Give some examples of everyday vibrating objects. Wm)1nrqmx1l)cc9w m+u hich exhibit SHM, at least approximcw9c+1)q r xmmml1n)u ately?

Is the acceleration of a a eln/u m/f15ssimple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an en r1i-g0bk6 qautomobile engine is approximately simple harmonbrnqk601e g-iic.

Real springs have mapg,f lfo4;sdb*4m9rp ss. Will the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end ofopmgb;s 4 l4r9f*p,d f an idealized massless spring? Explain.

How could you double the maximum speed of a simpl dwpni d0pz6h5(q53r7:jhr8qmt b(zpe harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scwc b d5hh,g4y7ale, and then is released. Describe the scale reading as a functio gwc5hd 4bh,7yn of time.

If a pendulum clock is accurate at sea levelcbm7b)4wl wfbl2k ,wx*he4t)eq6 1do , will it gain or lose time when taken 1f4) 2q 7 w ldww)lxke,mcbt6bbo4*heto high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 1 p(ze: y4ma*j-m5v4rg zebo-k jn:;wv1–48). How could you estimate the height of ee;o gz mw :mvr54kzj- pn-4:jv(ay*b the branch using only a stopwatch?

Why can you make water slosh back and qkdcy .21s*s *ptz9l)wtg8qe4 du x b3,(ixvnforth in a pan only if you shake the pan at23 stq9x t)k bzweun.4d,1 v8p*dx*(yi lsqgc a certain frequency?

Give several everyday examples of resonance.wx28n . zuzzb8m/vym:un0 xt5

Is a rattle in a car ever a resonance phenomenon? Explain.xa7fhntu )j)cp -f9 a3

Is the frequency of a simple periodic wave equal to the frequency of its sourco 2rfse*koith7 0ls0 ,e? Whe *o00hk2t7 i,lrfsosy or why not?

Explain the difference betw) vpmel 8u8 fg6m5poh- -*swmween the speed of a transverse wave traveling down a cord and the speed of a tiny piece of the com-epf mw) -65l*o swhvm88u pgrd.

Why do the strings used gaoq 7o/2s0 jqet,2rq for the lowest-frequency notes on a piano normally have wire ot/q 7sqa jo02gr,2qewrapped around them?

What kind of waves do you think will travel down a horizontal metal rod ifa9 mvisv ,l+o27pmw+m you strike its end (a) vertically l2svmv79 o,w+am+ ipm from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase79-,rwxzh g8pwy + kqw in temperature, but the bulk modulus B is nearly independent of temperaw9y -z,xqpw k rw87+ghture, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular watbfw,op,4:2 djz8qujafh .l 3 rer waves decrease in amplitude as they travel away from the sourc r32z,ol. ,4hpjf :q8aufbwdje.

Two linear waves have the same amplitude and speed, and otherwise are identical,3- 4fb.p( 3whgwm;zzukvm3iaf 3u w(g3kwbi3.-mzmap 4hzv; except one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave c .*h /dfwqpu3xrosses the boundary between two sections of cord as in Fig. 11–33, the f xh/f*3 pu.wdqrequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrawf +o+y4.cb*jl an exh)3ndq*ting in three segments, are there any places you could touch it with onh )+ yqne d*3a4c j.*fx+wbla knife blade without disturbing the motion?

When a standing wave exists v 8src234zq8 ys.bxh non a string, the vibrations of incident and reflected waves cancel at tz8h2 rsv483 sx.bncqy he nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from on ib apb3dg,:09f gr9pzf,z+2o)ou g2uv gqcc8 e place to another, how might we determine whether the energy was being carried by particles (mgc09o2,)pvup9fo:u +g2rg b cizqzad3g8, bfaterial bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total di*u9ka 4g v0coaaen ri/f7**igstance it travels in one per*4ciagen g/vok a*i afu7r0 9*iod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but dod ditz)mkzifs9* w06 7m7e2is 85 cm lo7z dzmdko 60iw7fsm ei)2*9dtng 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 driver gets into t38g(+jnp a*o +uygqeche driver’s seat. If the car goes over a bump, what will be thnjy (*83gc a ep+q+goue frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a)8jwc/uh 4 psm+ What is the spring4p/m jc+8 uswh stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a m)*aonb qh,*ktass of 0.60 kg is hung fromqt* n,*b o)akh it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position tunpa xr8ctd ;.4c8-m x of the mass in Fig. 11–2 at times t = 0,t ct8p8 t mcd;.xra 4n-u= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 wezsg63 psuy526pvda x1s wkz 2gwi3+v;b vibrates predomins v6zk+a;gs 6ud1sx32ppwyiz3vg w25ately 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 2io/kvpz c*-d with a frequency of 0.88 Hz. When an additional 680-g/o-piv *zkc2 d 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 per second w;8 )vcxu 3lpm854ewg2ff al vjith an amplitude of 0.2ag48;cj5fvlmexwpl 8 vu f)3 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 gnq a:ol;z)(n2oy*ed7x qx6sua.sg0 SHO half the maximum valdq*s;7x qg 6)looxun2nz:y 0.(ega a sue?$\approx$    A

A mass attached to the end of a spring is stretc )2;l d2d7:vjgfgek- mpjik;w hed 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 vertical spring 0.315 m. If y)94u1dxtm uh i nl/j8the spring is stretched an additi)ldm h/tjn9184u u yixonal 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attacdf(ww/kjei k4od ;p0 ,hed to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.jwik d e;p4(d fo/0,kw020 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 o-pshqo j.i4mxe.6 * jff a toy popgun 0.200 m to “load” a 0.180-kgf6jx.-o jpq .*im seh4 ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attachskcx7 q+qqr 5d))jw)sed to one end of a sqjc qs5)k) )wx7d rqs+pring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a 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 accor x.xw, kvndl27ding to the equation x = 0.45cos6.4t where x is in meters and t is in secovwd x2,x7. lknnds. 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 jjs,qyo : 3j,d-bp8waa SHO half KE and half PE? ± y8 pda3ojbjs-w, j, q:   A

  If one vibration has 7.0 times the energy f5dm;bhwjpz :3 v9x4lof a second, but their frequencies and masses are the same, what is the ratio of their amplitudd9pm 5 w4b;zv:hf3 ljxes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once everjyj* rx 9g3o+ly 0.65 s. lyxor+*j9g3j
(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, eaquj j9jf0g6vo1 40cn uch with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibfu4 0ungjjqv9 o6j0c1ration?

  A 300-g mass vibrates according to the eque ;,5bwcw0 :f)xt6wggy nfs4f ation x = 0.38sin6.5t where x is in meters and t is in secondsn,0;sf:wgt5wg bxy)cef 4wf6 . 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. F,tl /fy)i hinl7+q t/tor 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 horizonjna2ynlgk hh+z0jbziz5 20: + tal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed 0zz y j0:22 lhg na+iz5hnjk+bof 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 32y +pai:ypn-bi :bm.0gxjk* y05 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) wx+g*i0:2i:y b.b jy npa-yk pmith 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, ws9m il83c/domt e0k a)ith 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 attap0z, qj/t peb,ched to a fixed horizontal spring whose 0/ptzp,e , bjqspring 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. After reaching his lh:bpt4 l rtls w1x7:c7owest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level l:7trx sh 7bpw:cl14t 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 exact7ennuz5mgh fl1qn;900 s zp3hly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly +hw i ,5mfxi*mxd:6qm one swing per second? q mm,xd+ wm:56hfiix*(That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, wher n7 zve)z1jqeg. u*+dle the acceleration of gravity is abo1u*jgev+q ez7lzn d ).ut 0.37 that on Earth?    s

  What is the period of a simple8m p6ig9f;0k(sv;arqkski 8 w 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 pendulumto/r0- /xq 2eh ztpbfq);l 3ff bob has a mass of 365 grams, and e ;2xff-t3/thqpz)r o blf0q/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 0ob6 ye(* xpk6t.9930 m. If the clock loses half a min66eoyt kpxb *(ute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for th znn83jq u)6vuc ef1q2e maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz.)oa05/i4rwv rdhx8a u At it is released from rest starting at an angle of 15 d vr)58 4u aa0oxw/rhi$^{\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 8 m:yv+bct:lh of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves travelingmc+v:l 8 tbh:y?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with k*q+jiq15hg k s7xx /sa speed of 343 m/s How far apart sg7/xq * 5s+k q1hxikjare the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kt,:4 5k2aw m+k: 8 wfu7xm(qatutbucf ilohertz) and travel with 8qk,: 2wk :a4(57t ax+tuwmtuf umf cba 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 longc5jwjabl04 ,l 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 atp0fkj a* ajjmtg)3(8p 5w)mr s the other. In which rod will the speed of longitudinf0mj k(tjpa)rpg 5wa)tj38 *mal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched betweenqi.; qh1c ,jjp two supports 28 m apart. If the tension in tj;jq. h1cip,qhe 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 the top of a hill by a t*w5 lumr)u b: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 utmb: lr5)u*w 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 ,q0i1f .xqt 4uxco y.rsea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at tq ,r ty4q0..cf1ixxuo his point?    m

  P and S waves from an earthquake travel at different spee;cd /s8v.di6 x61ksp dmnpx:ods, and this difference helps in locating the earthquake “epicenter” (where .vm:8i ;kxd npsdcopd1/x66sthe 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 carmx9vlu)5css1b:jlxd6 *ab 4n be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequ9)cab1br4m*x s6xj5 lds : lvuencies), 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 i 52zo+d yq;a.z+tq+afb jj0kbdtva79 ntensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km frozot.+dqaa + j+b5dbayvqz9ft7k;j 20m the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is :apq --+soqh:r,bo zs measured to be ::opz,s r -qqah+ -bso$ 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 the same portiog :+o)qk,pv aan of the Earth, but one is carrying twic a, kg:+vaoqp)e the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same 3un5xrpxg06v;rm w o g((:snbfrequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two wav(vo(xxu p6r5: n3 grwbm0 sng;es?   

  A bug on the surface of a pond is obse ya5* a nj5xi//.jkpvmrved to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as .vy5nx/5*i ajpjk a/ma 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 movings, 23;vo-e:5)v+kqvw ebvq meb8ec kz toward each other. (a) Sketch the shape of the string at the moment they div3ov:q, b8cvwq mek;sek be )2v-+ez5rectly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibkmp)r )4--xtw bbuv2q rates at 440 Hz as its fundamental frequency, what are the frequencies o twb)k x-u-)rv4pq2bmf the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz*2a, dq ci0wrx when 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 of the string vibrates as a sta wd*ir2,0caqxnding wave.)    Hz

  A particular string resonates i13lmfwoe;b9)(n v wblsat -i;n four loops at a frequency of 280 Hz. Name at least three oobms i l1(wf w9;)3n-tla;evbther frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the freog4mfx(1mw +x4bh sa 0quency of standing waves is 475 H0ws1mxa+g b4m4x foh (z, how far apart are two adjacent nodes?   m

  If two successive overton72/9 2qg cy4)olleyrmprd cj-es of a vibrating string are 280 Hz and 350 Hz, what is the frequency of thlj2 rop97e yr)2-cygl 4qc d/me fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. i5) hf8 gqvmou.wz(;(x u -2ssbssyv4The distance from the bridge to the support post is L = 62cm and tosy2vq 8 m)whv 5sxiufs(z4 (;g.-ub she 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 aju ,5- qjgttymi:(yp7 8*(clloydag3 t 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string jt7y( m,py5:il3 yt8dg(* ocjuqal g-be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar st;8/ t7iyhmnwg ring is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? d wt;minh/78gyecreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical 60-/d ax sj60(,ycgq ob,rHz vibratoa0bs6/qrx(, dy, cojgr. 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 adjusted qax 5hdk/4xoc) gxdtj1h78,-x rkci5 by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be h4/8 xc h,)aq cj rd5kt-5ogdi17xkxxachieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth ibshj8h zku 4, 2 rmxr9*: ciuz8mkm+j,n a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency tos:kr2i9,zcjb zk84,*m h8u rhmm +jxu produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within thea4t vds pw((x0 Earth between two kinds of material. If it approaches the0 w4(staxv(pd boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes from 2.8/ 0t2t.qbezqg m/s to 2.1 ze q2t/gq.b0t 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 when it hits a layer of coldlji1hi6q ,dq g8:d6m bf)q x x*il+v(n, dense air. If the sound wave hits the colqq id*g8m+x fhl,)vn(:j q i ix16dlb6d 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 atbvysu y/.ir +0h(zz6 fe9hr)g a 3 yu ye(/zb +fh)gr6irs9 .0zvh8 $^{\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 manual, +z84s** yti.nlx h jua6r/vatmy n6s/ the dish has to be pointed in the direction of the satellite, but 6nv+ynl ma ax h*rs//z yt*t 6s48uj.ian 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 veloc+ md3nvsw2c v)1p.jvri iek;2ity 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 t1)m.sni2r d3;w ve2ijvv + cpkime 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 a spring stiffness constant of 550x4 mgabe ekbb a (,f:ee5f9qmk/8f03z kN/m Find the maximum compression of the bumper if the car, with mass 1500 k4e:z0megxkk b5 (afe3, 9befq/f mb a8g, 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 stretcl.jz/ii p jv) w:gf)6q8f qz s094iucghes the net 1.1 m. Assume that the net behaves like a simple s :q q.jcg l6v8)i0fs gizw) fjip9z4/upring, 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 spri -t*mu- pqsd +v:g:xxsng. The mass then falls 33 cm before it stops and begins to rise. What iu- xtq+g:dp-xs v:s m*s the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), vlsomfv4ig: c.n/a(**uyh9 o m 4h7qa compressing the spring 5.0 m. (a) What is the spring stimo9.7gi*mv :u( *hly/ a4scaqv ohfn 4ffness 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 5o1 l 1njyd n;qtrwb qy:34vz:8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over rv5q:yn n4y1l3t q1d:zoj;wb the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm fl8tux(i; 1ltsu y*n8qrom the center of a 33-rpm phonograph record have a wavelenyi8lu81 ;n*utqxlt (sgth of 1.70 mm. What 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 is inpn3w (gnqpxhuz/ 5 :l2 meters and t in seconds. Deter5 xh2 3luwz/npq:np(g mine
(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 frequency if it accelxwslgwn-n- +21z 4chzewl+2-gcn1zxw n hz4-srates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. Wkdtq qy4*b , e3p6yzg;pu+:wwhen a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the;yy6:u w,gw tqqbez3dp*pk4+ 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 tunedno f 8fqjo6d 1,tm6hynf3dbb:z 77 5yt to play at 392 Hz (G) and 440 Hz (tq77: 83o5o zd1fydbfnbn,6h fymjt6A).
(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 of Fighbj,oo.frcx 3cjt/nh,6 80jx . 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavie.j, x/t6jjc0fxornco hbh3,8 r section of cord or the lighter?

  A tuning fork vibrates atueu xe7 ncz z7j2(v*;u7s6) oasdr ub- a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to eitu*xc7;7s(r2ez) ejzdv sb u nouua-76her side 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 oscillates with simple harmonic motion of frequency 1.5 cycles pete; va77jbb 0tgcoreebhypl1.6((( gr second. What is the (b6 j.a t7gyrh1(egtbb (vee;p07olcmaximum 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 “y,9; s(yl gy2lhvn+affree” end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrationflv ln;(ya2+ shy9gy ,s of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing takes -s;hdp1mkez m ;o6wo91.000 s.hkdw- oe; mpzm;6 s91o
(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 ca9e sqxcmdx1lc3/q4r:eue2u6+j,nwd n oscillate 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 osc:,c exlquxj 64 9c+3us d1dw/er 2enmqillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A pulse 9jm+,s0t8pqa97 jazjt8jrfd is generated at one end, and 20.0 ms later a second pulse is generated af9 7zdr m98jaj0jqpjs8+t t,at the opposite end. Where will the two pulses first meet?    m

A block of mass M is sw*m xw 11hyd9 5f;q7w;yi0 dpxgygt/iuspended from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed1 ;9*g /y1xh5wg;f yd w0i pxmwqy7tdi 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 junkyar-mi6n ui60xk 8u8yoj kwfx-s,d. 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 -kk868- ym0i,ufwi6nxujxs o period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown.vpyvhi/b48vyg x 6cs+ zi:,l 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 frvl vc gx4yb vyipi6, s:+hz8/.equency 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