Give some examples of everyday vibrating objizv)7*a4f/e6mxi ej tvm/l78rf k) fyects. Which exhibit SHM, at least apaz7j6me)kiitefvx4 m/)y* r7 l/fvf8 proximately?

Is the acceleration of a z.up oa4: 5c ucst8crde*t0,usimple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automod-rojj .q0m b(z igny52. 5wyxbile engine is approximately simple harmi .dg q(yzj0x5yo-rnw. bmj2 5onic.

Real springs have mass. Will the true period and fr 8p3 lnq0jg5rn +8nso883xvbxmpn zk.equency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring?nvpkp n3lq8 z gmx.8os 05+8b83n nxjr Explain.

How could you double mhia0e) xcp +al -au6.the maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then is td )amtv lkdf (6po86x.lvv :7released. Describe the scale reading as a tt(d fdxvalk)86vvpo:m .67lfunction of time.

If a pendulum clock is accurate at sea level, will it gain or lose time wheyu56id) jdspihg6c07tuvzw6 m9ie1 + n taken to high aij7 y suzit 1dc9whug)6d+605vmpei 6ltitude? Why?

A tire swing hanging from a branch reaches neag- s)1c rkhn2xrly to the ground (Fig. 11–48). How could you estimate the height of t ngx1 krs-c)h2he branch using only a stopwatch?

Why can you make water slosh back pp8s)+ 16,ffhxewh .kxlrz k) and forth in a pan only if you shake the pan at a certwfkh e8p6,l)shp z)f k.1rxx +ain frequency?

Give several everyday examples ad 9r hzc,wc,)of resonance.

Is a rattle in a car ever a 0tbo p js/xo6o*zc3;p resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its s*o,yrw4j sagvov./. o3- gebghz 11qpource? Why or qs. or-,gpowgbj1h/g3v 1z v.o*y4aewhy not?

Explain the difference between +c(4 w mi; 3aq rz wjxyodzb;:zunj0jf8) 7m*nthe speed of a transverse wave traveling down a cord and4fa 3i :o7;j+zn0m* (wzmr)njbzd j;wcuqy8 x the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a ( ti*cj(cx(s-dt2i: mb9w p zupiano normally have wire wrapped around them?(t-sd(2*9j:m tiip wb(zuccx

What kind of waves dodujrv3lz8vw4f nq:3 ) you think will travel down a horizontal metal rod if you slrz48 q)vjwuv3nf3d :trike its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in ihfd.n.m+m/t lw p)x 4temperature, but the bulk modulus B is nearly independent of temperature, how would )mhm+.i fd x/wtp.nl4you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular wate dpq -*h-ixd bsxa3(0dr waves decrease in amplitude as they travel away from t h*(-x bsxpd0qdida3 -he source.

Two linear waves have the same amplitude and speed, and otherwise are identylb3l ;u;,aw mical, except one has half the wavelength of the other. Which transmits more energy,b3a l; ;lywmu? By what factor?

When a sinusoidal wave crosses the ews; .35z kt)zlqd;b bboundary between two sections of cord as in Fig. 11–33, the frequency does not change (although;ws zbz5 tl;.d)3 bekq the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there af4v wabq 3f+q4ny places you could touch it+vf4 b34wq afq with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident anow7-l(fo.c r/l 2pwagki* hj-d reflecte/ w pkf-coj(7gaoiw-lrh l*2.d waves cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from: ln ,g8lyyxwy z j29/exo+,cn one place to another, how might we determine whether the ener:x,co 9 yznl8yglj+wx n/ y2e,gy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is thij j/c20/93* 3xkkxtwe lk okge total distance it travels in one period?jc kxkl33 ejkt/9xkwio/*20g    m

  An elastic cord is 65 cm long when a weight s.4xml) yzrh0of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cor.yz 0mrls)h x4d?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets 0 m s9teg0j0xfinto the driver’s seat. If the car goese0txg9mj0s 0 f over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) Whata. hycf/4s c.n is the spc.anyh. / csf4ring 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 vibratgevt6lo0 ; is37l;mo mes with a frequency of 3.0 Hz when a mass of 0.60 kg is huvm3 ol7mlt s6e ;;o0ging from it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mas7 bvpcnj1 81o,djv7xas in Fig. 11–2 at times t = xb1, 8n jvdc7paov 1j70,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 spi rg-x m0a bp(*pxn4i.nder’s web. The web vibrates predominately with a frequency ofg*xrbn-n.0mp4a i (xp 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 w:hp-e+d sq(asith a frequency of 0.88 Hz. When an additional pda-sh: e+ s(q680-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per sec2+ 15ffeenf+-d ksgezmfiw9 -ond with an amplitude of 0.13 m. Determwfs-g e-2fke mef1+ n i+59fdzine
(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 eqp3 rjsx(l.w +hgl:c-y uilibrium is the speed of a SHO half the maximum vals3l x+yg pj(.hw:lcr-ue?$\approx$    A

A mass attached to the ek lory/i18 ,(9h kxzby+t0 fuxnd 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 vertical spring 0.315 m. If the sp5m72xg...bfnhv25or4slt6ltsp0cek a 1eu a ring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium positi1c2s lvh2p6b5. 75lgo.k 0eumx e4trat sfan.on again?    s

  An object with mass 3.0 kg is attached to a sm t (acl7jy2w.0eoc5tpring with spring stiffness constant k = 280 N/m and is executt0y w75l.tcej c2o ma(ing simple harmonic 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 sprin, rg ijlwbu()5cc fqtb+ 8c5g9g of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ba, bjl8 wu cc9c5r)qgfb5+it(gll leave the gun?    m/s

  A mass sitting on a horizontal, frictionless 8 9-6pfogoti qj7sty/ nez::vsurface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of wortyv-6:i:n zsoo9t fq/ je8gp7 k 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 according to the equation x = 0.45cos6.4t where x is in 5lyd4ixmfp k)f-,2 4y mzssd: 4(b jfsmeters and t is in seconds. k(z y-:4sfb45f2idl m ,dmpssj)fx4yDetermine
(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 KE +zi/.) apu(wbvf szg-and half PE?wv/z(g ).puaz-+ ifs b ±    A

  If one vibration has 7.0 times the energy of a second, bu:1 )r 6vvd z9t4rg8z3k e)c(mqaiyyqct their frequencies and masses are the)( iv6cr)9qyr3:1t8z 4c ydvek gqzm a same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a verticohg,2urnl b9 9ally hanging light spring once every 0.65g2ourn9l bh,9 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 parzjd6mbg;nz j,nr; 2l b+) *huzallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of;ndb g nzrz ulbz2 h);*j6jm+, vibration?

  A 300-g mass vibrates according to the equation x pgpv7vmi py;e9 ;zc.kg 8.aa(= 0.38sin6.5t where x is in meters andm8c pa7kip(gv9epya.; ;v. zg t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A o:h dii30g2d/oxbh*vd: /x a aand 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 sp1aa8b v2 p0rlzra :m2ering (k = 124 N/m) is struck by a hammer, l0 mr :ez28br ap2av1awhich 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 constant 305 N2 yjyodl.3 d4f/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The massyj2dfl43d yo. 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 con0kzsrbk 7 u,zu)rsj+2stants $k_1$ 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 horizonta97ltou(y m.7rbss b2 tc;i1s6g0bbw15u ka gil spring whose spriwti bms(ssuc;17b92b 7bu ogy0i la5r. g6k1tng 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 reachingp1n y6,v 0v rxg7qf9fu his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the s0,n67rufgv1v 9x pfqypring 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 vibra1cd: +rv7eo./qj djv ctions in exactly 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 one swing pejn1.ts2i-58gve5 yxq wr5 aww59qpuyr second? (That is, one comple x9aws5y51rjw2. - 5w5 pqeyniu8gtqvte vibration takes exactly 2.0 s.)    m

  A pendulum has a per56wjz p(qd cs/iod of 0.80 s on Earth. What is its period on Mars, where the accelerati5 s6zpjq/cwd(on of gravity is about 0.37 that on Earth?    s

  What is the period of av pp/kcn- 53ub simple 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 penrt30oaj(mnb5h nh ; 1wdulum bob has a mass of 365 grams, and it nh3tho5nmw(;1 b0 aj ris released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. uznhgf,a3m j )oye -ft43 k5d0If the clock loses half a mafj ,303-du)mn zefh 4yktg5o inute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speed +tt0hs- uga om 99 s+epzt+7pcc yr7;c$v_{max}$ 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. *w10-ddsee7lt difu+5 Hz. At it is released from rest st w i*7 01d-efdelut+dsarting 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 oy0a .*0)h* kds ot:xvlwbfg(c f his anchored boat every 3.0 s. He measures the distance between two crest*v ok h0 xlbas(*df0y cw:)tg.s 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 o2 m3r01 *ehlwlhe/oqof 343 m/s How far apart are the wave crests (compres0/31 l*eom qhhw2re losions)?    m

  (a) AM radio signals have frequencies between 550iss h8( d-d0/aayc *zr23uek d kHz and 1600 kHz (kilohertz) and travel wd2 (i0 sd3k- er *uzc/8sdaahyith 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 longitudino00cbsk ,/ab ayp:2gsal 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 as the opb t;69nc-(x2 b zgfwother. In which rod will the speed of longitudinal waves be greatw-p (f;og9nc6zb 2b xter, and by what factor?   

  A cord of mass 0.65 kg is stretched between two8 rhf n79op/yohl e((v6id ya4 supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel frloa9/(y rh6nf oiphy 4e7d8 v(om one support to the other?    s

  A ski gondola is connected to the top of a hill by a sx6fd gqy*o fw g22pmh*y l1d) g34raw;teel 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 pul13 g2 ogr*q2gpxm6;*fdhl)d wayy fw 4se 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 x9 -ytoed ;3xpthe sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this yd-t9p;xoex3point?    m

  P and S waves from an earthquake travel at different speeds, and this differencew(+lkj8 gmykv. zpa-9 helps in locating the earthquake “epicenter” (where th w9klmak+8j-. ygvp( ze 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 trw ;8un3 6db 3)gc;7ifixf ;vf fwpnxc*ansverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact 3n*;ff ) pf n u78b;;3gxwifcvcixw6dwith the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intenszr+/cpfor wg7tia8e ,-*rz (jities, and (b) the amplitudes, of an earthquake P wave passing 8f,c r +igjz/(pzrt wr7ae*-o through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passin 5w;l z,bzf,.kwn9qd(upk)n sg through the Earth is measured to be w 5sp9kk lz,d w)bq. z,;u(fnn$ 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 through6f(v,3kq if-ssyuuf*ur+v2z the same portion of the Earth, but one is carrying twice the energy. What is the ratiyqvvi,u-u f 2f3sz f (*+6rkuso of the amplitudes of the two waves?   

  Two waves traveling alongtpv *4pyf :k2a(g) iuz a stretched string have the same frequency, but one transports three times the power of the other. What is the ratio)uyi 4*vzp2pkat:g (f of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to mofbje./b*n 1mt ve up and down a total vertical distance of 6.0 cm, from the lowest to the highest pointmtbn1 *ejb/.f, 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 mova+zv jbw7ty8: ing toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at theyt :a7b +wz8vj moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as itng8(gxgc jj,o, (fm5gs fundamental frequency, what are the frxmgn(5ogg8f,, c(g jj equencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 H /y;mnffhwpvj9; ea88x sth-(z when unfingered. At what frequency will it vibrate ifxv wf;;9ma8t yjph8nshef /(- it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four ochd p3va9 7 aa+8yhg.loops at a frequency of 280 Hz. Name at least three other frequencies at which it will reso o pdgyc9 73a.ahh8v+anate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the -7k2v2xx fuxg0 )gpc tfrequency of standing waves is 475 Hz, how far apart are two adjacentu 7-p2vk cf )20xxxggt nodes?   m

  If two successive overtones of a vibrating slfx p,d ea/816 7qxdvmtring are 280 Hz and 350 Hz, what is the frequency of the fundamentap,6 78xfxaq1d lm/dev l?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. + pr,)4svwawf9mg zc 5gpdl45The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520pm49,dgfcvgzls 5+ 4p r5)wa w N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, oi;atrboovh /8./x2mqd pa;4but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?Soxh2;a/ a d qp.8o 4mir;/bovto the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 20a1lpfpy)eu0fy.f3wdb d 4 : o60 Hz, but it is measured to .w1yb o:dlfaf0fpu) 6 eyp3 d4vibrate 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 mechanioi 7) 0k+pgsgccal 60-Hz vibratoo 7i)cg skg+p0r. 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 by m-xv lwed. p/g *.c-wiloving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standingxe *pv/l.w-cidg.lw- wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the r -asp,5e 3b+huhk/rhz jes*o;gj . es9ight frequency, the watp+h- re3k;z,s sbsa e5. hjj9ho*ueg/er alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave wxosg (+8roh+traveling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approacheg+oohx s+w(r 8s the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes from 2.8 mh2mjp:hj1 vm.p*jwtm/m; zm 8y9 tq2 i/s to 8zq/y;hj j2t mtm:1 mh2vw mj9mi.*pp 2.1 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 when it hits a laj doc 0732mvk eji-n*1e xez9ryer of cold, dense air. If the sound wave djz 2-0jk1o7r9* im3cnvx eeehits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strurg n8s 4tih2 nhh2;j4ikes a boundary between two types of rock at a 3nh gs 2 2r4jn4uh;thi88 $^{\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 k-b-xu3kau; vej t 01 qqao/ (y6zmb7zdiameter. According to the user’s manual, the dish has to be pointed in the direct(qa1yu/m kakv- zxt0bj76 ob3u z;- qeion of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 /clo75q*xzbf 09ef iu km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an uzqfu e9*cb0 o5ix7l/f nusual 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 bumper hasr1dm 9:zl4uz t a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collitmudz 9r4z :1ldes 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, wh+ c wriq :a sn81co7z(i quri8ihm7ef5d,c )*nich stretches the n8hi razri,iue7+ncci)81* f qcdq: 7m(5swnoet 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 freely hangin*oh12hog)h ai33vopm tq)3 cfm.ej9 u g spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of t om1p3h. 32q mco))* hvohe9jit3fugahe oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 s :uyg;rw)e,xlfb26x;d x y:y m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness lux6 ;ys:2x xfb,w ;e:yg)yrdconstant 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 (diamj - p vfr (ye+:gyhnv( cf6e1x;0 xrt3e76msixeter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estim7gvme1y0 6- (ye (jni3fr:psf6+ h;xxr t xvecate 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 phonogu:r7.9 xjc kznraph record have a wavelength of 1.70 mm. What will be the frequencyc xz9rnju:7k . of the sound emitted?    Hz

  A 2.00-kg mass vibrates accordi5a eh52qcorgyiede p6 5b9f/7ng to the equation x=0.650cos7.40t where x is in meters and t in segq5idb5po6 e c29/ 7r yee5ahfconds. 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 fru uf 9t8:cm+iwequency if it accelerates at uu: c8f+imw9t 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands onzpxvt6::-fm i the raft, it sinks 4.0 cm deeper into the water. When hevf6zm ip: -x:t 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 61lw u4d+mjq xplay at 392 Hz (G) and 440 Hz (A u6w41j mqdl+x).
(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 cok 1ly- j/(indprd of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections.y(i/jdn kl1-p Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tipptbn dl, /7o/y of each prong moves 1.8 /p/ to,dbl 7ynmm to either 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 cyc,vccp5 tm / tbp9:(w txrve+3ioc0k-lles per second. 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 duri- /0tcm3tripx:5ck9w(bv+lpt ,ec vong the oscillation?

A string can have a “free” end if that end is attached to a ring9xv 2 8ztln2rg 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 829tnvg2 rxz lthe other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing takes d vxarq l)7a3hoo* 0-m1.000 s. o*)q xa-rlm0 7vho3a d
(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 oscilla oia94lx:m2d. *3vj vco+-bzdqat/ jgte in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, thg/. qo*ma+z4ijc9o d tb- 2x3djl:v vae period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension o,.6/nn dm cwfxf 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses firf,dcx 6mw .nn/st meet?    m

A block of mass M is suspended from a ceiling by a spring with sprg;ie,+gs 22j zqk:sny9 mag, uing stiffness constant k. A penny of mass m is placed nszg2 ue:sy,+aj9,;m kgg2qi 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 crane i2v3uwmxk4ze 9-su v*cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period*xk4muv3vwusi9z -e 2 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 th dgkv-4lo8qykl; ,vm.l 0.gqse 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 ong4.osl g-qdq.;v,ky 0lmv8lk 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