkpe.s in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna fs/8*,jm upbhom:ji:x(6i ge on a foggy day. Without warning, an engine baxi::8f/jugh6 moe b( ip*js,mckfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. ccgf-pf:po. x7- +h,p t7egnf The splash it makes when striking the water below is heard 3.5 s later. How high 7t7ofxhcfn-epp- pf.:c g,g+ is the cliff?    m

  A person, with his ear to the ground, sees a huge stil,vgir1wv/6;/ejmn / qctg3 one strike the concrete pavement. A moment later two sounds are heard from the impact: one travels i i gr;njw,/mecq3/tl6/g v1 vin 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 sw-eh,u3zaju z e1u o6l;r qn3gn. -tor4mc-8error made over one mile of distance by the “5-second rule” for estimating the distance from a lightningz-creo et 3sron 4 nul-quh6z3 8-w 1ag;,mu.j strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity o ln5s ul 90mz tqunr5s(;c(p9mf a sound at 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 level of a sound whoft41krgh7bcw+ 3ikcx ) g,;hs se intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a soupe0t.brgyudcqvn,*4(qix . 3 nd level of 95 dB when fired simultaneously at a certain place, what wi.i gn(*yqe 0ux3. ,4vrcdbpt qll 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 fou2. .kzvm bos x4.sd y3m2obs2vr equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities,..vmvmy z2b d23kb24x ososs. not dB’s.]    dB

  A cassette player is said to have a signalc q50. xgxso.m-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 eacscm0 q xo5g.x.h device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output )ej *n8e2.w9jqpj(n.hbifur of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformln(ref ej.j.jn2 *p 9wuq)ih b8y 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 en x+si3zry rj 9h9x7h(ardrum 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 ne vn 6nf b)kwro/fo,n 8eu0l4n-i w05more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m f oloi5n/nvfbn04r ,6ewnn0 u8- ew)kfrom a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placedsjx :ou8d6;o l qeinu6288cbf 2.8 m in front of a loudspeaker on the s 2luu:c;is8 d8qeb6f86xjon otage.
(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 level of 2.0 fbfh2epo 63ay-.zliz1sv p+7 dB. What is the ratffophes-z.1+6y27bipa v l3 zio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a 7f q5 /7) dghgbk.dzsnsound wave is tripled, (a) by what factor will the intensity increase? Increase by a factor ohdks5).7q nfg 7zbgd/ f    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the freqit gjuq9,j80w uency of the other. What is the8jwq jugi,90 t ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air0mixrjmx;na o9o8 1b1 that corresponds to a displacement amplitude of vibrating air molmx101xmi; 9nbj8 rooa ecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound m gqa0..ptf2c y)s av6level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (Sea6a) g2qmyv spt.c f0.e Fig. 12–6.)    dB

What are the lowest and highest frequencies thy1o5wu im1o tam 4dq40 kj;/hzat an ear can detect when the sound level uywqm1 0z/1m4hijto ;5d ko4ais 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of soun /xc*cw)gryz- d levels. What is the ratio of highest to loxzc/y wr c)-*gwest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin or74wom f4y bj:l+4pwv:or ,sjda6-bczk+z6has a fundamental frequency of 440 Hz. The length of the vibrating portion voo:a+4wczbp o 6+b6,j ly mdrrk:4 f7-zjsw4is 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. What are the fundamentalgwbrie-c. a;.t* .w cd and first three audible overtonestwecgw i*. d .br.a;c- if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect frz 7xt*) 5m-sd1o ptswohhx1p wov+0r 4om blowing across the top of an empty soda bottle that is 18 cm deep, if you assuso5 r)-+0 hpmwsxpxo 1vdtho*7z 4 t1wmed 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 the5bl1gugxk-sqp w uy+-l16l 7/z cw0bw range of human hearing (20 Hz to 20 kHz), what would bw blps +gy-g5/b1 6u1xkqlz0uwc - l7we 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 third harmonic. What willbs8en 5m 32.wd ,7ugbzds8gpo be its fundamental frequency if it is fingered at a length of oguo ms ed.83wd2s,bnz7 5p8bgnly 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle pixfvo.bxq- 9 l*4i7m C (330 Hz).i7plbx i9qmv .4*xf-o
(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 7c 5 uj.vflp o)5jo8cfemits middle C (262 Hz) when the temperatulp5jfcjcoo . 7vu85 f)re 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 6d kfalkpki5 j,9,6wx k 1t kk9ag6xn(at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of x/2fpp0ssy: wn 2bv;cthe flute in Example 12–10 should the hole be that must be uncovered to play D above middle C asv p:cxsnw20f 2 /pb;yt 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 pipbx+2 5dgp2 cy ah.j4l/;pxzqpe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why tppz hbcyd;.x5l/ paq2 j 2g+4xhis 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 (kwq*,crqk 7w;nkcv0 is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330c(wq*v c kkrkqw;07n, 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 3ptkt,*l 3jvfchq7k / $^{\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 pregtp m9xqm,1jq o9k zg(1wml -8sent within the audible range for a 2.14-m-long organ pipe at 20 g8,x9 zm tlm9( qj1mq-op1kgw$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxima,4ermjlz (t k0tely 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. Whate tjzk(,4 lr0m 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 rm7z vl4,us(mgzs.br1 ;w 9t :ojvb(twhen trying to adjust two strings, one of whicst,gz(vlz:mmrj oubtr(w4b;19 vs . 7 h is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency q5e6k zs2ld2j 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) operate*/32ujjshc /tb(g tgc y8 pr9 v0m,0pwey+vyls 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 grs/y/ 9vp+ buyhtv0cye l(j 23* ,j80 wtpmcgsimultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string producesj/n zyh/, lij; 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounj,nz/lji ;y/ hded with 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 e */+mz fndr5rfrequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will rmf+*n5/edz rbe 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 C (pzo /,4rbvgpe9 ow * 438nikoz262 Hz), b/ zoowpkin4v,*3ob4z 9e rpg 8ut one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, anh*8)q3 qrf bw6j5d.r ld fj*std C. Fork B has 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 together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together? hd)5sfr83 frqjt d6wl.bq*j* $f_A$ =    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. 0:xkgw)cm bc6t af1f-7ji v3n00 m from one speaker and 3.50 m fr j-wx c0 aknbv)tmg6 ff1:7i3com 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 suppox,*b 0wv-.h4pjwtur dsed to be vibrating at 132 Hz, but a piano tuner hears three beats eb- jdhtupw4 w.x, vr*0very 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of0chi+*refr u;7xmsi. sj1m /t wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = rm1suci es0ht f+7.*;/r ijxm20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engi(r wg8ykeu, v z1mhu60ne’s siren is 1550 Hz when at rest. What frequency do you detect if you v16 ghukm(8r0ywe,z umove with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequz,) gh m(awn4oency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32mnhzw a,( g)o4 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you fk+-z avyor3z2yj 0x 8at 15 m/s versus you moving toward it at 15 m/s Are th8xoj 2ayry3 v -z+zfk0e two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frtk 3upc-u;hk0 equency horn. When one is at rest and the -hctup0;kuk3 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 = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and rj iosscyg+1v tq*.;;-a7cntreceives them returned from an object moving directnis.y+ g at-c;c7jv;1* toqrs ly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 ..d3s* 12k 1 d *ubaweqzylozgm/s As it flies, the bat emits an ultrasoz d21ab1s..*qu k3zd*eo gywl nic 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 Doppler experiments, a tuba was played on a moving flatt tvpzh n1.p*lc14(w x 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 approa.tz* v1p(c4np1htlx wched the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wav-be0cey(5 r6;sjbya yes to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed obyry-c;ye(b0 6ea 5 sjf 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 frequency8l* xu /mjb5iz $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hrl:l* c16haaiixl4wlg, il8 .z. When the wind velocity is 12 m/s from the north, what frequency will observers hear who lail*.li ,lr6 :lx1 gcwah8 i4are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its sp0 eo1ylu: 3nrteed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) W6ldq 7hbs5w-jc u 47mihat is the angle the shock wave mak 7h5lsujm4dc7b6 qw-ies 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 where tmrz ;v3rnaca1z1(i1:np6 hl vhe speed of sound is only about 35 m61(mcl ahria pvrz 1 z:nn;1v3/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 strikenkj8z jr, d .kajm-lq.) -0msxs the ocean. Determine the shock wave angle it pro0)jaqzxmr -.jklmkd8n ,.js- duces
(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 x2g7-tvnu39w 6h;rrqpo q wdh-: 3e ph$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plak (v*1pwe)uw tne exactly 1.5 km above the ground flying fast( wt)kp 1w*vueer than the 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 device that sends 20,000-Hz sound p:b hsyx1 0+bu*v1gxdlulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in+ux*bg1s :yld0v bx1h fresh water)?    s

  Approximately how many octaves are there a:b/ egh 3qey)in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewefoemo 43-n 8-f kg33wei0 vt9o5mlnper pipe symphony. It consists of many plastic pipes of various lengths, which are open on 3fl-o nm04 w5g9 oevotn3emp3 8- fekiboth 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 5xe,v1bx 3jl ca person makes a sound close to the threshold of human hearing (0 dB). What will be the sound lx5xl3j1b e,c vevel of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB 1iv9 4t42y 4 fagdtxphsound are heard simultaneously? t4xid9hy4fvap41g2t    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Wh o f4e0tzt8 qpm2 (pxh6lw5;wgat is the acoustic power output (W) of the speaker, assuming it radiates o ;q2t5zflhpw (0pmg8 6x4tew equally in all directions?    W

  A stereo amplifier is rated at 150 W output at c8whwan/1vn5u. q5 mz c9t/ex1000 Hz. The power output drops by 10 dB at 15 kHz. What is theun5wxc9 / z8t/hq eacvn1w.m5 power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices vyxkbb6e k qe (z/j938over their 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 ikx8 byb3 (vqj6z/kee9ntercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications cztg-k+ngq8 td(5(l ns td): psystems, 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 m72 .ukjvd*fgkga-dpr)m *9v 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 betw8z u jihshxyfzi8(-*/ohw-+; xsa9db een fixed points with a fundamental frequency of 440 Hi/x x-(*h+uih 9zowjzy88fs;-ad s bhz 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 f 6- ; rlcr-y/sk6g5jqjyq3 +effgw2grilled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequenc+rg3-ylcq2-q r w f5gj6syegr;f /j6ky of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one ennz np/apzb2 b4(vfhn qcbn81: 3z bb*8d and also 75 cm long. How much tension should ben hp3zqbv8nfc:na48z1z/n2 b pbbb(* 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 tcyw4k,eer ; 1eht k 64xx7cw8eo resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–105*:y3vjm 4h 9t qvfzax00-Hz range coming from two sources. The sound is loudest at 5jz:t*qyh4vfxm9 a 3vpoints 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 source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistleq0oei6s dy 9hspt/q 66s. One train is stationary. The conductor on the stationary train hears a 3.0-Hze/dqiy6ho stsq9p 66 0 beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train3,; l6 jzelhottq 9yy7 whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How y qo; 9hzy,jle3tt7l6 fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listeo pky)v76e3ck ning 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 e3pk k)6 coy7vfast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequen2;-fko brm7x q;uey1 zcy of 11 Hz. The shorter one is 2.40 m long. How long m2xq er;uzfk-17o ;yb is the other?    m

Two loudspeakers are at opposite ends of axs q2qc,;acod-x8:ldg aj zg0:c3z f ( railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, z2lxfjz cq-g,cqg3 ;0 s:o8:a c(xdda 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 :f fzg,qtfe0v:y gp48 the aorta is normally about 0.32 m/s what beat frequency 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 sp04zfe ,8vyqfg tg :p:feed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a uaag4 tgi vekc82-, v)moth 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 5eak-t8ic4,a) 2 uvgvg 1.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of hi: cl pc.hu0 msfh+2k1vgh frequency sound pulses as it approaches a moth. The pulses ar+km u1pccv02fh hl .s:e 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 next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to sendq93.i yhep)5 8qfb 4)dmkntd k 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, t h)etpq9 imk 3k5bd.fn 8dy)4qhe alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be com)yue u -iu)iz3promised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this ro-) z3uu)yiei uom.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singfh,:/wnmd j:cp*k;bv c d+n y3ing rods,” involves a long, slender aluminum rod held in the hand near ,:;/dnk hn m :jd+ c3bfpyv*wcthe 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 t*x kctf(+i 9hyfyp,/c he human ear at a frequency of about 1000 Hz isic f,t(yp+k*9fx chy/ $I_0$ = $1 \times10^{12 } W / m^2$ 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 hear-k j9pj--j;gjj r3 wrqij-8az s the sonic boom g3 w-qjj;pr- j-i 8j-kaj9r jz1.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbnfbiye 9cj:ybx+z0 ,q e ):p+woat 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