Give some examples of everyday vibrating objects. Which exhibit SHM, at leaks6rv+k*ma1k7jb ) j7 fh/iuy st approximately?kmkyvk a1b7j6f+7 s /hurji)*

Is the acceleration of a simple hab5jf2 k: gii)crmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile en* aaro:ewh 3s+gine is approximately simple haas*a e:h3wro +rmonic.

Real springs have mass. Will the true period and frequency be largerh)dhsi ab- oex.z*g6v vn:-w, or smaller than given by the equations for a mass oscillating on the end of an idealized mashg6 vb .vwax:dz),o- * nh-eissless spring? Explain.

How could you double the maximum speed of a so.lalnh +8y 5rimple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scalvu 1g;vf-xltf4 e 0w(de, and then is retuvlgd10x;(- e wfv4fleased. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea l: trnm+bl0av2( u qb2level, will it gain or lose time when taken :unr20m +(vtbb aql2l to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the q0i, agho(sk) ground (Fig. 11–48). How could you estimate the height of the brasho 0 gk(aiq),nch using only a stopwatch?

Why can you make water slosh back and forth in a pan o ank);usho1khybc7yx 3r+7 o2nly if you shake the pan at a k chy ayux)s2oob; h rn713k7+certain frequency?

Give several everyday examples of res 7 5 f/ujhqzu/btaj mk.v0z.,z8cd/jaonance.

Is a rattle in a car ever a muo p8skved v;1h;:5gresonance phenomenon? Explain.

Is the frequency of a svw axzz3: -pg2imple periodic wave equal to the frequency of its source? Why or whz aw gv:x3zp-2y not?

Explain the difference between the speed of a transverse wave t5s/ar +i )uazzraveling down a cord anz+5aur)as/ izd the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes onv/usnzpm*a gg 5vf3l/eo.84k a piano normally have wire wrapped 3elp/ vu szgmk gno54v. f*/8aaround them?

What kind of waves do you think wi9xjuk69jfgz8*,ngv e9 r w6rg ll travel down a horizontal metal rod if you strike its en z6w gjj6nfuxk,g99grevr*89d (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but the :wdhd h6w wzyxz51,ir6 7k gqah4h8l 9*c)xel bulk modulus B is nearly independent of temperature, how would you expect the speed of sound wh* hgq 6i1 r5kc )w:a ,hedlzlxwxh94dzw6y78aves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as thq+oa7u 52 a5qq 7qjmnnm0 (4/pevu zjrey travel away from the souv5q7 (q nu754mjaan /qj or+umzp qe20rce.

Two linear waves have the same amplitude and speed, and otherwise arew* 4;p g,jgwvl identical, except one has half the wavelength of the other. Whi*, wlgvjgw; p4ch transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections kas1p pq (y2p95cg5feil 12apof cord as in Fig. 11–33, the frequency does not change (although the wavelength and velociqa9c(5e5sl p akp1i2 2pgp1yfty do change). Explain why.

If a string is vibrating inn2 b:70,g5owxand( jmo/ 7uvq qmm, wi three segments, are there any places you could touch it with a knife blade without disturbing the motion?xmd ov 0:qobg27mnjia uw5, / ,wq7n(m

When a standing wave exists on a string, the vibrations o m8l/9efy3ku7floqb) 0*havz f incident and reflected waves cancel at the nodes. Does this mean thef0l l*yq3am9f ho/ubz)8 vk7at energy was destroyed? Explain.

If we knew that energy was being 2ja v((reftms -/+cc3 iu+huqtransmitted from one place to another, how might we determine whether the energy was being carried by particles (material bodies) or by waviam(c/cu3(vsq 2-rj uet hf ++es?

  If a particle undergoes SHM with amplitude 0.18 m, whaxjzq(;d8s7mh ,xg x-rt is the total distance it trxs mz(gdr ,7q-xxjh;8 avels in one period?    m

  An elastic cord is 65 cm long when a wv f2:p d4k8ccheight of 75 N hangs from it but is 85 cm lon4d2pchc8v: kfg when a 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 its 68-kg dudi/2h ( te2ueriver gets into the driver’s seauh2i2e te d(/ut. 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-k96 dd.ro1po ,f hhwc;z9:wavx g fish hangs from it. (a) What is the spring stiffness const,a; 1cdfhx: . 9rw6odhwop9vzant $\approx$    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 frequency 7.*zxoe4zvkeo 8yv;k of 3.0 Hz when a mass of 0.60 kg is hunz 7*vez vx48oky k;oe.g from it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the*2rp/xa lnuw 2 position x of the mass in Fig. 11–2 at times t =*r/ wplxn2au2 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 i1,uc )/eh ,mgu5eysm g/xf:mzs caught in a spider’s web. The web vibrates predominately with a zyg/hs,m)5e1u:g m/,c mxfuefrequency 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 e l02(j ,taerrfrequency of 0.88 Hz. When an additional 6r l,0re2 a(ejt80-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times j;rzr 6cfm x(l(;-toxper second with an amplitude of 0. cj zt-r oxlmf;r;((x613 m. 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(fyjud 7n8 hb3,epuw- the speed of a SHO half the maximum valjf(u dwh78eb 3,-np yuue?$\approx$    A

A mass attached to the end of a spring is stretched a distas,d- 7xvpy3/gred; z* xbye. vnce $x_0$ 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 strq ,vcmyh8q0ura ( ub(3etches a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and ru0,ayvc 8b(qhq3 mu( released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to onu0ix:4f g7u a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object iuo nf0x:g4u7i s 0.020 m from its equilibrium position, it is moving with a speed of 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 to3 snbv2:+-e4e5baqj)efzg 4bw5b6yzv tl*ll compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball lea*)bz5zjyb ellnt :flq+sw ab-g v52ee 43vb4 6ve the gun?    m/s

  A mass sitting on a horizont m5p nv:sc y*75t0f. o+o 1wcz(zhypzxal, frictionless surface is attached to one end of 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 experio 5z:(0fc cwh ypnzvzty51*+o.smx 7pences a maximum 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 = 0.1v*9 ,t0bp(dp hxkw p-eibh 1e45cos6.4t where x is in meters and t is d 1w0(9i,*px e h1bphb -etvpkin 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 ts 7q 6ooc//9shpw7yz*rbq4kp he energy of a SHO half KE and half PE7p9s7opwq*qbk4h /o /6sc z yr? ±    A

  If one vibration has 7.0 times the energy of a sgcjo p(sc)tqa(ru u w 1q;w;/ch0t/; 4ewl, ncecond, but their frequencies and ma ( e;ascthjt /on w q;,l4 guw(;cp0uwc1rc/q)sses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hangingj8e6p obh* itl xc6omhe 3a9x2/xhj 1 y-o8v.f light spring once every 0.65 s. j3 m-9 6ap8oc*/8v6exe ty2ih xjh1hobox. fl
(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 springs, eac/v*3bn8f.)smb bw 3a8npjuq dh witmp8v/3bajns wf b nqd3.)u8*bh spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sh (idxd/6 21kfdakwj4 in6.5t where x is in meters anwf 4dkj1/h(2d i6xdakd 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 A and B. For eat d ;.zhi2:oirch, 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 restan4iz) (b w)ba on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives taz) )4(bbniwahe mass an initial speed 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 vibrates wit cxd6 jpxv(*-qh an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passecx(6pjd *xq- vs through the equilibrium point (x=0) with positive 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 spring stiffness constanlg z))dje2lp( ts $k_1$ 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-.w5ozxf-uv* qf xd o*2kg block attached to a fixed horizontal spring wh *wd2qoxfuz x5.o-*vfose spring stiffness 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. Af+0 y4gkw x(ixuodpz5,ter reaching his lowest point, he oscillates up and down, hitting a low point gw u+4,xydzok i0(x5peight 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 the 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 exac et6zh 4kee3 rnvvu+4za1 qu6:tly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pend*im d6,pqy*rrdsk 7pupry: 1*ulum be if it is to make exactly one swing per second? (Ty67r*:pkd1 pdqp srr yium,** hat is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its peri t 2tw4t(apjfxsf3:q, od on Mars, where thef2 tfx3q ,wpjts4 (a:t acceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm long ssf2 m19 d2ten(j0ye c
(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 mixrcj+i0pbs)q b3 new/yi 7,7ass of 365 grams,ew+bip/qj0xrn )3 y ,bcs7ii7 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 0.9930 m. If the cl4.o7v)yxh* r2 urfexgab tgs e: 9/0qrock loses half a minute per day, how should you adjust the length of the pendulum? ag0*2rex/ :. b4qe97frhtu y)gr oxvsshortened by    mm.

Derive a formula for the maximum +0rj7 f5cn+fps-6 b jyol7n6 qyyh6om 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 +*xxeat w6fv,*tj ;o likdau*i w-. /nof 2.5 Hz. At it is released from rest starting at an angle oat*;kvf+ntu-,w.l x axjo/6de **i iwf 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 tq -hb6g/)obh4(fe ;z6jml m*tkof5rm wr 2q5phat wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance b/m 4b(;j5q-r)5wf2 hzfhr m6k bg po qm*e6tloetween 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 with a speed 86 h ot2nck.gq; x8oeb;ir sb*jztk:2of 343 m/s How far apart are the wave crests (compressions)? rct8;x62 b ; 2s.kejb8otz *gkoq:ihn   m

  (a) AM radio signals havewx w81zh 5tzh8 frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed ow w8xh hzz851tf $ 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 of longe b 8l:df 2ydsjql4r5.itudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense s-1jrxie6-+o6 rqruol 0 h0nnas the other. In which rod will the speed of longitudinal waves be greater, and by what fl0irqh-6x+nr oj eru016-son actor?   

  A cord of mass 0.65 kg is stretched between two suppopn(b6nr 5r4y u2w) i96isn :y,ior mnwrts 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one supporyn6 ir:2 ouyp nr irn9wi 4bm,ws)(6n5t to the other?    s

  A ski gondola is connected to tu uf ec,w 8wom/4pu/q4he 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 termine4w,uw// p4cu 8uofmq al 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 surface of the sea.ov;jr+ 1 tq e dpqi1wtk4.io(4 He hears the echo of the wave reflected from thewid ;ojk.+1e4(4qqv1tip rto 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 spee3 rg- es)g st3i4psf.xds, and this difference helps in locating the earthquake “epicenter” (where the disturbancs xs.)r3tg-3 psieg 4fe 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 surface wave can bglu1nkf j7i ro;7 1z5ae approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the groun r71igaln7kfu;o 51zjd? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) y2 m*uzry 0p6wthe amplitudes, of an earthquake P wave passing through the Earth wp2zy mur0y6*and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured d4jotlkqis:40p1p i8t b+ m.tto be bj1qil0t4id o s+m8 ptt:p.4k$ 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 through, yk:jtm 38icb the same portion of the Earth, but one is carryb3ikc ym t,j:8ing twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequex9msqdmk-e4m )4o oh- ncy, but one transports three times the power of the other. Whamk o9 4)m4xdhe-moqs- t is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and dy84vo xa0atml3r k( ;gown a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease ;y0x34a (ltgm k8v oarto 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other.ej7w ly3tbn9ls,*3 vo (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 str7vt,yw9 3jb *lne sl3oing is straight. What has happened to the energy at this moment?

  If a violin string vibrates azfh+r7v3myhjg+ zbh. : q jp14t 440 Hz as its fundamental frequency, what are the frrbf jzhzpg 7jy+1mhhqv+43 .:equencies 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 unfingered. At what freque huu-wn,vq4+o l- ra16enra 3rncy will it vibrate if it is fingered one-third of the way down from the end? (That is, onln-e6lurhrqw o-4n3 a a1vur+,y two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency ofyam2t-rrzw0a. /y h )h 280 Hz. Name at least three other frequen)tmza-a/ryyw . hrh02cies 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 frequency of standing waves z 7knw o o0i9q4ukqz2-ge.0lsa(z+ qd is 475 Hz, how far -kuw9e z0n 2s.iq(dog+a07kzl4qo z qapart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, whanvur-0 :f9u:9 6eyufp ohnz ,at is the frequency of the fundamental? o:auu u n9r9zpe fy60,hv-:nf    Hz

  A guitar string is 90 cm long and has an02u-f 3 wxcco mass of 3.6 g. The distance from 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 fundamental and fifuc - noc03x2wrst two overtones?    Hz

  A particular guitar stru4ll6 nc4bfn 5ing is supposed to vibrate at 200 Hz, but it is measured to vibrate a6blcn 4f4nu 5lt 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200(u 6- .dmxzyhmm)n -i/ehr3pk Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string bee-.3uh(xi6n)kmmhprd -/ z my changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-ampljb tee /2(;q+rcy pfj3ff4cs /2jy-ar itude mechanical 60-Hz vibqr4/tjjf fy( s/y+er;p cjbc3e-2 af 2rator. The string’s mass per unit 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 mazv g6-brpj ;ypws35r5 y be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave y 6 pb5jsv;rpr w-35gzpatterns 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 ju9hs-d (nwhqf 8jip x:pz.cf, cm17/wy st the right frequency, the water alternately 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 0p 17s cwi:/(,pd 8y9mq.h xhn-wfcfjz.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 wi +feppk lgbnbqonbg3 *6*c;3 -thin the Earth between two kinds of material. If it approaches the boundary at an incidenf-cpbq b3g eb on3*g* n6+kp;lt 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 “sh9iof+2hus t 6ielf” where the velocity changes from 2.8 m/s to 2.1 m/s If th+tof6i i9ush2e incident wave crests 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 lyvns-d 0ww3ydf2lm lb52 eq7 *ayer of cold, dense air. If t53fw* 2yd- mlqsyv7b ndl0we2 he sound wave hits the cold air interface at an angle of 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 between two types of rock acj+a-uz3l9 :s ra4 xezt a 3a su3car :j9lx+e-z4z8 $^{\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 in diameter. According to the user’s manutfl+63scjbp1 9ki5 m nal, the dish has to be pointed in the direction of the satellit1+j5bm93 kf nipcs6l te, 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 kman 6,4s.h wktd and velocity 750 km/h travels 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 knowledge and ws6wh4k an,dt. arning, 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 stiffnesig5*gv7h;i(b4 igaq d s constant of 550 kN/m Find the maximum compression of the bumper if the chi* dqg;57 g4v(biia gar, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretches th hw8rix68vr,wq jle l+g4jd4 2e net 1.1 m. Assume that the net behjjx2 wd4lh 884l w,+ ri6rgqevaves 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 spring.we7c;du2h tv . The mass then falls 33 2.vt;cue7w d hcm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–5 bbknm:korb c45.-fq -4), compressing the springnrk m:- .cbb45qo kfb- 5.0 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 coffee (diameter 8 cm) at just the right pace of aboxq)k,:ytmizsveev.um,/z -0r 4t ete 0e5nl5ut 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speedr5),5 s x0k/evty0vim- zmtl :ue e4q.z nt,ee of waves in the coffee.    cm/s

  The ripples in a certain groov4hst;+ riv; obe 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be thos;h vb 4;+tire frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates accto5aytx tc,si55/-z +.z onvj + boh,lording to the equation x=0.650cos7.40t where x is in meters and t in seconds. Determineoo,yhx-j5 z+t ic/v nb.z5+t,sto5 la
(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 with frequency q,bj,2bw)(jd,(5s aqgdta cq f. What is its frequency if it accelerates at 0.50g (a) c (d bb2q,awadq5s ),jj(,tqg upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-ksz 1 2,jz/c;jqeiler5d/ 6cilg man stands on the raft, it sinks 4.0 cm d cre,ld ;zsicjq/1/2lj5e6i z eeper 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 instrument are tuned t+ 68-2d v)qu*vvl;vc2z kr f vqzh0orpo play at 392 Hz (G) and 440 Hz (A). o- r;vqr+8)vld0k2v hc qzp2v uv6 zf*
(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 down the stretched two-part cord o4 qhy. )xkca yw.il2l5f 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 theikw2a.54qy x hylc ).l two sections. (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 of 264 Hz, and the tip of each pro3nwh )b 8)8 s:pzs/pf/giajcjng moves 1.8 mm to either side of centeip ) a3/: wgsf8j8cbsn)pj/zhr. Calculate
(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 of frequeu)by prtorpcegk:) *0 ov r (itm:/4,sncy 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble place):rb vtrie,op go*/tpk syru(m:) 0 c4d 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 thats jbnq a*1nq-5 can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with *sqbn5qa1 -n jone end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — mc rdn po08*dj:86x.xdm xh4ieach one-way swing takes 1.08.c 0jdmd xr8mxd:6*i4pnoxh 00 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 direction or can swinh7hgod- *tk fn9r8y 9ng as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or thy tf9kdo-nh 7r89*nhg e 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 123z w1v2wlr8e5 h g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms 81hvrlw5 ewz2 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 from a ceiling by a spring with spri1t(7n x vtikb6,umfsh 1bw* p1ng stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscil x 1,hms71k* 1 u(inwvbfbp6ttlations 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 junkyar .m4mda8rrymqb mj) i4 t4z2:hd. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of a:byrrmmzq jd4t)m2 .ih 48m4 the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a pw pcj9a 8q3 72 2e4wbakqa9hbxlate 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 that the shear modulus (Section 9–5) of jex9q chaq28e3 ab29kawb wp74jllo is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz