Give some examples of ever 3ban ;6w*ly5q,eieyoqspf6p63 j2ki yday vibrating objects. Which exhibit SHM, at least approximatelbw*6jlesniyq ea66 iq2p 5;fokpy3 ,3y?

Is the acceleration of a simple harmonic oscnoa if4k5az-mg/gdh;5ju s q u1g60p0illator ever zero? If so, where?

Explain why the motion of a piston in an a /pzxu 7c3f5xeutomobile engine is approximately simple harmo7 exfc3xzpu/5 nic.

Real springs have mass. Will the true pern,z )aip:4 vhmjhbhfpq+0 x (/iod and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an j mnpvqh(+: i/, p a40xfhz)hbidealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillat jf 9;v,-tg/gf7 euqpl)) grztor (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and c)l u(rns4t, rthen is released. Describe tn) ,rrct4(slu he scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gas /9i,dhgeqg/7 u9d; 9lnkum iin or lose time when taken to highs9k n9uiugl, ei7dm dq/ ;/hg9 altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48). ;s 700 tkozkwq+e,lzoHow could you estimate the height of the branch using ok0qo;tklw 7z,o se +0znly a stopwatch?

Why can you make water slosh back and forth in a pp.p0 es7jxr;ran only if you shake the pan at a certain frxs7jrrep0 p;. equency?

Give several everyday examples of resonance )b-l *:*aeovdt nhm5y.

Is a rattle in a car ever a roe mq2kr;:us8x-hi/+kpf 4 kpesonance phenomenon? Explain.

Is the frequency of a simple periodic w*j.ulsv /wi1l ave equal to the frequency of its source? Why or wh1w. lls*j/u viy not?

Explain the difference between the speed of a transverse wave traveling down a nb: db+i(i6m niyco:+ne. nx;cine :+b mxn.io(nyd:6c+;nbi ord and the speed of a tiny piece of the cord.

Why do the strings used fo,3nland5 n9j;q b9xzmy t 7bv)r the lowest-frequency notes on a piano normally have wire wrapped aroun3 mxvjq lby 95dnt)9;ab 7,znnd them?

What kind of waves do yuz ns5mxnvezl8e+ e.5k q-pxw(v a5n5u,3; igou think will travel down a horizontal metal rod if you strike its end (a) vertically from8ns.a5zuwx,5e ;mqi5 zn(5ex-p uvlkg+n3v e above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, buzx;m u*6 m i+s c,upk;cma7x9dt the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperatuz6x9mx* u,kmp7dacusm +; ;cire?

Give two reasons why circula+scyf35q0fx ( mufn p6r water waves decrease in amplitude as they travel away from the c0yfnu 3xfqs+6 5p(fmsource.

Two linear waves have the same amplitude anlv a;1*exbwyfl m e+vs542eq )t6z. wld speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more ene.fa6wly ee1 v4b );s2vzltmle xwq+5 *rgy? By what factor?

When a sinusoidal wave crosses the boundary between tcfaisn5h tv 7 aa(q--s+vm,c8c0,j xtwo sections of cord as in Fig. 11–33, the frequency does not change (h8-,at ( vcf-cas j,qt5n7ca+i 0xvs malthough the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you couydu7 y8z) uf+hld touch it with azf+8ydu)h u7y knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incidee 8d58 p9it ljvv bvh1i4+x*nunt and reflected waves cancel at the nodes. Does this mean that 8 8b+*v e459xpd1it jvvunlih energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how mit 7 bnnvgb-p310w+ mzight we determine whether the energy was being carried by particles (material bodies) or by wa 3vbgnmt-7znwi p 0b1+ves?

  If a particle undergoes SHM with amplitua.oqin;sg +o13kw+m jde 0.18 m, what is the total distance it travels in g + oqaj3.wis;om1n+k one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from i.* (i-zje4qym lo 9kqz-z s;vlt but is 85 cm long when a weight of 180 N hang(o k m;zqjil- ezyl. *qs9z4v-s from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car c(t+o zlry2z0s ej. ;ywompress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of y 2swzy+lj0 (er .z;tovibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs fru:3;s sq cz 0zaa5cn-pom it. (a) What is the spring stiffnqc5 -z:ps 0;acaz 3snuess 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 aq1qno3y;apaby50 / kj frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its fr qq10 nj5ak/;aoypb y3equency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of thpubv gv;(k phojum)u v va8a18hrvb (7b04 y:;e mass in Fig. 11–2 at times t = 0v:g b4v0v17pvbhk8 b;apau v(; ou )y8mu(jrh,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 spider’s web. The gf871ggyk+ e9wvv //km qv3vt web vibrates predominately wt 7kgkq9 gv3/ 8 /1vyevgv+mwfith a 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 wap*: ;*i v 4fxoutp9uan additional 680-g mass is added to m, the f9;*4 uvp*: px awoiutfrequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a08p,: mk kn2y f75 qvlfzs/teu spring vibrates 3.0 times per second with an amplitude ,0 ptkff k5yel:smz82q/7 nuv of 0.13 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 the speed of a SHO half the maximlotsf 4q-0t6; a6tqfkum value?-tf6; fq6l4ta sqtk 0o$\approx$    A

A mass attached to the en;gxd dbd tc-5 y0pcpmp+ 6a/,vd of a spring 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 stretches a vu(em zj 1f sfmx 5gn2.xdms4;/ertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to mumxfe5/sxj2m ; 1 d4zgs.(nf reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring w)sngb* gt imk60vb okc1im); s 0n5a7xith spring stiffness constant k = 280 N/m and is executing simple harmonicn gsi0s kcxn0* ;og m)b16tkb mi7a)v5 motion. When the object is 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 to compress the spring mp)(tomq h70prr1vyrj,7,dyfh 8se3 of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball lea()07er ftdo1vmh3r pyy m,j 8rqph,s7ve the gun?    m/s

  A mass sitting on a horizontaqew-m+h. ap n,l, 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 rnp .,m-h+ aqewest with the spring compressed, the mass experiences 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 accorwkyj68/ pl3t6hk52swqt z+ buding to the equation x = 0.45cos6.4t where x is in meter66 w+k sjpk/q3y 28ut 5hlzwbts and t is 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 half K)z+pvi gi i,qtt18d ;jE and half PE?qp j)ttzg,iiv1 8;i +d ±    A

  If one vibration has 7.0 times the energy of a second, but - ack3pgxnx74 their frequencies and masses are the same, what is the ratio of their amplitudes?kgan4x -c7p3 x   

  A 2.00-kg pumpkin oscillates from a vertically hangingll hzr1z(uot) zgcud 4 .4.5pk light spring once every 0rd)zuko(hp t1l czl4.z5u g.4.65 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 par o*yb/+ dftmtbgcn2+ 4allel vertical springs, each with spring stiffness constant k (Fig. 11–49). What wi 2tdnty/gb+f mo*b+ 4cll be the frequency of vibration?

  A 300-g mass vibrates (lu4 uf*gn7yraccording to the equation x = 0.38sin6.5t where x is in meters and t u(4fln rgu *y7is 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;lbokz -6,lw-ip vdn 5 examples of SHM, labeled A 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 il/jxh2 -8gchN/m) is strc82 ih-g lh/jxuck by a hammer, which gives the 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 c,equn,fzqy6 +onstant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mfn ue +6,,yqqzass passes 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 constanltebju5owg 3+ 8as+ i: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 03ouq; (quk s5vv-gwi 99gdn ,,8yygbco. zysa 0.600-kg block attached to a fixed horizontal spring whose s (;gd byn3vzygyo.,ko iuw 05g 9qss8c -v,9qupring 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 6 (b8vwi leqlc :j)um,(5.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more timesm:8(jb,w) liv (ulceq 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 exz5w rr4nm-ebcv2sg :3actly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simpl1ovy z wb q-qaf;94bh,e pendulum be if it is to make exactly one swing per second? (That is, one complete vibration takes ,v-w aybqq4 h;fo b91zexactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, whel c z* ml3-nbw u*cgs6qfe6))jtcz+8jre the acceleration of gravity is abougumqlblz j ecf +*))z8- 3w6 ncj6s*tct 0.37 that on Earth?    s

  What is the period of a ska g4mmfzid.2ejroti 1, r;-)imple pendulum 80 cm 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 massz r- vmztog/0k oszug *b:g7,a-lua+w m/m((j of 365 grams, and it is released at an angle of 12.szmg akmurmz gw-:vg ,o(+ / 7jlt/z0- (uo*ba0 $^{\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 lengt4s8x+ triurs 0;8*-mc5vs 7lzo izhxdet ke1(h of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length odcs *0 ksr1r4st8ez8 ze- 7thmv(;ox 5liui +xf the pendulum? shortened by    mm.

Derive a formula for thed mv-+)vm;,ifyuh+x1tgh 7j d 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 fr pkk2,0lrgrh26;nyd c j1 xa;xj3lw r3equency of 2.5 Hz. At it is released from rest starting at an an21 ,;;p23xd3rrcakj6lklygwrj xn 0h gle 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 every 3t7a: j26 w9ixpi1eis t.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waxw:ap is17j t 26ieit9ves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a ,mcraoi6g *l/.(/co b-x gahbspeed of 343 m/s How far apart are /.gah6o cx/crbagl ob,*i(m- the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between0n v0(9kxeqwo 550 kHz and 1600 kHz (kilohertz) and travel with a speee90kvwnq (xo0d of $ 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 w-y.s 5jbg(+ml*qqn d ch( s3aof longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same ela3;)zr/h syr4wilqtl o;l 7:cf stic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, andth l34z:lris)f;; or q7lywc / by what factor?   

  A cord of mass 0.65 kg is stretched between two suppo-i-a5s,ups xe7 cozm )xy38nrrts 28 m apart. If the tension in the cord is 150 N, how nsp,xc-s 75)e rauzyox -im38long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a ey z( /b,cl reup )l6ar(+lcwg4pdk 43steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into thugr/ka (6e(b wl,pc dp y4ez l3+4clr)e terminal 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.(1c pndf9 fdc( He hears the echo of the wave reflectcpfc(n1 dd f9(ed from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travet(1lfs 2d cbt.- ys1h; ) bmwcl/m1xmjl at different speeds, and this difference helps in locating the earthquake “epicenter” (where the dm l t bl )yhmxc(m1.;2cd1-ss1/bwftjisturbance 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 su vaov lcjs;5()d)m nz+rface wave can be 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 b j;n(s))o+5mdca vlz vegin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes rfo .5cbp29n6-g afay, of an earthquake P wave passing through the Ea ffgn- yp2o6cr.a 9ab5rth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passingv,mkt3cgrc5,uci 8 ,l through the Earth is measured to be 8,,,gict3um5cvklcr $ 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 travgwt67i8xem5.hbq qctl3 ; fy4el through the same portion of the Earth, but one is carrying twice the energy. What i.qg3w mf5h qt6 ;l xtic4ye7b8s the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have tf0 knwwsbttz (4xe--3he same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of then w-t4sb(z3 w f-tek0x two waves?   

  A bug on the surface of a pond a00t755 ic3o in cegfais observed to move up and down a total vertical distance of 6.0 cm, fr7i0e a 0 c55cofa3tingom the 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 shown in Fig. 11–52 are moving toward each other. (a) S45xqu tke0tf i7.-o xxketch 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 ene5o 0-.xekttifu4 q7xxrgy at this moment?

  If a violin string vibrates 10k 2mq xc4,ajklfb mlyb,7z/at 440 Hz as its fundamental frequency, what are the frequencies of the first four h x ac7,4,lk 0lkm/bzjmfq1by2armonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz whe. ywq;)8a slnkn unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds .;l8) aksqny wof the string vibrates as a standing wave.)    Hz

  A particular string resonates in fht*8*ro(m gslp09 ttuksxkx 1y)p3o7 our loops at a frequency of 280 Hz. Name at least three other frequencies at which it will retkh*0 )gtps rm39p*s x(lx u8 otky71osonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If th/-swpjmilw4 n b i,c- vt k7iw0pkfgxf7;1+2 ce frequency of standing waves is 475cf s7m7w+p 2 ;/giw l,t vi-ki-bc kxfnw10jp4 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz anysbn0dk.) 4x pfx ;kn0d 350 Hz, what is the frequency of the fx.dy p4 bxnfn k;0)s0kundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.wfer :1pmve 7-6 g. The distance from the bridge to the support post is L1vefm-:w7 p er = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measured zs6cu fs;:m0z to vibrate at 205 Hz. By wh;mcs:z6s0 uf zat 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 ec. a j2n9ujs0is supposed to vibrate at 200 Hz, but it is measured 0j casj.9nu2eto vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical 60hdfqn6lo,9 -me 4a9kn-Hz vib9lam dn69-h4 ,nkqfo erator. 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 may be adjuswug uk tt0o,e+6nc;k1ted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by vary1tuu6oe w+c0 ,kn;t gking L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right fre9hqvy7ji ii*sn r s(uq*-3 5xkquency, 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 vu*-i9 5 ikysrq 7(h 3qjsx*intub 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 boundaru;vtl8p2 c mgan.m-2oy within the Earth between two kinds of material. If it approaches the boundary at an incident anglel.vum-mnp 28g o 2atc; 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 “she vhsp0 u22e2ynno,3 g1)lp sfylf” where the velocity changes from 2.8 m/s to 2.guo),elhvpyns2023 sn2f y1p 1 m/s If the 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 .:-y tqne cdgg4 :o2rowhen it hits a layer of cold, dense air. If the sound wave hits the cold air interface at a.oyoq -r et4g:ncg:2dn 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 jhd-z+ (kp(wms. gpj0q we*x9between two types of rock at a 38qwxshk m p(dzg+*-.w(9pj je 0 $^{\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 manub;isz. xwa1z(6r)bromzs +akq/5 .h pal, the dish has to be pointed in the direction of the satellite, but an error z16is 5z;p/xba r.brhamwk)(s ozq+.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 tragi9d;c*d 6 7zorm kri2vels across the Pacific Ocean. As it ai;kc 6o*g7rrd29 imdzpproaches 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 warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumcuqc3;luujdz+ zj c vk139f,+ per has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, cd3zjv3zc +jf +qlk;,9u 1u uccollides 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 belou a1:a6nsg7gu9cw k u1w, which stretches the net 1.1 m. Assume that the net behaves lik k:aggc67a19 snuuuw1 e 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 freegv:1 76lzh7;f:yjf zzrgv l) wly hanging spring. The mass then falls 33 cm before it stops hvvz7 j6gy )lg:r:l zfz;w1f7and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge sprinvd a*o9jq2c ;4rqiwbghne +6+ g at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 mibo g jwh 29v4 a6nqr*ed++q;c. (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 yw0;7z2vnne2dky u3bx76 ze j just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over th3672zen7 b 0uwyvy xzdjn2;kee top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the centen:a g*ajz3 sx.r of a 33-rpm phonograph record have a wavelength of 1.70 mm. Wha3:a asnjgx*z. t will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x a,wuvcy 7e :vc* 9ayj:is in meters and t in seconds. Determin*c y7j:aw,9vye vc:aue
(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 freq 0:qi emyi2c:ouency f. What is its frequency if it accelerat0:q: iioymec2 es at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on(v 6hq9yy f 4gaoq-k y(f6dk(e khj;q; the raft, it sinks 4.0 cm deeper into the water. Whha ;-g4 9y jhkkf q;6feoqv6 k(dq(y(yen 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 to play at 392 Hz (G) ajwj 1*i8in2g wnd 440 Hz (A n*wi18 wgjj2i).
(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 dow ttndo:nnr+i7- flg)3 n 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 wavelent 7f-r i)nntld:ng3+ogths in the 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 267hatxf. whz, wp tfl(hz7.:t8 4 Hz, and the tip of each prong moves 1.8 mm to either side oh,.ltfwz7a8 w thf(tx hp:7z.f center. 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 ofzt f ukd/.y:.;yw gt8f frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order tty/td;k.z fgfu 8 :.wyhat a 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 can *wv)vp j o2j)jslide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and t jojpv))*vj2whe other free.

  A “seconds” pendulum has a period of exactly 2.0 2, /eikmcgwcle6 :/hm00 s — each one-way swing takes 1. cmi,6 we2l/hgc/m:e k000 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 ver v.ij;ru6zh 0ztical direction or can swing as a pendulum of small amplitude, but not both 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: Letr jv 0uihz.6;z $l_0$ 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 tension of 255 N. A pulh foc/+2v:uec)1g vkg se is generag ohef:vv k2) 1cc+u/gted at one 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 from a ceiling by a spring with spri7 mg9- mqxrpv1ng stiffness constant k. A penny of mass 7-m r9mpgvx1q m is placed on 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(lpg v +nb:d1t wjz/h0 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 ispgbvj/0:wn tz(1hd+l the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gives t3z593t nz j-rgdjgo j3he dimensions of the block). You push it siderz5g9g3 3- d3jzjontj ways 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 jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz