Give some examples of everyday vibrating objects. Which exhibit SHM, at l7qi3 ;2go vidnx9*dtaeast approo9d7 *i; dxtgav nq32iximately?

Is the acceleration of a simple harmonic3l ;ch jj*a 3 l9xh6dnwp,gq0z oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile le9blh2ttfc; .,6 j7jdu+ rmw engine is approximately simple harmw +e,.2f;d 9t6ljb c7j mlurhtonic.

Real springs have mass. Will the true period and frequency be larger sv1 a*yyed, +eor smaller than given by the equations for a mass oes *,a1yvey d+scillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a sim,6eail- js mg.oxf6 -mple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertib1me sdo9, lg,cal spring scale, and then is released. Describe the scale reading as a func,d,someb l91gtion of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when tahl 1ky9x;u9ra ken to high alti 1u;x9 ar9hklytude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48)ntpkm4 5c.c m(4sf:ignzp( ) g. How could yog k5(z)n msp: in m4.p(cgtfc4u estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only ili-;h im*t8(unxh(chf you shake the pan at a 8(;hit*x-cn hmi u (hlcertain frequency?

Give several everyday examples of resonance. s hli(/ucy,z1

Is a rattle in a car ever a resonance ph w/ m*:/ see1lwliee5eenomenon? Explain.

Is the frequency of a si,*031g drz 9iacv7t+ yiwxvagmple periodic wave equal to the frequency of its source? Why or dw y9gravx0i1t ga3z,+*7 v ciwhy not?

Explain the difference between 0 8z tvbmw4v,+wx1ykfthe speed of a transverse wave traveling down a cord and the speed of a tiny piece ob tk4zf,w+8x wv0y1vm f the cord.

Why do the strings used for the lowest-frequency notes on a piano nohrpnl+x5v o;7 rmally have wire wrapped vnr h+o5 7p;lxaround them?

What kind of waves do you think will travel do4mar b h46c/j lvvtb+*zcoim*vvf);2wn a horizontal metal rod if you strike its end (a) vermt o2cbc+b*h64i* v/ fmzrlj4a vv);vtically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an incs k*lexsw: u/ d psi9vapjhh+ (c+*8,wrease in temperature, but the bulk modulus B is nearly independew+kd:/ uhwh* 9sa8v pxlj+ s*( pe,csint of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular watvo)c m1ld. 9dzzrzg8+er waves decrease in amplitude as they travel away from the l.dm 9+godrz zc)v1z 8source.

Two linear waves have the same amplitjh b( 0bd4(oeaude and speed, and otherwise are identical, exceo b(d (jhe4ba0pt one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord as in Fqo4pbvh. r8yd/et -iteb0pm 7 (6:xa mig. 11–33, the frequency does not change (ra y ti4/m0x-q.:p 8d moebbh7(evp6talthough the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, )0 xtan 83/tbkopqza0 are there any places you could touch it with a knife bntab8t0x p/)q ko 0a3zlade without disturbing the motion?

When a standing wave exists on a string, the vibrations of inch ni :idb(u1 9utjg4s6o*fye*ident and reflected waves cancel at the nodes. Does this mean that energy was hiy*utu e9bg6j4* 1o:s(ifnddestroyed? Explain.

If we knew that energy was being transmitted from one place tz4rs;l o** v4k ll+cito another, how might we determine whether the energy was being carriedilv4 sk*+ olr*;t4lcz by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplit;5)i0 2 pvats (ouz:ar iqi4epx4su:iude 0.18 m, what is the total distance it travels in one peru ist5(or:az : ia2 s4u pipi)v04eqx;iod?    m

  An elastic cord is 65 cm long when a j 8x7peq)ab1w( g03 n z+3o tsysi.fpdweight of 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.3s1qdf+j) 8 px bai wzyp 3gso07nte( this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when hvb)a t*knmu)j . .frh v9m;p7its 68-kg driver gets into the driver’s seat. If the car goes over a bupf)mtuvvn;9)7a r.jbkh m .h*mp, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 j 8 dmql8mijzs-za /5sp 8)c/vl*a op.cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness constant 5/jv m idla/azj-p.cozsl *s88q)pm8$\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 kg is u5 j.g:kh uz,g (bl:dphung from it. What is its frequency if only 0.38 kg han:z:g , udh.kpj(5ul bggs from it?    Hz

Construct a Table in):gwpa p wg.zd 9( -w2cz,a);vjbspk qdicating the position x of the mass in Fig. 11–2 at times t = 0,t sp(jgq9z dkv ).paz:-p),wg;cwa b2w = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 we 3b57t8 awtg 7nqyqyq1b vibrates predominately with a fre8yg13w5 q77q ty nbqtaquency 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 14ve4, mk7w gl 0ar1ri*uhsjtvibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to mreijas7v4 0g1 t ,rhwm1l4u k*, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vw h+xa+*s/nlfbc/+3x2e egr j0v4 ysn ibrates 3.0 times per second with an amplitu +jvs/0h *3+xla2/c4rn sfyx eeb+gnwde 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 vqk8 8pmgh/i.e 85e*s .hjkv ptalue?e5/ kv p8*8k pj.ethihgq s8.m$\approx$    A

A mass attached to the end of a spring is stretcheco +ub, zn* 8q,0wb2y afv(zyfd 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 0.315f3k( kts6p ;gdy- jlnvsu6+u) m. If the spring is stretched an additional 0.130 m and released,kus3d gt6)j uv(fs6ly +k-;np how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness co)yrc +b4lmn 6zc.l bp2nstant k = 280 N/m and is executing simple harmonic motionyb zn4 bmc.2lr+p6 l)c. 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 tt;*;yty nlsw ssuiz/2m3l.q2 o compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave t2 z.w st2uq;/*l; slm3sytniyhe gun?    m/s

  A mass sitting on a horiz8:b hy9n /gbfaontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3. nbf8b/:9yag h0 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 according to the equation x = 0.45cos6.4t where v obk 40g + ;k*2);lghdcuqufgx is in meters an;cg ud)g;gklh*20obk uv+q4fd t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO h,cag4)hod1gg o jm ;z8alf KE and half PE? g1za8gd4m, ch;g o)oj ±    A

  If one vibration has 7.0 times the energy of a second, but their frequenc+ idy/9ls1 b9he5b usdies and masses are the same, what is the ratio of their amplitu/blbiyu sh s5919e+dddes?   

  A 2.00-kg pumpkin oscillates from a verticall))ua1wwebgo /8dz81k1. keh2 tihbc ry hanging light spring once every 0h121u8kr) wb )tc kzb1ig edw.ha/ 8oe.65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs, evpqlutc )(: p)h- 1:t 1frb1m kht hxn5ft3s,yach with spring m:s)5 (p3ttukh -f):q 11tt lnhch xv,brpfy1stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is in ufr) dqmge() 5meters ad)g5fqume r ()nd 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, labeled5( fc5nej/aipv y)blkxr, a5 ( A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124 N/m) t6gb 18,nxe x jutrh4+v5njw9 is struck by a hammer, which gives the mass an initial speed of 2.96m/s Detnt,1hjgw x+e64vt95 n rxb8 ujermine
(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 cons m5v0ak5d.a+zle z1a x8:givj tant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs x zzag8avedia jk+.:5 m51l 0vfrom 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 to3 szl)(gahmbk1 nd bb ;.og4a, two springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached w2u3v2e4 gsu /q9gni ito a fixed horizontal spring whose spring stiffness constant i2n 2eq gv igus/iu4w93s $ 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.y.xx6o u+tlu*69hj -r2yw4gwhela w+ After reaching his lowest point, he oscillates up and down, hitth*gxlr6y o9uh +uxeyaw.+6jw2 l4tw-ing a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrationsdo2v 5uke k)u( 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 ma(dxpa ;ld*0 u3*zehs fke exactly one swing per second? (That is,d x;l0f* 3pu(eas*d hz 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, where+eq- 7hm2ofgg the accelerahmq7 +gf -g2oetion of gravity is about 0.37 that on Earth?    s

  What is the period of acan3s*j3kb pofwc6p :9b.z 5m 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.qqw4poh -.uz o:;i znh::o5xm760 m, the pendulum bob has a mass of 365 grams, and it is released at anomqnz;oihu:p -.5z: xo4w:qh 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 ofimlsu 71jsc: afb.iwtsag, 272jh b 08 0.9930 m. If the clock loses half a minute s8um i22hi at7fb b1c7saj.j,gls :0w per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum/d4;h 9 v herf*uv00 2dxoe5fx-kzycr 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. At s9f , g/p(*crcqm3nyh it is released from rest starting at an angle of 15 sg f3(,nhp c *my9/qrc$^{\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 asywu7rj iek /lsd.j 4wl8/e i -c,g*(lnchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. Hoil .c,8 u jdsk*l(-4jig/s7elww ye/rw fast are the waves traveling?    m/s

  A sound wave in air has a frequenc+rzvx8sad 71.sfjtz7+4 ggjny of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compressionsv7zzg4d r n1ax+s+jst7 jf8. g)?    m

  (a) AM radio signals have x3av: i z6ad v0vds2o8frequencies between 550 kHz and 1600 kHz (kilohertz) and t02advioza: xvd86v3 sravel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of long6yzhit5c :jv1itudinal 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 x/ukqzyg/67j -i fcq* as the other. In which rod will the speed gqz x-c i6*/ju7/ykqf of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. Ifv d3o -t8c(qkxm8 eft7 the tension in the cord is 150 N, how long will it take a pulse to trav8tc8 f-o tmkvd3e (q7xel from one support to the other?    s

  A ski gondola is connected to the top of a hila1w /ohgur 04dl 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 h4 0r aou/gwd1into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just beloqr:b y3dc e,*: (ksvfow the surface of the sea. He hears the echo of the wave reflected from the o dc: e:sy,rqo vf*(b3kcean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at diffeyrkj 3,(m+ sthrent speeds, and this difference helpk mjht+sy(r,3s in locating the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a+bu6,p+nmc6 z (qa fyn sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitu znyu+ac,q+m fb 66np(de is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, gj1 c5f750i um eq xkw+zksg0*of an earthquake P wave passing through the Earth and detected at two points 1jfxgw+75*05ce0kiqs zgmk u 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthqrqj hh+);hnx.uake wave passing through the Earth is measured to be r;hj+ x.) hhnq$ 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 through4-j j g:if il8rfy8zn,l:x,bz the same portion of the Earth, but one is carrying twice the energy. What is the rji8y -njzilx:f8,r,b4gl f z:atio of the amplitudes of the two waves?   

  Two waves traveling along a stretched st(3km3t )ceyxpring have the same frequency, but one transports three tim k)c(ym3p x3tees the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to mov ad*tos1z)0vq oc,clmf(e n0 8e up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor dozl0n,)fe * (os8m vdcaq01cotes the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other5h c(sp8ezqiu c1 (kn;. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later;h zi(e 5q1csu npk(8c. (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 vibrates at 440mlfa o: b3i(x4 Hz as its fundamental frequency, what are the oifbam4l :(x3frequencies 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. At what frequency wi1r2hnpef3d: jll it vibrate if it is fingern31hf:dj er 2ped 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 frequency of 280 Hz. 38i n)barfj5w Name at least three othe aijn3)wfb 85rr 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 frequee.qnxv; +a n(jncy of standing waves is 475 Hz, +nenxv .q(;j ahow far apart are two adjacent nodes?   m

  If two successive overtones of+ hxnw v; zfuo1cz5 v56u/a:zv a vibrating string are 280 Hz and 350 Hz, what is the frequencvcz+fuwhn;a:5 6vzzv1 u5 /xoy of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6;g i*0mjtix7 b g. The distance from the bridge to the support post is L = 62cm and the string is under a tensionbt;i gix0 7jm* of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is meak wud3d4*9e7aokin9g sured to vibrate at 205 Hz. By what percent should the tension in the string be changed todoiwuek* adkn743 g99 correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar - ahn-q4v3 -bt obwfg3string 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 corr q4-wo-tnav fb33hb-gect the frequency? decreased by    %

  One end of a horizontal stri1ol9dl1 * d/2mgg l4qt ch2pcrng is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per hcg/49 d1cd2*rllmlp 2q1 ogtunit 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 b9sq-d) l .ios5ybmz w2e adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between ds9 .qsby2l o -wmiz)510 cm and 1.5 m?   

  When you slosh the water back and forth in a tub s.3 ah) 9kjiucgar5grli*o u/b.,y t6at just the right frequency, the water alternately rises and falls at each end, remaining relatively ic k./osbhrgiul63*ra59).auj , gtycalm 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 traveling at k.0 km/s strikeqld,; mhv 7tl3kt xeo/n (9x4ts a boundary within the Earth between two kinds of material. x,4nt7(xd /lotl3; tqk e9h mvIf it approaches 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 b/xk :bg;d qm5changes from 2.8 m/s to 2.1 m/s If the incident wave crests make a xk5:b/qmb ;d g34$^{\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 cold, da; 8i:-cx4odzs 8cqhzdv4k4 ukkff / 3ense air. If the sound wav 4o-:q3k/f x4fdczkichv 4 d8;zksau8e hits 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 earthq nzv)9xabxnl 4lpz:.1uake wave strikes a boundary between two types of rock at a 38nl x)l:x9zavpb1 .4n z $^{\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. 68s,fi yn+ qn1c,q7gp g(fxlo According to the user’s manual, the dish has tonn,ly q, g(6q1sf+f pxg7 8cio be pointed in the direction 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 km and velocity 750 km/h trswn fj,x;spq9;t v0i 28gvk-v avels 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 tsutkq;vx9;jn 2v-v0 fswisg 8p,namis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a,u t p8yrj9)au spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s ytr 8jap)u,9u(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, wh8 z)fftu7q:ox ich stretches the net 1.1 m. Assume that the net behaves like a simple spring, a7foq)8u fzt: xnd
(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 l, wmao-k:0semw;0 dvthe end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. Wk;w00:emdo sam,v l -what is the frequency of the oscillation?    Hz

  A 950-kg car strikes a hugeft *qsc .ox1 zf-81cze spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness concce.1ozfstx- 8f*q z1 stant 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 bpcx(o7k2op,s im ** mcoffee (diameter 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). Estimate the speed of waves in the coffx 2, pismc**oo(k mp7bee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of6tn7r b7lj b8x a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound em 7r8t6jl nbbx7itted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x kxc w-; aks:x6n:4ftz is in meters and t in swx:x ;n :f6tkz sc4ka-econds. 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 frequency ifwh pek5e*(dp0iisdqv bp+e++ 0ls;h, it accelerates at 0.50g (( ;sliep p sqeh ikv* h+0pdd,0+5bwe+a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-w8t1o699zbsp0o g-n.fci v ix kg man stands on the raft, it sinks 4.0 cm deeper into thei1w8xi-v9f6zto0 obp .9s gnc 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 tuned to play rswfn0sspm j4g)ps4b:oz y.k(f b):4 at 392 Hz (G) and 440 Hz (A).g.ozsw0r: yps pb(s 4js)b4: f k)4fnm
(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 stretcn8m qkrqd,ka6q5+r.z3q zux :hed two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengthskqqrz k+mr5dan 6 z 3qxq.,u:8 in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, w 4j4rmt1rd-euz.j8k ox) zl 1and the tip of each prong moves 1.8 mm to either side of center. Calculate oz4j4 rml.jzw1rx )1t8e -k du
(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 v1;0abyi coy r)m*e, e1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble y)*mroay, ei;c 1ev 0bplaced there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if tqs:fz8 lm3a6gki* c ,lhat end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibratios *3,mk: lqlicgfaz86ns of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — eacy qu 9+w/ s wf9gjhr+)3q)dujoh one-way swing takes 1.09 j) fh9)q/wdyo uwqjr+s+g3 u00 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can 17atstrr7 - l1l.l vodoscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both atrvl1d al t lor.s77-t1 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 mass 123 g is s zppfynidq2y3vr1:xun :0:d- tretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later dd0 npy :nqp2i1xz uv- y3::fra second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with sprin3+a:tdw ld e-lwo5/ apds* v.sg stiffness constant k. A penny of mass m is e+ad 5t/l3o-dlw*wpvs .s : adplaced 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 cable i;w / s kzcvi6pbrh** 1yhuq((ns 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 t hn/ bc16r**vqsy((u wk;zpih he period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58bwtzmd**j/6 jxk+v6 l (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jellozwv*jxb +6td * j6kl/m springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz