Give some examples of ev-g+ bbtc4 vw-g +:yzfveryday vibrating objects. Which exhibit SHM, at least approximately?z cy-v+v:f g+wtb-4 gb

Is the acceleration of a simple harmonic oscillat, drbx;q 9kat7izx9gb ix n--4or ever zero? If so, where?

Explain why the motion of a piston in an autod 33i-t 0 r- xxljv8blaf7ls,rmobile engine is approximately simple x03arstrdv3f-,7-lbl lix8j harmonic.

Real springs have mass. Will the true period and f.s , iktwhx,.:m3vgaazc: v(zrequency be larger or smaller than given by the equations for a m,.:(zt:izawc x a.v,s3 hmgvkass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (SHO)?0otq(phc 7f7 k

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then is uem u2d.f-/ukreleased. Desc-ueuum ./fk2 dribe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose timcubam9ln4 f )3s9hmc)dh0gu7 e when taken to higaf)n 70 9)uucdh9l43mcs hgbmh altitude? Why?

A tire swing hanging from a branch reaches n*;p-zn g0t- mnczut0o gsw9)iearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a znonpt-mg)*ztus ;0 -0 g9ciwstopwatch?

Why can you make water 29rdjiugv vd6; ;d4zqslosh back and forth in a pan only if you shake the pan at a certain fr dgjdud26z;9 4v;r vqiequency?

Give several everyday examplesj97-t4pi s yho of resonance.

Is a rattle in a car ever a resonance phenog 8myjgf8re ;3menon? Explain.

Is the frequency of a simple period68s6l,j 9twitdwhs j6ic wave equal to the frequency of its source? Wlditt,9j 6whs68j s 6why or why not?

Explain the difference between the lw.;,.sgzjl c:y8aogspeed of a transverse wave traveling down a cord8jyclg ,. o:lwz ags.; and the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano norm y./ mn d)wuo;u/;wyoially have wi)ui.;dym//oy; unow wre wrapped around them?

What kind of waves do you think will travel down a horizontal m ou9l)3)eu:vvqtgh *metal rod if you strike its end (a) vertically from above and (b) ue)om3 gu*vh)l: qv 9thorizontally parallel to its length?

Since the density of air decreases with an increase in tempebyhu5rp f:w8v b5;6hurature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to;5wbu:8u yrvhbf65 hp vary with temperature?

Give two reasons why circular water waves de arom4b y,72dzcrease in amplitude as they travel away from the sourczrbam,27dy 4o e.

Two linear waves have *1 bzo)utm kf,f+qy5 dthe same amplitude and speed, and otherwise are identical, except one has half the wavelength ou*zf5fkt,1 )+qdyob m f the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary betw(j1./y 4pyfqrb yw- izl+ ulagjp/48ceen two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do bc4ypylwuriq+1/4g8z(.y l/pf- jja change). Explain why.

If a string is vibrating in three segments, are there any place:dcig, b71ibjs you could touch it with a knife blade withoujc1gd: bb,ii7 t disturbing the motion?

When a standing wave exia82v1n njdrs-3 fln a;sts on a string, the vibrations of incident and reflected waves cancel at the nodes. Does 2l a;sva1d3n8n-n frjthis mean that energy was destroyed? Explain.

If we knew that energy was being transm v auu--vf2 +-nk-z9 cn7q,hqipr giz1itted from one place to another, how might we determine whether the energy was being carried by particles (p1qfn9ga 7vu nzr- q+zh-i-i- 2cvk,umaterial bodies) or by waves?

  If a particle undergoes SHM with ampli qq)3 nlwnq9;szq0ov.0a 3azmtude 0.18 m, what is the total distance it traz3)q0qa.q3mq la90ow ;z vnnsvels in one period?    m

  An elastic cord is 65 cm long when a weio f+4z;3rmyi3mm ai d0ght of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “sprin0;34dmi r yi3amzfm+o g” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg dri2 kpwj)xkm 8k/ver gets into the driver’s seat. wkpj 8)2kxk m/If the car goes 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 hang7e)-: o4carhh +mzxsu h xnxx *tbh0/,s from it. (a) What is the spring stiffness constan4,h xrschbh0*/x: etmnu+xh-oza7x)t $\approx$    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 +n rfa6ed;* 8df ju( mel2/yrj0n,tib3.0 Hz when a mass of 0.60 kg is hung from iu,bnt08dy lrfd6(n+/;*e2 j fm iajr et. What 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 ah0*m aw3xi/9 pjh abp,pu et 4aiizqy63a88i0t times t = 0,t 4,p3 88m0au ib eh9*jyiapq tz/p whaaix0i63 = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 web vibrates p04y uc duaan*;vp-h, aredominately with a fre ad;u0h-puv 4ya,*n acquency 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 ofu-xwa cadm8 jzt/ y2nj88x9q3 a spring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added-xm j2yq8a88njx/ dz39wuca t 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 spriu k50n4chin0yd+g )u k7wy/yjng vibrates 3.0 times per second with an amplitude+0gu/ njnhi70cw )ydkyy ku54 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 pi5nm o* q:s)rof a SHO half the maximum value)*:o5n q spmir?$\approx$    A

A mass attached to the end of a spring is stretchedv4stxx.h/ n9i 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 sprinbh y - 2f0pkn.9t;wi n*r6edvjg 0.315 m. If the spring is stretched an additional 0.1302.p nw6ribyht9;e 0f-dj vn*k m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is pek b+sbtkv*v3b l7+2attached 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 itsbp 2e3*b tv+k7+skbv l 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+cacray c7oe/ 3,9 iff.0 N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gun?i3/, 7eaca c+ ofc9yfr    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end93e on7yd7h99sukagr 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, the mass e 9h7e ra7g 3uynosdk99xperiences 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 vibrag-esdq l49: hites according to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. l -:9i qdh4sgeDetermine
(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 ha,2 nmhmvc t8 rmazy) 2.5 7nd,q8nldrzlf KE and half PE? ±, .zq2,ldtrmyhc88 z vmnn m52d)ra n7    A

  If one vibration has 7.0 times the energy of a second, cgpq09mqz49q; o8lz qbut their frequencies and masses are the same, what is the ratio of their moq z4lq c8 zqgp0q;99amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging (hkar-: p d3nclight spring once every 0.65 s. hakc -(3d: rpn
(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 vertinm*(m(pfmxxp5/f yfv+qx)- rcal springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibrat(mx*fn m(-/+)qf x r5fmpy vxpion?

  A 300-g mass vibrates according to the equ4- zd1y;f lus3 +skks mwwy3e6ation x = 0.38sin6.5t where x is in meters and t is in seconds. Deteryk;6el3w s1 -ksw3z4 sfm+yudmine
(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 orsw 8q9au) ct0z3wa tnk3fx7- f SHM, 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 sprinz 7jn.7ruae3 hg (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed o.j773huze arnf 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 stifftc xhp /h5:q:kshw+g. ness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the e5h/g: xw csqp:hh t.+kquilibrium 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 constantn6vt1spgr j +9fdffj;o4 ( .rbs $k_1$ 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 horr kd/qs s2p1kwi ;9al:ez/j8 oizontal spring whosr9 dq/es8:ws2ki;p1o a k lz/je spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reac1 6romsk.ah.1m*a ewdvej p /c,5jog- hing his lowest point, he oscillates majo*m.5 ha6w1 g- sck rpve/ 1,oj.deup and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in e1 dlzx o6h-*d0dpt 5xnxactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simplefs hvt*qg; h/f0,ocs) pendulum be if it is to make exactly one swing per second? (That is, one complete vibration takes exactfhhf*/) t ;q,gs0vsco ly 2.0 s.)    m

  A pendulum has a period of 0.9p kbgu;xf+ t580 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that ;g9 xpu5tkb+fon Earth?    s

  What is the period of a simple pc 4wb d4gwbodlqh1 co;29,i, ozh s65oendulum 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 pendulum bob has a mass of os.r22mlf xnd,1kit1365 grams, and it is relkn xf rs 1mo2i.l2,t1deased 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. If th7h;5xq5frlpj 0y -ir:8ipk x ye clock loses half a minute per day, how should you adjust the krqyh i -y:p8 l r7p55jx;0xiflength of the pendulum? shortened by    mm.

Derive a formula for (:h sj4xec+n (ddas 0wthe maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz+9zdnx vm)l :q. At it is released from rest starting at an l)qmn+xdv: 9z 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 th s62 lpm8p yh-vc-lc(eat wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to bep(svm -cpl82 ylch6-e 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels withgl,a1cwg m7 w bpz611hu;t h-m a speed of 343 m/s How farpm1 uz,lh7 m6wwch bgg-1 a;1t apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequenco4660 w0dgbrnoa-vl f ies between 550 kHz and 1600 kHz (kilohertz) and travel wo 6d4gvbo f-lnraw 006ith 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 longitug *j 1d7bb+nti2gwivjf-a /3ydinal 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 twiceuuec8w q5e;l 8 as dense as the other. In which rod will the speed e; 8ulwcq58u eof longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretch691 udh iy-h71kgdw 7lzc)f pled between two supports 28 m apart. If the tension idh1u- 77g1llch9 dkzp6iwfy) n the cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable ofxh4h xbm hg/6vaku1x+:2*m-o*bgawq 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 16vkmb+h* -1ag qh/ho4:w62xbxxag * um 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 bs syp18sg, z2felow the surface of the sea. He hears t8 2szs g1p,fyshe echo of the wave reflected from the ocean 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 different speeds, and this diff1wnpo jmm44/ kerence helps in locating the earthquake “epicenter” (where the disturbance tookwm1npj /m4ko 4 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 approximate6 x,-ugl sfyv+23n ng( htnxs4d by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical x,4xsn+sg ny tlhv 23nf6-(guof 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) thef7l; apv- lq5g amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a p5ll;af -qgv7)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to by;d9e h8i tth*e 9t;yh*ehi td8$ 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 sa8)*nwsi zc 7,aqtxy;nee 0 lz/me portion of the Earth, but one is carrying twice ta0/z z8w*ltic) qsyexn7e ,; nhe energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same fr7a4qji1wg ei/ 4oo136z apmdip cy+e/equency, but one transports three times the power of the other. What is the ratio of the amplitudes of+ 4i/w7i4zidm1ace y31 ap6ope/ o gqj the two waves?   

  A bug on the surface of a pond is obse.ccqc;6rlv i w (2o+kc )q0ozirved to move up and down a total vertical distance of 6.0 cm, from the lowest to the2l6;c o) cqovrwk0c(.+iq zic highest point, 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. jb ;hx i9v58ib11–52 are moving 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 the moment the pulses pass each other, the string is straight. What has happened to the energy at this mohvx5j9 8i;bbi ment?

  If a violin string vibrates at 440 Hz as its fundamen)*fk7:x3 l8ibsqd m7;t vnaxg tal frequency, what are the fixkm3d v8 xnb)s 7t q;7*fl:agrequencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibratese(1i4xmqhmfti o w s,ju*88, e +jb:bv at 294 Hz when unfingered. At what frequency will it vibrate if it is fingereie ovj fwqem,*t(jm+s8:84, 1bbhuxid 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 frequ pm/br62((2nwut fr5t *y vxfoency of 280 Hz. Name at least three other frequencies at which it will resof (yx5wo pmbrvr t2/f62u*t(nnate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a strinbj ky -mpo amb*,)2)7gi ljt4toqof+7 g is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjacen l*tbb j4jo7f-)oy k+tmg ,opm7)iqa2t nodes?   m

  If two successive overtones of a vibrating stm- ul 5 i.u0owrkr-jf/ring are 280 Hz and 350 Hz, what is the frequency of the fundriu frwl5-k-/mou0j. amental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from thj3*pjpw i*uarf/u 73 be bridge to the support post is L = 62cm and the string f *bj /*jip3wup 7ua3ris under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measure+;c3iit)n1(hzin 44ye utcwh d to vibrate at 205 Hz. By what percent should the ten )wtnn 4iihuz1 e4h3(tc+icy; sion in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but i -dwy,(o zfo*zt is measured to vibrate at 205 Hz. By what perydf *,-w(z zoocent 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 mec: 4dfc;n)/ j6dcvcq1l soc9lihanical 60-Hz vibrator. Thcsnoc l;vcc qdj/df)6i 4 9:l1e 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 y/ki+im 2 mdg8k,+eovmay be 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 betwee i+v8y2 /ok+dkgmmi, en 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just thelwanqdyr u)y8c3,yhp.7ta87 w bm 2,7 npn0e m 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 0.85 Hz. Wha78qyl7d 83u)pnrwy nn,p2 c7my0.eathm b,wat is the speed of the water wave?    m/s

  An earthquake P waveeuivg*4g6lwks w9q xt;1-0gc traveling at k.0 km/s strikes a boundary within the Earth between two kinds of materig i1u k4v6g*w9t;lgq0e wc-s xal. If 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 changt/ ;m4j ovypm*es from 2.8 m;myv*tmj/op 4/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 wheng2zzy l zr0(m- it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an angle of m-2zr lzyg z0(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 betwe.r*ij qo4sy )snh;2 rren two types of rock at a 38 n4ys2 q* jhr. ;)sorir$^{\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 diame6y4kv 9ix v;qy mg-h5eter. According to the user’s manual, the dish has to be poxkv gih4 y9qy-5ev;m6 inted 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 travelhummldz6d. a/dw65br aj4l47 s across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much ti a.67dmlw4jz6b/ 4urlh madd 5me do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/k v x91nu2.wgkm 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 (approximately 5 mi/h). [Hint: Use conservation of energy2n9kw.g ukv1x .]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which strq nd*bh )r)0b t+)*fhfqylw/getches the net 1.1) 0w n b/f+ b)hqtd*hgql*yf)r 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 ofylkg9l*6-l;p/a /x a1 kzukij a freely hanging spring. The mass then falls 33 cm before it stops a-9aly/ uajzigl pk1/ * ;l6xkknd begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), compressinxmhpekq2u, h.i 4iqhe7)-9jqn 3je)bg the si73xh49-e,e j)n q.bhqh2e upikq )mjpring 5.0 m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the4uinq l9b,g+l right pace of about 1 step per second, the coffee sloshes more and m ill n,bg4+q9uore until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center ofm5k gl8i9q dr7 a 33-rpm phonograph record have a wql9mkir7 8d5g avelength 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=0.65/3 lv6svuw o i: ;8pipu9zyrk40cos7.40t where x is in meters and t in seconds. Determine suv 3yip8k9zu4r6w:;v/ ol p i
(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 frequeha(1z4v ow1tl2 ds-c lgtzw+ 4ncy if it accelerates at 0.50g (a)(-wo dlzvc1hl 4t+atz1 2 gs4w upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft,a q)km g/z5- :f;foyzd it sino/zfmz-: ;yqagkf )5dks 4.0 cm deeper into the 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 instr0:dwfjb7e/qp2ag r : g*ufl m3ument are tuned to play at 392 Hz (G) and 440 Hz (A).2rl0e7gwf:pq/f: gd ubm3*aj
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig. 11–gd *0*,bt bzzjiv 4ogwd8 ;ump 6zv7c433. Determine a formula (a) for the ratio of the speeds of the wave in th74b**zzwup;di v 8cjd4,o g0zgbtvm6 e heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz,9p;l:6sq:8rpmxom *c rj ks* l and the tip of each prong moves 1.8 mm to either side of center. Calcpl: q pl:6*mok;rm9 *j8ssxrculate
(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 cyclrzukm m3 :5vzevvr8uyr * *b4:))dx oles per second. What is the maximum amplitude with::e5x vmu*) dkvyruzm38 z4 vb)lor* r which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached t mwye64t/r2g s(pi1 mmo a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fix6 e2g(mmm1t4yr/ip sw ed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing t ema5ib/0wt5qakes 1.000 5m/ai t 0e5qwbs.
(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 oscillate in the vertical direcqznye3bbbiq/t /qt ),*gm)l2 tion or can swing as a pendulum of small amplitude, but not both at th2qttz/ )*b)qelqb b,3 ymg ni/e 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 stretched under a tension of 255x l+tjgf8;3 yc N. A pulse is generated at one end, anlj3xtf y cg+8;d 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 suspensocw(jra y5j +qi92y+ded from a ceiling by a spring with spring stiffness constant k. A pe9q+ awi5jyro(c+ j2synny of mass m is placed 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 steelhgptu: c+fnvsgd w,j0k-)8 2 w crane cable is 22 m long and has a diame -20+u td,nkcv8 :gjfpsw)hgw ter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a p0fex jsmxls-i) ,wd ,9late as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. fixewsm0sd ,-)x9jl,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