Give some examples of everyday vibrating objects. Which exhibit SHM, )xj 1ath4ulb8etsi8)9k( xym at least ap)eit amuk4tx( 9sbx)8 1lyhj8 proximately?

Is the acceleration of a simpvkngg5q o1gm8 d,)04(za air zle harmonic oscillator ever zero? If so, where?

Explain why the motionp9 f,be0g 07u/yjpuy y of a piston in an automobile engine is approximately simple harmonic.y 0fy,u7 g jb/ppyu0e9

Real springs have mass. Will the true period and frequency be larger o;np4vy1pf1v* kmtpbh l(/e (p;u g4 ifr smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Explain.4fv(fpk;(i1n ;* lypbheumpt p/ 14vg

How could you double the maxi*r w:3s:p7y se5jdylimum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached tob2 .wsik5ys+*w 7r0)j zd xznm the hook of a vertical spring scale, and then is released.riz +d7 sw.25)nyj0zmwks xb* Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea levekv7 lrknbh,1 bp +0pv,l, will it gain or lose time when taken b,0kp,1bhkvv nrp7+l to high altitude? Why?

A tire swing hanging 1lnua ba;.-khfrom a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of t- bu n;lakh1a.he branch using only a stopwatch?

Why can you make water slosh 3ir.lo3b s nr-u)pmioe,.+ hgback and forth in a pan only if you shake the pan at a certain f +,uo3.iirnbgm oh-)s e p.3rlrequency?

Give several everyday exampleq ydxx( 6t*4qts of resonance.

Is a rattle in a car ever a resonance phenomenon? Exwk,m 9vfgd x 01bk;c7nplain.

Is the frequency of a simple periodic wave equal to the frequency of its s;u/ s4dp a3gvvource?3 pgvu a4s;vd/ Why or why not?

Explain the difference between the speed of a transverse wave traveling bo7oba1o 7ff,b--l2 jje/utb down a cord and the speed of a tiny piece fe,a-1 t lo- bo2ujb7bj bo/f7of the cord.

Why do the strings ub():lusn9gr csed for the lowest-frequency notes on a piano normally have l9b g(:rc nsu)wire wrapped around them?

What kind of waves do you think will travel down a 0zrr) eixhj81horizontal metal rod if you strieix0z 8jr)h 1rke its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, -nv 5 ssitqb-*v4w-a fbut the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound wavn--sfv ts*b5 -wiaqv4es in air to vary with temperature?

Give two reasons why circular water waves decrearh y)8ddq:ribe,d ). kse in amplitude as they travel away from the sou8)qr,de.bdky)ih :r drce.

Two linear waves have the same amplitude and speed, and otherwise a2huxzcf63h gotv4:7rt1/y)c 0 aaef 3iargu, re identical, except one has half the wavelength of the other. Which t)i:1zry3f,2ahuct 3 c7/f6utxg e ra4ogv ah0ransmits more energy? By what factor?

When a sinusoidal wave crosses the boundary b dz3a3k//mdwgxc56d+k;u lnt etween two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do k+cnadk mw;/ /tldx35g6 ud 3zchange). Explain why.

If a string is vibrating in threcq (fedr/*li/hg:9 nwe segments, are there any places you could touch it with afg/ndlcr: wq9i/(*h e knife blade without disturbing the motion?

When a standing wave exbl d5w/5knk u5ists on a string, the vibrations of incident and reflected waves cancel at the n wn5bk kld/u55odes. Does this mean that energy was destroyed? Explain.

If we knew that energy was2kka bjubw40; 5ivei61b yui6w8v gn9 being transmitted from one place to another, how might we determine whether the energy was being carried by particles (material bodies) or by iik0;yvw6ive 68 uu249n1bg k5b jb wawaves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distan- 6kmmpk,jmoe 4f4 0cece it travels in one perio ee mo,c-kmpkf m4604jd?    m

  An elastic cord is 65 cm long when a weight of 75 N .k2l 6akgmhp+ r yk,j(.th1zn hangs from it but is 85 cm long when a weight of 180 N haktmrajg, 6k2ph (y .kn z1+h.lngs 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 driver getsc,5m29 zo/kxmdh iqy. into the dd.c2 zm,59/kqiym xohriver’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm whe8 d,1g-:*irvhsi gsgj qb-al 1n a 2.7-kg fish hangs from it. (a) What is the spring stiffness consta g,-qs1 lgi-*idgrvj s:ab 1h8nt $\approx$    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 of 3.0 Hz when a mass of 0.60 kg is ie2mi8yh0r* yjw 41efxi(ky(hung from it. What is its frequency if only 0.38 kg hangs j 0hw2ii(*f ixry8me(14eyyk from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at ts19q4yd0sb:5 ti *oqbzwd; tximes t = 0,9sz;ittd*oys14xw5 bdq:0 bqt = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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.n8m ode-9u d/y u,cb3l25 g is caught in a spider’s web. The web vibrates predominatl 83bu mdd9n-e/cy uo,ely with 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 wi* 1 czpexnr3.6hve:+rua3 uz dth a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequendz:hvp.x1n*a e 3+u36er cuzr cy 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 tim.-op o 69mt09fz hukjwes per second with an amplitude of 0.13 m. Determi u6ok9 p-f9 tj0m.hwzone
(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)p vc x(;nn ,clzn/qkj)-alk+ from equilibrium is the speed of a SHO half the maximum valuenl(pkl vaknj +c c)q /),xn;z-?$\approx$    A

A mass attached to the(xddre47;wfr:rut azj7h c3g.2 y 8jh end 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 strexb s*p)(.b +asy/fssnr;lbvle ;ry4 uy3 i.7etches 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) equilibr;a*lly/.i +4sbr; pynu x(v3re7.fby) sbe ssium position again?    s

  An object with mass 3.0 kg is attached to a spring with ,ipogz70 g-bwspring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from0 g-7z,pgboi w 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 y6di*30exzkv tmz,:q,0o hk/8lm ahv of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will lzhx: k h ,3q,8 km6*id0mzo0eyvta/v the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is atags k;f p)-h;ttached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is req; psk a);fgth-uired to compress the spring by 0.12 m. If the mass is released from rest 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 o wm8a 4io6zm )ui,h6kaccording to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. Determim zh ow66k,8io uiam4)ne
(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 fp 8;(xn o/fr 0xtrl7va6mz ),:tzfybequilibrium is the energy of a SHO half KE and half PE?vx,f7a nyf;) m8rtltr px z(of/6:zb 0 ±    A

  If one vibration has 7.0 times the energy of a second, but their frequencieshj j xg31c;3qn and m;hc xq33nj1g jasses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hy5y),mr 2 nx:8arse uianging light spring once every 0.65 s. ,:er2u axs5nr)y iy8m
(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 supx-uom -u k5kvxt+0d .nif k:9fported by two identical parallel vertical springs, each with spdifk-ux k5untf-9 xv.+ k0mo:ring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates )s2q, wok p2ozvn4q9f according to the equation x = 0.38sin6.5t where x is in meters and t iskownsv922 fo q)q,4 zp 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 each0 oxud*bvv*) r, 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 horizontal6hx b 0d5n7*h6 k;stax zz+mpu spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial s6u5h a;t+ nm*6zdsz 0 xkbxp7hpeed 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 stiffne*dlpl8 wf. p t)9pn.klss constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrlw fldp*.9p. ltp)nk8ium 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 connected6/c(xozwrrm hqo.2/a to two springs, with spring 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 horizontal spriks.8nvha8s9 (x qoa5 5xt ctp;ng whosetc(5kqt ;nx op9h8 s8ava.xs5 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 massy1/jneu 9u gx5 65.0 kg jumps from a high bridge. After reaching his lowest poinxu/ 51 yegjn9ut, 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 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 vibratirrempe: wg8/: rd0er-5nd4u gons in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple p0m:l j)(bzol eendulum be if it is to make exactly one swing per second? (That is, :j(0 o )mblzelone complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth.1otmvvl 2p. 3e What is its period on Mars, where the acceleratl1e 2mtvvp 3.oion of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm ifb-kp:q3wq 72bd jl ;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 pendulum1:uslrw 6 jwkxr0:lkj22,5mntf rt 6j bob has a mass of 365 grams, and it is rewj1jnxm0:s 2j l r ulr 2ktt6,56:krfwleased 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 0fsdfr :*-x;y3hm aqs4.9930 m. If the clock loses half a minute pe;fhsy:-rq4 fx das m*3r day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speedf5jke+ d*z6+g1k5 h+ikfxlub $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscil1s jj8 wj/sb(*9g1cs kqpf-jj lates at a frequency of 2.5 Hz. At it is released from rest start*j9jjqj cks8(/-bgjf1ssp 1 wing at 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;6ecq*m s2vsbd 0 aa5p his anchored boat every 3.0 s. He measures the distanc0 qcmbap 2s6eas5 *v;de 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 with a speed of 343 m/hta7md-;, vy hznu,0us How far apart are the wave crests (compressionsduzavh0 mh7y- ,,;ntu)?    m

  (a) AM radio signals have frequencies b8qft 8f+zna- getween 550 kHz and 1600 kHz (kilohertz) and trav 8 -ft8n+gfaqzel with a speed 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 of longitudinal cd,wf ..8,tjdu*mku lwaves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elazq; ,yt: rmou:- xb;ynstic modulus, but one is twice as dense as the other. In which rod ;ybt,q: ;omn rz- y:xuwill the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretcnby*ej ;apo),c5krf5zk0y a 5hed between two supports 28 m apart. If the tensi)ja *y0z fark5 e5oynb5k,cp;on in the cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to aj/ *her5v8 mdswq(h9 1;fukqobk0z- 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 terminal and sends a wave pulse alo9ds whb/o(e z1j v*uqrqmh-8a k;f0 k5ng 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 thehdk 8h+tlmg (, sea. He hears the echo of the wave reflected from the ocean floor direct( m+lh8gdh k,tly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthygx9dy*8z 2 /y w3-uyn 8hcikoquake travel at different speeds, and this difference helps in locating the earthquake “epicent83 y xyuno29zc-gh8/yiw y*kder” (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 surface wave can be approximated by a sinusoidal trnv7yze ;et t47ansverse wave. Assuming a frequency of 0.50 Hz (typical oevt 7etn7y4z ;f earthquakes, which actually include a mixture 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 amplitud;iee2o 2ed 1spc5ygl4es, of an earthquake P wave passing through the Earth and detected at two points 10 k gp i;ode2l41yee52csm and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to be,dl n) 2njrzsf6vh1v 9 z1n )r6vv,f n2d9jlsh$ 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 7 mhn0bku 7w6xof the same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratinkbh 7 u70x6mwo of the amplitudes of the two waves?   

  Two waves traveling along bj ntswv9h19 3a stretched string have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of v9wh931b snjtthe two waves?   

  A bug on the surface of a pond iz,9.o4q5q1 lufvcq/h sljxm 5s observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factorc 9ms,x/1 oq5fh qqllj uzv54. does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketchop*z/; )- 3xmoffbv2 r3ab ded 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 pulse f/f3mvpzoda o3 red*2bbx;-)s pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibr9 8oi:)hj8va/7ra5xi v pmz gkates at 440 Hz as its fundamental frequency, what are the frequencies j5v : i 88gi)akzxr7voam9 p/hof 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 whfi imsdsz t6gv 7iv6:0vxh ,0(at frequency will it vibrate if it is fingered one-third of the wayg7: xv idt006if6( ,vvizsmsh down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 28wuf j b1 *xqsfsw5idy-8h 71wk2m1z w30 Hz. Name at least three other frequencies at which it will reson5q7 wfsid1m1w z 2- 3hyjwws 8b*ku1fxate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is1vuj)(ur6i v v0.-*b s2e+q s*yamlu 9oh bham 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjacent nvumh.s9*s2ubrq ho 1i*j(a 0y)vabum +- 6evlodes?   m

  If two successive overtones of a vibrating string are 28 n2 f *-9y/3tyuz xoidjb74efezd.b-o0 Hz and 350 Hz, what is the frequency ofb*9oz/fd o.bdeyj24i-73 t-zn u xfey the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance fv69qtn46 lq yu 5 gpmzm6/yso0rw-cl2rom the bridge tou6pmgz0yw/s 5l26 cq9loynv - 4rm 6tq the support post is L = 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, o2kiq t *hqh-j-*e3qz but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the 3h -oh* qe*qzj-k 2qitfrequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, 5ap65* ne 0dap, xhvlsbut it is measured l5a6pv0 spn ,*hdx5e ato 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 attacha2)jem ,;nvtyed to a small-amplitude mechanical 60-Hz vibrator. The ynm );ajt,2vestring’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 ledk8zb, i3eadhc q/86 vngth of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may 6/ ezbiq8 av,3ckd 8dhbe 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.xk1a l ta9s-cght frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a .k s9 xtc1-alastanding 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 travel)2xf3hftn)hh02b0 v nq, dikaing at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the 0a k3hv nn2)tfi 0hqxhb),fd2boundary 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”1j 6ughtd ez6+ where the velocity changes from 2.8 m/s to 2.1 m/s If tez61jdh6u +gt he 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 wa llk4k2 fahr/6rm air when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an angl6hf2rk /lak 4le 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 be94 m dc nkc oxymc-83eax13uv(tween two types of rock at a 3vn1 m8(axyo4e3cc9u m ck3dx- 8 $^{\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. Acc:2lvgq/8lyj :f+0w5bb sz uvkording to the user’s manual, the dish has to be pointed in the direction of the satellite, bukz::0 bjl5 /wyfqg8ls v 2+buvt 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 75 rbdr.qcuj625 0 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea leve2bru.6jd5 qrcl 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 bumper has/4bk:e c4ikpz;odv f 4qss9z* a spring stiffness constant of 550 kN/m Find the maximum cozdzqb4fk / 9;scpv4o4ek: i s*mpression 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: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which suos+-7jdce8t8 wuq 8w+xd+ catretches the ndus a eo7++c dwx8cjw-88+qutet 1.1 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 fr+1sseyzw,p- x eely hanging spring. The mass then fall-,sx z 1yspew+s 33 cm 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. 11–5mbc-0 vbstp j.ddl:vau7;iu;fkp9 -0c,g.j q 4), compressing the spring 5.0 m. (a) Whj.c9p 7qci .;s-,mbvj ddv k0p;-u0gt:afbul at 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 (diame-kxgx * 9-5vqhe;uar; xavp* tter 8 cm) at just the right pace of about 1 step per second, the coffee slakxrx; tvgxu 9-a;-5he pv q**oshes more and more until eventually it starts to spill over the 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 center of a 33-rpm phonograph rx d wl s;ixwbjtw k..8(sm-9r6ecord have a wavelength of 1.70 mm. What will be the frequency od-isl (kt .rj.;9ww8xwsbm x 6f the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the u)6:bi moci t4;xie0n*8bkm t:ebf/sequation x=0.650cos7.40t where x is in meters t4n*:c u8ek fei6);m/b:b m 0i ixotsband t in seconds. Determine
(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 f. What is its frequenrv (tz(l7bct ;cy if it acceleratb(rtt l(7vcz;es at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. k7 i8nf.eap 7zt4vee: When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he ste4 .8fakezpv e:t7e7inps 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 insdxlnw:ynvjw /04- ;vntrument are tuned to play at 392 Hz (G) and 440 Hz (A). /dv4 wn-0nyv;wjlx: n
(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 u 4x gp5flx8aj4li7p(cord of Fig. 11–33. Determine a 85ul4p( fp74jglixa xformula (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 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 uz ) 9oa7gou*v2pwcoqco0q)9Hz, and the tip of each prong moves 1.8 mm to either qqo c7vua 0ugoo*cpwz))299oside of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillajjad+dy 7+ *w0al5df nw4ni7 ;vuo f0nn-zyr 6tes with simple harmonic motion of frequency 1.5 cycles per secon-duflno+nwy aw5d0 r74ij naj7*;nd6 vf z0+ yd. What is the maximum amplitude with which the end of the board can vibrate in order that 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 q+:il)bghp 4eq4* cheis attached to a ring that can slide 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 the otb4i*+pheqeh) : cgq4lher free.

  A “seconds” pendulum has a period of ex6r; c a5iv1h4img a i;c98nwnjactly 2.000 s — each one-way swing takes 5mi9a;6i1gw4avirn n 8h ;ccj1.000 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 oscillat9y 8ccx-n :onsg+7 jfye in the vertical 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? [Hintxf-cns c98o+ :nyj7yg: 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 tension of 255 N. A pulsppz; rw6i /(d-je-qx be is generated at one end, and 20.0 ms later a second pulse is generated at the opposite ep q(eijx; /6-dpzr-wb nd. Where will the two pulses first meet?    m

A block of mass M is su )qg6li67vj7m akips0dlso//o0l o 8 cspended from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. Whadm l0 7los80qjgi6l)o //pvcas oi67 kt 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 bk9, k; e*nhbld3y8byk-oc9b car at the junkyard. The steel crane cable is 22 m long and has a diameter* kb9obyl83 b9db; eychk-nk, of 6.4 mm. A breeze starts the car bouncing 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 f9+m wvbnnh9: a plate 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 9+fn h vmbnw:9back 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