Give some examples of everyday vibrating objects. Which exhibit SHM, at leastp9svms sc);zb*8 0gbj appz)8smcpjgsvs b0b9*;roximately?

Is the acceleration of a simple harmonic oscillat0rm *x+y,mu) nikq td+or ever zero? If so, where?

Explain why the motion of a piston in an automolxbybb zdt)y 67)e.q)bile engine is approximately simple harmodqbx. byyle)t))bz67nic.

Real springs have mass. p/ kp6h1ooy / w2k jcx,-fhp/yWill the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized ma /hwpjx-p6/ cky,/kyh1p o2of ssless spring? Explain.

How could you double the maximum speed m-pihe0qi 0d 5of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertio xqrot 8x;gv-+fqzm80sxce1:0 -v lk cal spring scale, and then is relea-8 fskxc1grz0+tq qxo8xlve-: ;0o mv sed. Describe the scale reading as a function of time.

If a pendulum clock -qf wozqc3u (,is accurate at sea level, will it gain or lose time when taken to high altitude? Woq(3zu- cqfw,hy?

A tire swing hanging from a branch reaches-ehfl6ry:t77t aj1arzd* 1gt nearly to the ground (Fig. 11–48). How could you estimate the hei:1edah-*z77 t1tjfr6gltray ght of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the,b6)1-p)vcesqwig ot9q a68yq (vc rh pan at a certain f18 vqveb)wp9g oc6q-cthsi )(q a6 ry,requency?

Give several everyday eg u 4 n(tgyk)ckwj..s2xamples of resonance.

Is a rattle in a car ever a resonance phenomenon? Explain. t;,-vu+ clha7s2p kubmgy9i*0mkgh4

Is the frequency of a simple periodic wave equal to the(p,kg9tmyp 7t frequency of its source? (k9gt 7ptypm, Why or why not?

Explain the difference between the speed of a transverse wave 7ir(:ox4avbk. +btb ytraveling down a cord and the speed of a ra+oxb7 .yk4btv (b:i tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normay2gyo i2 ,h:jwfyp43jlly have wire wrapped around p4w:f ,yyojjhg22y i3 them?

What kind of waves do you think will travel do) k- tshu1f*:nbtrj2rwn a horizontal metal rod if you strike its end (a) vertically from above and (b) h- krr hbst1*j2u)nt:forizontally parallel to its length?

Since the density of air decreases 5:ir uob 1 *a2ut8x,t 4dcjorlwith an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in a rtjiu8bt2 roo, 1ud*5 acl4x:ir to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they travel al --7m tiox)qkway from the sourclo iq-x7t-m k)e.

Two linear waves have the same amplitude and speed, and otherwise areqc -pp2va: z6/gwmw6spa2ya. identical, except one has half the wavelength of the other. Which transmity/paa2amp :p2czsg.w6- qvw6 s more energy? By what factor?

When a sinusoidal wanap i3n/sa4st- mo8 ,u1-v styve crosses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velo8s ai1-vpasot u,tny34mn/ -scity do change). Explain why.

If a string is vibrating u;l2fi,u zqe/bm,w*min three segments, are there any places you could touch it with a knife blade without2z; uq/ewmuml,fi*b , disturbing the motion?

When a standing wave exists on a string, the vibrations of incident pc z7rkkoh647 and reflected wa7z c6oh7rpk4kves cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, hog v.)u58qhn y5+kq vejw might we determine whether the energy was being carried by particles (material bodies) or by wa + qv)ny j.ek5qguh8v5ves?

  If a particle undergoes SHM with amplitude 0.18 m, what7)e7eda jxp 9o c3z)xw is the total distance it travels inpoeje7cxd w))7 9x za3 one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 cm l5 zb7unnx-lbdm5p (a.d6kalq p 2b/9 fong when a weight of 180 N hangs from it. What is the “sprinnbl.x(d9m 57azab2/ulb- d5 f p6qkpng” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when iy21vftce*ea +d.yx li mq,1 e4ts 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will 1 .4f2 ,etyvm+xilyce1qa*ed be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches . 2.3ss9vmp0(yzib n v: rkcix3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring s0i9ix b s:yk3(rvcvp.sm. 2nztiffness 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 j sb-xi/mbf)6 *x8csx4v h6fwmass of 0.60 kg is hung from it. Wx mxh6is/*6bw4sf-j8 )cvfxbhat is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at tt c-c(z6eyeu: imes t = etzye:c c-u6( 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass s,tsr e6vzl eh**7.r l0.25 g is caught in a spider’s web. The web vibrates predominately with a frequency of 4.0 Hz.z eellsts.6,r7h rv**
(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 virtrk 3no196wmelbv28jid8k, 0 /j ulfbrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is i9no/ ,l 0jk8m6d l juwr31fbrtv28ke0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per sw;: :mmie; rkbecond with an amplitude eb;k :rm:m;iw of 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half the maximum b7tqb 95jielb7rt9.k valu7b e 7 t9brq9tljb.k5ie?$\approx$    A

A mass attached to the end of a spring is stret dc 3 5j;ty0d uj+cmldr8ph70kched 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 st8xpw7k4 :ko* 2k zltraretches a vertical spring 0.315 m. If the spring is stretched an additional 0.130xz 2wk*p4 tal8k: o7rk m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass g1t d t7e(ja;a3.0 kg is attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from i1gtedaa;( t7jts 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 e:ijqp a fm) p151sp d.4kwxi3compress the spring of a toy popgun 0.200 m to “loa51i mdq f.sk3ia pep )4:wjp1xd” a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surfa)zr+oasbt flms8y +p;)g;n: ice is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, s+b)rl; )is g8n+f:t;ozapm ythe 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 = 0.45crcl6:9h w-pca os6.4t where x is in meters and t is in seconds. Determiacpwrh9c- :l6 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 equilibrium is the energy of a SHO half KE and half Pg (l7npqu qc uh/u+b3i7+5da cE? ± qq+ch+cgba 3u5l7/u ( np7idu   A

  If one vibration has 7.0 times the energy of )gma54+n 41bdx.odbl, fphxc a second, but their frequencies and masses are the same, what is the ratio of their amplituo5c41bp., )x4l+ d dmhafxbgn des?   

  A 2.00-kg pumpkin oscillates from a vey-x me)2 j.ztj,43 9eyhsvn8:sjjpdz rtically hanging light spring once every 0.65 s.y zhj)eys e94j8jm,s :vxj2tpd- n.3 z
(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, 0-g5+uqd-a jszy q/b seach with spring stif/ aqdyb-zq- 5j+sg su0fness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to twr8 bvh3 gwq6,he equation x = 0.38sin6.5t where x is in meters and t i8v 3rbwh, gwq6s 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, yk5b d(j ,vnjok4;x,y labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal gul:ivmac6 18y 3 . a/8jmpajxspring (k = 124 N/m) is struck by a ham gcyjm3i88p1: ax. vjm a6/ulamer, which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring wi2n pyqbdc 1z5/th spring stiffness constant 305 N/m vibrates with an amplitude ofnzp21b cd/5 qy 28.0 cm when 0.260 kg hangs from it. The mass 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 stiffe jbh9-i0v7c;cwuh1f xb 61bkness 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 aon3;ohpf 3mz s4a:d*jttached to a fixed horizontal spring whose springhj*noo4z:p3; f3dm as 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 he p55px 4p;jcbridge. After reaching 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 of5hpc ej4p;5px 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 vibrationqh2;zu ;xq/u3 kowi ,ks 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 onejbeuw gwkl9 (ube 6-ry:i*mt83+ fl:h swing per second? (That is, u3:gfibjywml reul ktw*-b:8 6 (e+h 9one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Eart*4po57 urf g( wnmg:zth. What is its period on Mars, where the pf r5g*4u7wtng: oz(macceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80yxf (dm )5do(o cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple peng0.2v eq.wib -oijx b8+l/flndulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at /0gnl +bwv .e8.lifqix bj-o2 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 op x4iy+x r,o+a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shorte4+ i,+x rooyxpned by    mm.

Derive a formula for the maxi38nfje ,a+ w5 6eflsppll6yw3mum 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 *p 1xxcl78x lz*(zpb( )ckr7 xh89.xg pwjs iqof 2.5 Hz. At it is released from rest startin.7*ix8)9z q *xlxckrhzx( 7( scgxpw pp1l8jbg 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 his anchoredgj3doha ee 6n3y-h cd3y9b6 5ki:xw,x ,j,xkg boat every 3.0 s. He measures the distance between t3dj,gbexh- 9cj6e dw3kyo6xhny 3,5, gix:akwo crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 m6ysq;l kv -2dHz and travels with a speed of 343 m/s How far apart are the wave crests (comprk2q msv6l -d;yessions)?    m

  (a) AM radio signals have frequencies bsn2h ql*s ;bj2etween 550 kHz and 1600 kHz (kilohertz) and travel with sl ;hn2*jsbq2a 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 of5bte pqti: 5x3ff2a k. longitudinal 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 twij p.k+ppbb1 mu/p2-zdu-bw r)ce as dense as the other. In which rod will the speed of longitudinal udpbj1 -p ppz) b- 2u.r/wbk+mwaves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supz u1kyxkiips/k)c,u6*yu/ )q41 m g tyports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support toum)k,6i*1tgcx qyuk4py)ysu1 k i /z/ the other?    s

  A ski gondola is connected to the top of aja 3- ,(5p0xtx/ gozicvpwy6s 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 along the cable. It is observed that it took 16 s for the pulst-j,3swy 0i zcppa5o(vx6gx/ e to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sea. He dkw7au3 +1 lx)2i km(fll l/fkhears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep i)7wl xa(u mkl+fki3l/l1kd 2 fs the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and tx5ioe) f-u4 vshis difference helps in locating the earthquake “epicenter” (where the distursf 45x ioev-u)bance 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 aub/.n /csuj 9j1 ixsk: sinusoidal transverse wave. Assuming a frequency of 0.50 Hz b/ c u9 s:nksj./x1jui(typical of 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) mf4r+wfyd r6) the amplitudes, of an earthquake P wave passing through the Earth and detected at tw6 rrm4ff +ydw)o points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is p pb-dxf:tg7/14yi1aya,pa wmeasured to be / apwiyfd,1 y4tg1p7:axpba-$ 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 portion of thkv 2b cw04clk yyw+9b8e Earth, but one is carrying twice the energy. y0c+9wyb8bv lck4kw2 What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have tv kb 4lf+g8q 4:u5kkunhe same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two w8+u4ufkgkkbqn5: l4 vaves?   

  A bug on the surface of a pond is observed to move up and down a ow4q.dinu ;f; total vertical distance of 6.0 cm, from the lowest to the highest point, as a di; fnouwq 4;.wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketj yzsr ied,17,a (j ;no+t0firch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened0i,fr, st;7 ijd(o 1zrejan y+ to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fl ml5uw 80ee5jcja6r)undamental frequency, what are the frequenciece)0 arlj5 5ml8uewj6s of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. g4 btoiiju*kc,r7,+t9 nmu8 k At what frequency will it viu+ j9,ui nok*,t7mb4gk r ci8tbrate if 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 loops at a f1/u xbvsc7 ,,p( ,fbmtdd e8ofrequency of 280 Hz. Name at let,d( f,b8su,m x7 o v1becpfd/ast three other 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 frequenc )bm8co ;zc3hek/ k9czq,f5idnh 4p5s y of standing waves is 475 Hz, how far apart are two adjacent noohkbcs5/kfn8; iqp,5z4emhc 3z ) c9 ddes?   m

  If two successive overtones of a vibrating o.mfi8 iq/ub6 string are 280 Hz and 350 Hz, what is t8b/qmf. iio6uhe frequency of the fundamental?    Hz

  A guitar string is 90 cmwkad9 (h80rnu long and has a mass of 3.6 g. The distance from the bridge to the suppwr8 k9d0h(anu ort 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 ibramg u .ez.f1p-*,x ts supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percexrtgm.-1*p. b za,fuent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar strinm dc3ezhrd8,u :7md g1g 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? decreased 3gh8mzcmded:d1 ,7ur by    %

  One end of a horizontal string is attached to a small-amplitude mecha3pu8 w)v5g /wy* c60eljsudaknical 60-Hz vibrator. The string’s mass per unit le* 6lup3ucjk)yw5sv 8wde0ga/ ngth 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 mo+6f;.itd ezy3e ybam g,:mgb-ving the pulley. If the hanging mass m is fixed at 6+ biye-,tefamz g;.db: 3mgy 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forthh+h5 ..cog ,t1(x;aq upsbdnh in 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 to produce such a standing wave in a 65-cm-wide tub is 0.85gh(1apuqt 5bho nh;,sd+.c .x Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling bwf;tcq4ph 3luvo ( ;h3k5y/sat k.0 km/s strikes a boundary within the Earth between two kinds of material. If it apptkh(5 uf w/l3bhovp ;y4q3sc;roaches 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 velocitydt3iq p8z8 *si changes from 2.8 m8z t8dips*3 qi/s to 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 it7; *( igp7lk:les;uq9c oy wwe hits a layer of cold, dense air. If the sound wave hits the cold air interface at(cw7ep9 wq el;l*ysu;gkoi:7 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 typesw us)uesab6pj5 fqc6 7 .a-:xv of rock at a.b6x5pws :j6va-s ueu7f )cqa 38 $^{\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 , gmg8c,h7 h1v-oz s. 9reipnsuser’s manual, the dish has to be pointed in the direction of the satel,-c8m7er gshgn .ih,vso z 19plite, 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 25eshr7jv5 w. 5t0 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attract5.7v tjwh r5seed to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumpev:jk/w ,:j xfa x-w+jpr has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the c /:-kx,wj:f j+wpjvax ar, 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 jumpsg11pbgz xm5 c:uh+p1f-o.l 7eai3u .r nsse1c from a window to a fire net 18 m below, which stretches the net 1.1 m. Assu71ofcs a is.ce1uxpp1.:en5z3h u+lmrggb 1- me 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 freelwkr5pfr c s73h4i( 4ghy hanging spring. The mass then falls 33 cm before it stops r r3h5sgihf7w4cp4k (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/:;a tkc*ph 2ffs (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant h*:ftpf2a k c;of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right pch;btnsz- t ++3tb b0ri-ffv2*m7j ccace of about 1 step per se;cfi7t0cn2b t+mj vh3bbsf+c*z rt-- cond, the coffee sloshes 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 cmvghv h3a l3a2m(yh 2rnzl):,p from the center of a 33-rpm phonograph record have :al,pa2hrn(vghz 3 yl3)2mvh a wavelength 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 3o b )t:2 fc.7e6eehjz h7oucrin meters and t in seconds. Determine o3br hzhe7ue:6e7 c) 2cojtf.
(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 oscilla by.6h8y 4; p*fiezd27zoi idxtes with frequency f. What is its frequency if it accelerates at 0ipzyxb o 28h*yed.i ;z6i f74d.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft esz+y p.i2ff ;floats on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibz .isy+2 pfef;rates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play ap 0w 5 epkd6j4icbr(l5t 392 Hz (G) and 440 Hz (wbk(4p6cdei pr05 5jl A).
(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 travelin9hdy4w/ tar -y5; xiogg down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speedy9-xoyw4hd ra; /i5tg s 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 frequencyvxy p 99imwy l1d02. m-angrh, of 264 Hz, and the tip of each prong moves 1.8 0x .a vig1y2y9mlh9 r dpnm,w-mm 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 frequenckdpje3-vs2 g8 y 1.5 cycles 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 during 2- p kg38esvdjthe oscillation?

A string can have a “free” end if that end is attached to a ring that can slipgq3/nj 1ql 7rb/dw f/de without frictio rj w/qgnqf7/1 l3pdb/n on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum 8 xo7*shbcy.v has a period of exactly 2.000 s — each one-way swing takes 1.000 sho*cb7x y 8sv..
(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 oscillatepwzfyx(2z ,reez h5+4 in the vertical direction or can swing as a pend2zpz4 z +re ,e(yxfwh5ulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: 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 massdoq . zx;zdo24 123 g is stretched under a tension of 255 N. A pulse is generated at one end, axd o2 4zdo;z.qnd 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a sprinu4,zaa al 59pwlo/ v1jpnedf3w6,l7t g with spring stiffness constant k. A penny of mass m is placed on top of the block. Wh4t7won av9ueadl6zp,jw,/ l a5fp3 1lat 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 b2s(cpg -l6ol7i a)u ysteel crane cable is 22 m long and has a diameter of6 s(la -gipculb7) yo2 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 a plate as shown in Fig. 11–58 (whic 8iccxj4qfm(4y o3 tr5h 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 vibftqy rmxi5 8434o (ccjrate. 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