Give some examples of everyday vibrating objects. Which exhybs2otr q:,u3. w;vgoibit SHM, at least approxim2qt.oo u y3bs, r:v;wgately?

Is the acceleration of a simple harmonic oscillator eva,b1)*ftgtx* iwjek ,i6the 6 er zero? If so, where?

Explain why the motion of a piston in an automobile et:(gjfk,o7;otf ;9lggjm pbp7mi -,h ngine is approximately simp-k ;(tfm pp ggm7t;flhigj 7:j9b,oo,le harmonic.

Real springs have mass. Will the true period and freqjr)* 6 gv,+ m ec. cd95je*rh1skwgfztuency be larger or smaller than given by the equations fo1gt,w 9 +*)dj .rzvjskr*h egmf6 cec5r a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the mahkyu v)m9a(r8ximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale/(kk b o:l+o- h pcu+xgcam9v+, and then is released. Describe the scac++xkbkpuo vmc/ ha :og l-+(9le reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose tim:-kus .fz j3arj 7b 8rciourj.a* *k9ie when taken to high altitk-rk7i zcju 3. :. is ojbufaj9r8*ar*ude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11*h.5kem dx zzn.k 71do–48). How could you estimate the height o* k n k5d1d.7z.ezmohxf the branch using only a stopwatch?

Why can you make waterz i 1)9nh9rmdxog+q9e slosh back and forth in a pan only if you shake the pan at a ceeq)zr99 g19 +onmihdxrtain frequency?

Give several everyday examples of resoq+zsow*r c(3chv0b8q nance.

Is a rattle in a car ever a resonance phenomenon? Explainy*f) wc(p9jrz .

Is the frequency of a simple periodic wave equal to0q :fs mxai:1s the frequency of its source? Why or why not?xm:1q 0s: fisa

Explain the difference between the speed of a transverse wave traveling d tih19: m 53bv1hxlwwaown a cord and the xm19btiw15h v:a3h lwspeed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a pian1: tkfoa4lvva ots8o) j+8z:oi0h0 o zo normally have wl1stkah +fa o 8:4ovo ot z8vj00o:z)iire wrapped around them?

What kind of waves do you think will travel down a horizontal k+mm *v ,exwym(,qpm:metal rod if you strike its end (a) vertically from above and ( ,q(vmxky,e*mw p+m:mb) horizontally parallel to its length?

Since the density of air decreases with an iqz i+mqh d;*r 7*u)tcmncrease in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to t;um r+m*q*h cd)z 7qivary with temperature?

Give two reasons why circular water waves decrease in amplitude as thef)3o1cyp ond5/x 5olcy travel away fropc 515 n)foycxo ldo/3m the source.

Two linear waves have the same amplitude and speed, and otherwise aretv6n. beugqy r s a0tsz0n,862 identical, except one has half the wavelength of t ny6e 0n.qsz2gr8av0tb ,su6the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary bet7kw uwu004 b;qwu jc,zween two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity0bc7;wk,wuuq uw z40j do change). Explain why.

If a string is vibrating in tf4po4/ez.zz l r0;uop rlg 1/whree segments, are there any places you could touch it with a knife blade without disturbine f/ z14w4 /.zgo;r lupzr0olpg the motion?

When a standing wave exists 5hzi+p6g2u c45 -ziih7beez q on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that ene p- ecgiuzq5527 zhhzi6e b4+irgy was destroyed? Explain.

If we knew that energy was being transmitted from one plachphwqjm b b7ba h:.xof213z(, e to another, how might we determine whether the energy was being carried by particles (material bodies) or by b,mhhwx3bp1q.(jhb7o2 :zaf waves?

  If a particle undergoes SHM with amplitu0rjf:4onwsdjam*hnz65 g x4 k0r w37ade 0.18 m, what is the total distance it trav4 w*0a 57ogrh a3nr0zdk nxjs:4mw f6jels in one period?    m

  An elastic cord is 65 cm long when a weige,avy1kpm v*c mj-1grm8t4:cht of 75 N hangs from it but is 85 cm long when m:jpa ,y* m1v ck8-14rcvm tega weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when ;uk/xeo : uv j *ioh)7mhsgb)usw6,h.its 68-kg driver gets into the driver’s so,k./v6 suihh )s;*ubugm :exo wh )j7eat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-k/ihyl 5t0mw,p1fznglq2t 7 z9 g fish hangs from it. (a) What is the sprwpfl5t/tm,q z ihyg01l 927z ning stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a freq6l*fo/b tg*s a41 swo s4pll/ruency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.3s14l6so/p/ *tgwar*lb fs l4o8 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 af 8):ket qlnsh6em.55 mkin +gt times t ) +kkt 68mnnhmi.5eg ls: f5eq= 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spi7vqc/g l. h,. s*bafq 5to.odider’s web. The web vibrates predominately with aofa..o c,dq5v7q.gb/ hilt*s frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. When anh*ojb 2- ouih0 additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the valuj-*hibo2h o0ue of m?    kg

  A 0.60-kg mass at the e xx-sc1ln8xi -qse)h1 .vla b7mg* 3mlnd of a spring vibrates 3.0 times per second with an amplitude of 0.13 m.1le 1 s )gcm3xvmx-nx 8*. -salbli7hq Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is t9rw m (5ouj*n+aq0 dke l9u9gfhe speed of a SHO half the maximum valuel9j(ru *ng uwfqe09+ o9m5akd?$\approx$    A

A mass attached to the end of a s(qg 2x6r co8jnpring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretch89h6ost 4h c/ .3h9dqhe3m;j sncrl wcs-0hques a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium c9s.ch-d06 r 4/q; qhl jshetuo8nhw3hs mc93 position again?    s

  An object with mass 3.0 kg is attached toy;oo ;-tpix.o a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed otxpo;i-. ; oyof 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to comprese;m :jjb hg)n h8r-8pqs the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gu h8;jb )jn:qrgh8pem-n?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end ofmh+nhch (19ch a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximumhchh hm(19c +n acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t where x is/buabc- 6.f gtlbi*hg f1),ab in meters and t isb 1/,bagf* bi -flugt6cb h)a. in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO ryr 5cxr)o9d2half KE and half PE? ± r rd25o9)cxyr    A

  If one vibration has 7.0 times tucrm5 8j) f+idt /v(qthe energy of a second, but their frequencies and masses are the same, what is the ratio of m d)t /(v85fu tjiq+rctheir amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once every 0x6a752d o:c z9z ;wzixspoxv3.6os ax9dwzv:xz x6i725p3 oc ;z5 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springt0o 5xcj( pgr-s, each with spring stiffness constant k (Fig. 11–49). What will be the frequency -rx(tj0 cg5opof vibration?

  A 300-g mass vibrates accordi 6g;+rr2cbtpbi5*dhc cfeoes;385b bng to the equation x = 0.38sin6.5t where x is in mehie 5b6 bb+c 2 dgtp85rfoecrs ;c3b*;ters and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled e :7txobb -2ltA and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124 N9,pgp bb;kr/qm0mw 4dt ,ei) l/m) is struck by a hammer, which gives the mass an initial speedpbibtplqk0mdwe 9,4, /rmg) ; of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrate:qkv)g dxq +;vs with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive;)g x qdkv:vq+ velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spri z:f0aozk /ae1lwc;m/ng stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horw h13a.r (yj up+o c+9lcsd9wv2nst .wizontal spring whose spring stiffness9ty +lnuw+1csw a oc32h9..p djwrv(s constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reaching his ler/r (y ckv3*m ww+hz,owest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and tme3/r(zw r kc+hw, yv*he unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in afj0,/ ci ento .9csk(bj02zgtrs (i7exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to cg) h.s4+,epfyv ,ho kmake exactly one swing per second? (That is, one complete vibration takes exactly 2.0 svpkec,hoy+s4.h) f, g.)    m

  A pendulum has a period of 0.80 s on Earth. What is itdv;4 thy cn.9,t/ ll:mxx4qt bs period on Mars, where the acceleration of gravity is about 0.37 that ovnx.l;h, 4ytmbdtx9lq 4 : /ctn Earth?    s

  What is the period of a simple pendulum 80 c 4a rx4)pr)/bwnpp t:tm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a ma agz, uhd,2l; dn8b:9 qm4wd d56qgiqkss of 365 grl iqaqhwkddz8gd6 :2b9dm4 , u5nq;,gams, and it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0:jufuq 6k r,5nkuk:r +.9930 m. If the clock loses half a minute per day, how should you adk 65u +rqj,:kn:ukufrjust the length of the pendulum? shortened by    mm.

Derive a formula for the 2u3-u jtn evsfwn2l8nq5-v:sr 4md;e maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. A2 ps gc4n+msi34m)p eat it is released from rest starting a) mn2scg4+eis pa 4m3pt an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat everywhddx9l8chht-a*w db( mcyan:; * y/* 3.0 s. He measures the dis/h aln(d-hb9xwma* h ty*cd8*yd: ;cwtance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels gylz :oi g6vbd1u520t with a speed of 343 m/s How far apart are the wavey vzt61u:2lg g d50oib crests (compressions)?    m

  (a) AM radio signals have frequenwe .2*vzed z ,07uywaq;b37ag j5i lcncies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed of . 2q,vyw;j7u3 zce nlba 0adegw5*zi 7$ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed os2wv0wea 4j. 6h6l wg-lhv ht1f longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elasticm2t11o.oxzmn kz; v2hnf 012ra2eiuh modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what factoroh.xre;21 2onf 1zkt1mi vn02 zuamh2?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If t,v n9oeon(a-+eohs7x he tension in the cord is 150 N, how long will it take a pulse to travel from one supporoh9n as en- +(oo,7evxt to the other?    s

  A ski gondola is connhh 8/whplqc 09ected to the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the termina/8h9whph0cl q l and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the sur5,/bh ze2fdkjsrie 4 9face of the sea. He hears the echo of the wave reflected from the2 j4k/ ihesd,rze 5fb9 ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and ni- zypo/ 4l5dthis difference helps in locating the earthqudi p /-nz4o5ylake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surfacsg (-b 0gxh4 hi-ud;abe wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixturdx4b-0 -uha gbgh (is;e of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitumk-aq(9 4p tnbdes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 204 m tkban9pq(- km from the source?(a)    (b)   

  The intensity of an earthquake wagg8rlez+l1bnspbqw /2+ 4wq.6o7phr ve passing through the Earth is measured to be rlb+o+8wp.nw l4e1 q2rq bsg /hzgp67$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel 4i- tpv40jvbo m a;c a/bial16through the same portion of the Earth, but oa4 ljat vb6ao4mip i bv0/c-1;ne is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have t f2m-hemk -v,jhe same frequency, but one transports three times the power of the otjhf 2-ke ,-mmvher. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and yg-k/whkrl 1yo5-hz.down a total vertical distance of 6.0 cm, from h.y-wz y/hr1o gl -k5kthe lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shownjica62 hde; q4 in Fig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this mdaq6i;4c2h ej oment?

  If a violin string vibratx u rajk u5t1paw4,,0(z7h4l;u phldges at 440 Hz as its fundamental frequency, what are the upkz ; jxta75hl014gp 4u,ua rwl(,h dfrequencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unc yx0-det/bhwz.z/ c 5bf:9l mr-r (fgfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, on 9f fwh:c-b (z.et-/rz/ rclyxbm0d5 gly two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonatefndzroh s (315fa90clpe dd73s in four loops at a frequency of 280 Hz. Name at least fd3en( d 3 5fdh1rl79csz0aopthree other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the fwt,7e :2vrelx,0cpprrequency of standing waves is 475 Hetprxr ,0 l2,v7w:e cpz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating 3nw2u:pq2 s q ;k1hk *-te, uhjiab)vhstring are 280 Hz and 350 Hz, what is the frequenc*h :3wj tbvhhkqu1 -,pi) kns2e2uqa;y of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance b99bg xt21mqxf8l+sqfrom the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fubt8 qxxb929 s1glqmf+ndamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, bd3+ k rpne7l)put it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the)3l7ppr+e dk n frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it)myh1vvk*3u8a1w pe:lna /vh is measured to vibrate at 205 Hz. By what percent should the tension in the string 3myhw uvl1v:ea8)pa*vh1k/n be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mec-thyn *8k zf:(yv; cq 2w1,lqizueo c4hanical 60-Hz vibrator. The string’s mass per un-eyuciht(;yzz4:*8 ,vqof q c 1w2k lnit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by jrh 0xmrg; e 27yyy;ngq62dm 2moving the pulley. If the hanging mass2 q2h 0j;d ;y 7rmmgg6r2enyxy m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the ri-3(ix+zzfhgm+;yc n zght frequency, the water altern3 zn- gxmcy fz(h;z+i+ately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Earth lox7:u2p8hel between two kinds of material. If ithleu2xp:lo 78 approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity chsnm+ aig-d; nroi14/ uanges from 2.8 m/s to 2.1 m/s If the incident wave crestsisd+1m a4n;r/oi gn-u make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense air. Icd9oq+;70n l u w8c qcge.b xo*k+xks1f the sound wave hits the cold air interface at an angle of+bscloq *ec 7.cu g0qd kwo +x8xk;n19 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary betwevgx k003 y;m,i) egkw jb hm4vt5hi88zen two types of rock at a 3eki80)vw jmy0vtg8ik;x5, bh h43zgm8 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m i2 5jqpi2o5hir n diameter. According to the user’s manual, the dish has toji 5io2qp52hr be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travelsyy5t8p/f5ho r 3yyowf6f74s c across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledgesfwr48c3yof yy65hp 5/ft7yo and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/m Finbe*:thr- yrr5d the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: : erhr*-ybrt5 Use conservation of energy.]    m

  A 65-kg person jumps from a windokrw6j;.; astg w to a fire net 18 m below, which stretches the net 1.1w;g;jr6tas . k m. Assume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging sp3r3ibmb h8kn7ring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oi7br n3h8k3bm scillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. s15tnd edf 6e c -e7ssm5m7yv611–54), compressing the spring 5.0ymtv cem5-snf1d77sd 5 es6e6 m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of cobu0rs(l9ozh) ww25 a sffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate t) 5swhz(l2rwsb u o9a0he speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the centeh0hss4ypf zh.2zm f:, r of a 33-rpm phonograph record have a wavelength of 1.70 mmszy zfh2 fm. sh,ph04:. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.68e i,7 lwbf26h bfbyw(nm;uk29kq5vze2 5 hku50cos7.40t where x is in meters and t in seconds. Determine yke52blf h u8,bk7k9fq ;hb evu65in wm2z(2w
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates withh: yy4tjgup trg;7yf r51 9.dj frequency f. What is its frequency if it accelerates at 0.50g (a) upwa .pgdr;ytuyg j75 yjfth4: 19rrd,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on thl/ zyqd4y (l8s,tm f+ce raft, it sin/l4,8ylz q+m(c sdtyfks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instvu64g nc 7ja7o 7 kbxsn -d:/wcie(j(y0 pz+lurument are tuned to play at 392 Hz (G) and 440 Hz (A).(ki xvjz7uy s/: bl4jce+60d nwu(-7p o ang7c
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling downkbq 4(z/nk9jpx y+9dj the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two (xjd4+k ky/ n 9qjz9bpsections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency be53 ww7: gwgk(ffj5aiqj:6q of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calcaeb5fq6gw5wf :i w:k 3j( g7qjulate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion ahy /wxtw5/i0 of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that y/ahwtxi 0 w/5a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that 2v 2g9/lcj 7hfeb:x jzcan slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a stringghjj2exb:/ lf7c z2v9 with one end fixed and the other free.

  A “seconds” pendulum has a perip +)g pvgbnq6,od of exactly 2.000 s — each one-way swing takes 1.g6bqn) pgv+ ,p000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direcp62 audq6;x (pfq:iogtion or can swing as a pendulum of small amplitude, but not bg6qdu 6p2a;i x:fo p(qoth at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a yqu,ua8hg e5p +w x-0wtension of 255 N. A pulse is generated at o5+w0u awy-uh,pe8 xqg ne end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended */q6omd kedd8from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed d8q/kd 6edo *mon top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane h3vn2/ y6cemtflux6v 0zjsop450 7ml cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncin yh7 opzu4 /mnvvj6006eltcfmx 5s 3l2g at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate0m.rfint6uub ). go 7-4jvqae as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given tu7omr6 i)0vubq.4g-f aentj.hat the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz