Give some examples offla(k+p6al t j; xjtla3oxn9: +a ae2; everyday vibrating objects. Which exhibit SHM, at least appro; a+9 apl;6xf eto 2lxjanj+: 3at(kalximately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, where? h -l,x) uzgq,tbmod7 mc./j.v

Explain why the motion of a piston in an automobile enm:f99sio l.r ngine is approximately simple harmoo: mri.s99nlf nic.

Real springs have mass. Will the tr2 dfb969t sr-9 zetxapue period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Explainp99t6rf9 s 2tx-bedz a.

How could you double the maximum speed of a simple harmonic oscillatypy 7ju7ybg+oze6b24 l8: l xuor (SHO)?

A 5.0-kg trout is attached to the hook of a verhed:ovv (( tk1tical spring scale, and then is released. Descr:kd( e1vvoht( ibe the scale reading as a function of time.

If a pendulum clock i i6/ua7tql6,fkyo5l w s accurate at sea level, will it gain or lose time when taken to high altitude? Wh67 t /lf k5ulqwiao6,yy?

A tire swing hanging from a branch reaches9c+1mecgj -w9 ihqp0l q+jlu5,j3k n b nearly to the ground (Fig. 11–48). How coulb+k jig9nwm,q5 +- pe93lu 0q1jhjclc d you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and fqk q at,2oatvh.l /7;eorth in a pan only if you shake the pan at a certain freqt v,o;a e72tkhql /aq.uency?

Give several everyday examples of resonanceagz2 wp1dasdb4)1( 2cr cmd;f4e)wk k .

Is a rattle in a car ever a resonance phenomenon? Exvj-orgcj0 n;*plain.

Is the frequency of a simple periodic wave equal to the frequency of its souyv4tfp-wl;i+5a4dk k xw.3 vgrce? Why or why npyvi wk4fd;+a.5-3wvt4gx lkot?

Explain the difference between tht0qc 5x-xdg w9e speed of a transverse wave traveling down a cord and the spetxgwqx 90dc-5ed of a tiny piece of the cord.

Why do the strings used for the;1 a:tar )u+q yh b(g*xsztf:f lowest-frequency notes on a piano normally have wire wrapped aroundffhyt;z* ab)uta xg(: r:s1q+ them?

What kind of waves djax9./wrwb7- mze +xao you think will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to it-/w a+ x .rzex7j9wbams length?

Since the density of air decreases with an increase in teh,sewjfj12a0p *py )dmperature, but the bulk modulus B is nearly independent of temperature, how woulsa1j*jpfw h02)ydep, d you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease i4 lqj4ue9ud;q8jft 91y hpp6r n amplitude as they travel away fj4u;y4qe9rd qp18u hpl 69jft rom the source.

Two linear waves have the same0ua g ;2gs-oi/gbozbb/zz4 q9 amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Wq ;4b-g0sb9g uia/o zz2bgz o/hich transmits more energy? By what factor?

When a sinusoidal wave m6 y9 oai9z);9lh twt-zv8isbcrosses the boundary between two sections of cord as in Fig. 11–33, the frequency does not69t9z-z bm oiahi;lt8) yw9 sv change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are -+h gcm ml wiai-*,h;roi+rb8there any places you could touch it with a knife blade without disa*,o8mb ii+l-r+wmgh-ri ;ch turbing the motion?

When a standing wave exists on a str qsen)/pq,o/ x v,lw*ding, the vibrations of incident and reflected waves ,*voq,psxl /n e) /wqdcancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being trave al23if.yn3 nsmitted from one place to another, how might we determine whether the eni.f3e l van23yergy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distance itzlgzus3 t0bex4- c-2a travels ibsl4-t2c0zg ue3a xz-n one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from gnq*ne ::s:xn f cy,5eit but is 85 cm long when a weight of 180 N hangs from it. What is the “s,g cnxy*:sn:5fqen :e pring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compre+wu wyy1 mfmgalz.o8q95 e2g;ss 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goq yy.au mz5;2f o8mwg9+lew 1ges over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretchl s2rvjm0tj) 8es 3.6 cm when a 2.7-kg fish hangs from it. (a) What isjlvr)j8ts m 02 the spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frnn: 5 5.jj ;h,ruulwtgequency of 3.0 Hz when a mass of 0.60 kg is hung from nur jg5;th:lw nu5,j .it. 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 at to/owc kr(wa3ljzpw vf-8y)y35a9 17 xaqv vy 4imes t = 0,v p1qv3yc8oa l -4vf7w(/zw)ay9y5 3wjor xkat = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 0s t za,gusun6y*p)qz:+p -c16 r 9yzwc.25 g is caught in a spider’s web. The web vibrates predominatelyqns-yp* zw cu1:+t s zg,ayu6r6)p9z c with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. When an apyd-ga:g j s:wm./ 4osxo 0un-dditional 680-g mass is added to m, the frequency is 0.60 Hz. What is thn-:yowma.:gjuo-0 xdss 4g p/e value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.00bj2kfy -zuz9 times per second with an amplitude of 0.13 m. Determineu 0zyk9b2 j-fz
(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 maxim8-tltywid:ud 2((zl* si 4 bqzum value-uzybl(q8dli2(w *z 4si :tdt?$\approx$    A

A mass attached to the end of a spring is stretched a distance mj y th7 vvu6)c 9lz oa1cq9c4yn;d1)fc1h r0j$x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring iscie7 py phyvw/,2bi;, stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium positioi,vc7p2w,i pe;yb/yh n again?    s

  An object with mass 3.0 kg is attached to a spring with sprin md sbpy.j42h sww/(p:g stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with4w( s:/y. bh2pwsp jmd a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring-p h( c)z npd6vsz:i,e1ae h4e of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the g hd4(i)eavehn 6 pe,zz-1:spcun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to ony j0y:qfc6 o,zyn15nhw m o8klr+a1ac/f1f5 ee 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, the m 5zrkn,aaj+ yycm8cfofe/y56 oh:n1l01 1 qwfass 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 zai/i-u/lix)en.x m+ the equation x = 0.45cos6.4t where x is in meters and t is in z n.au)ilime+-x/ /xiseconds. 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 eq g5v v bu))9feu+ttg9euilibrium is the energy of a SHO half KE and half PE? 5u)) tuevgg9f 9 tb+ve±    A

  If one vibration has 7.0 times the ener-br,5iv ynr9h/naxy) gy of a second, but their frequencies and masses are the same,) 5ba yxy-n9/inrvrh, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging ligh. uw,ew8v)r- .gkqze2z) juqjt spring once every 0.65 s..j) -)w.u,ue8vqw e2 zgrqkjz
(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 ide8lyqb( ek8h/h27nxv u27 0x7xpzh o rintical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be 2b p088/k un7xlxe7r oxhh2 iyz(7qhv the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x ihr t4c9j l,6hcs in meters and 6lj4ht ,9hccr 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 exampl yicq7rzjl,/:( rj e8fes of 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 ho39 szoik* d1-1+yp+nosa igay rizontal spring (k = 124 N/m) is struck ys1+3oagz-ky19dpon+*ias i by a hammer, 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 with spring stiffness constant 3 q m16q9uj2sc;p+ htvz05 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from q1s;utpmq2j9 +v c zh6it. 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 sqo 1hj:cby6 3.h+ sjestiffness 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 to 7tgulmjsxu 6 3t *2oap7:b l/ta fixed horizontal spring whose sp :7 at*32/sj 7olulbmxgtut6pring 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.-/yor8 wlt/jen.5j byh y y6m0 After reaching his lowest point, he oscillatjl 0byyt/hym-e 8/wyj.on56res up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the 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 exactly (d ejtn+fw,9s60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per seconic+ uf:ayfy0+ay0w2 md? (That is, one complete vibration takes exactly 2.cyfawy im+y+u0 :2af00 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its p 0)ziz3-dfxfn eriod on Mars, where the acceleration of gravity is about 0.37 that on Ear 0znfx-diz3)fth?    s

  What is the period of a simple pendulum .j4l f(2ax;x3z qiks nxo)ua480 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum isn0n+2/gajojo(ew-oe t hle 9- 0.760 m, the pendulum bob has a mass of 365 grams, and it is relea9gn2j0 oen- t+he /jeao(lwo -sed 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 the cloc2y7klohy7 c qkll9 0g/k loses half a minute per day, how should you adjust the l2 lkcq/7 kg l7lyo0h9yength of the pendulum? shortened by    mm.

Derive a formula for the maximu uxy7c7*(wacnm 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 oscil.-a+y5xp57.uk bsd0 oh m xwrelates at a frequency of 2.5 Hz. At it is released from rest start0 asxwy5x.k peh5+o7d-um b.ring 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 anchored boat every 3.0hb shd ,7bhal8ea xw5 12hro/5 s. He measures the distance between two crests to be 6.5 m. How fast arhb7ad, o 5x8 2ha5lbhwhser1/e the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 39aaw3ml 8c/ oa43 m/s How far apart are the wave crests (compressions)/8mwa coa3 l9a?    m

  (a) AM radio signals have frequencies between 550 kHz andlolmci me/+9 +,nue0wo dod5. 1600 kHz (kilohertz) and travel with ai9dnoe +oeldl+0.ocmu,/5 wm 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 longitudinal waves 5 :: tiodzwq.pin
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as t7-wqfbuh j(- l-ujt (nhe other. In which rod will the speed of longitudinal waves be greater, and by what factor?-( 7h jwb qju(tlnu--f   

  A cord of mass 0.65 kg is stretched between two supports 28 m nwxl6i,k3ll.le0 v .papart. If the tension in the cord is 150 N, how long will it take a pullpe.l3. v,6 knwl0ilxse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel s+ igd/; -hqtawl hx8*-q3jsdcable of length 620 m and diameter 1.5 cm. As the gondola comes to theg sqxlt+i h-j-dh; da/ws8 3*q 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 pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the stc (ya+l22*p) rvbz / ng3anrzurface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at )ltcrn za v(3 2+2yg/rzbnp*athis point?    m

  P and S waves from an earuk erdr+ue5.(4ir5 nejp(tn *pak;*rthquake travel at different speeds, and this difference helps in locat(kip4r.; 5u ej*eak5 *nrd r(n+tpru eing 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 sinusoidal tra4/mcq*f0.le /gkkd z vnsverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin tok md k.v4g0e qc/f/lz* leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensito5jc l0z:t+ euies, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km fro uo0:ltjc+5z em the source?(a)    (b)   

  The intensity of an earthquake wave passing thr0u+bf:1r0 (+az*jb2itxj5 lqi m afp sough the Earth is measured to be *i+as2 f5 zm0 l0buxpf q:+tj (1barji$ 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 travelxmv;r(v+j d.76-sceqxq nes 7p7sqh2 through the same portion of the Earth, but one is carrying twi67vnqpx .s+(j - xvhcdees2srq7m ; q7ce the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but /l+uj+uhc m d20rs4en one transports three times the power of the other. What is the ratio of the amplitudes of the tw0u jhse ln+rd/24um+co waves?   

  A bug on the surface of a pond is observed to move up and down a total verticpfub dqg2na)p2/jt 9 *al distance of 6.0 cm, from the lowest to the highest point, as a wave pa/fgt u b jqp2)na*p2d9sses. 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 momk4mi s1/r0h kving toward each other. (a) Sketch the shape of the shm1 r4mksk /i0tring 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 moment?

  If a violin string vibrates at 440 Hz as its fundamenex2s(wmfg+)h8 ian ; +f2wqzatal frequency, what are the frequencies of the first four harmo+azwnei awx)s mgf f8+q( 2h2;nics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when un;o:93mgc zsof fingered. At what frequency will it vibrate if it is fingered one-third of the way3sg mz:c;o o9f down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonyddebdsag7 pl7 (((u 0ates in four loops at a frequency of 280 Hz. Name at least three other frequencies(dypa s(d (7bl0gu 7de 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 thkg6fdmzi* 9k;qj ,j cl(c )cv8e frequency of standing waves is 475 H(gkz8v*)qmd;cji6 c, kc 9flj z, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what ist7f;aoq gfxz3z(w)l /f +e .nl the frequency of thfa7 etfwl3qn.lz+fo( )x/zg ;e fundamental?    Hz

  A guitar string is 90 cm long and hk0r9(fi9kmt kas a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. Wm krf9k90tk(i hat are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hzkn:hfwb :y mgjq*4 wpj,(a c40, but it is measured to vawpy0 c4 nwhf:b*4mgj q: k,j(ibrate at 205 Hz. By what percent 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 string is sup,cfvf zx:sm-z1 /q ;zmposed 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 cos/;zqxvmz 1,f-m c:fzrrect the frequency? decreased by    %

  One end of a horizontal string is attached to :4idwz cp4+c ea small-amplitude mechanical 60-Hz vibrator. The s4epc4 cwi:zd+ tring’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be ad8ci lr x 9hlqm(g;c 4b(9vkq7ejusted 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 betk g( c4c v97rlbqmex(h;iq l89ween 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at nj,p0zrtbz 0 2just 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 tubt r2z,0 j0pbnz is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave t 9lhl;v1ypcb7kt ;1w zraveling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approache l;ph7;cwkvl1bz1ty 9s 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 c uwh8x -d ks,a0d8/lx*kiz/lxhanges from 2.8 m/s to 2.1 m/s If the incident wave crests make 8/,a i/h*u-k0xsl dxwd8lxk za 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm airas-kx- 2:yj by when it hits a layer of cold, dense air. If the sound wave hits the cold aba:sx-yj k2 y-ir interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave stric a;6xy) zzt4dkes a boundary between two types of rock at a;tdzc)y6 z4xa 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. Acc y,vb7xjmx5 ;hme*4*zfm im p.ording to the user’s manual, the dish has to be pointed in the directionp*7yzm*5fm ,eb ivjxm4mh;. x 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 travels acazg: aoc3w(3k;m4 n qcross 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 a3aa 4cmkow cq:g;n3 z(bsence 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/m Find p5xd;yv05ah td3wux 7pzh0p- the maximum compression of the bu5z5 xhdhywu0-pdt ;7x pv a03pmper 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 energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, whic-3cxfn by hkg l.lk/,0h stretches the net 1.1 m. Assume thahn0x-.3lk fy,kb/lgct the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. Th dx3sa 7 mbz-p5e12a(xm ct4 mhrw3-lte mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillation(-td3 mcrh e53pb 17 sm-zmt2xwx ala4?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), comprcz h2f+mr - lc0wg:w7kessing the spring 5.0 m. (a) What is the spring stiffness coh -c0 kclgmf:+z7 wrw2nstant 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 (diamete+6l,--yvbycc sf ll7 q3c a(ikr 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 t37 yy c vc+ a-li-,kbl(6fcsqlhe coffee.    cm/s

  The ripples in a certain groove 10o 5nh(zknxd,ol0ap8g(9l c c)o c9 ql:i* i*pd.8 cm from the center of a 33-rpm phonograph record have a 98,ldi(ka * lix *o qn:d zlco9(gcp5co)p0nhwavelength 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=0.6x*c z0pg /*xzn50cos7.40t where x is in meters and t in seconds. Determine x*gzn pc0x /z*
(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 frequenc;jjozfk, kwe/l-4 qx-y if it accelerates at 0.ex,o; j jwl-q4/k-k fz50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats o z c3lie8xbe5 3siu9lv5b-v-s n a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, t8x3vuzb3es5ls i-9el icbv- 5he 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 instrf)n rnc n0xcwvf-+3h b;n81 uuument are tuned to play at 392 Hz (G) and 440 Hz (A) +nrn03f8vfuxbcwc; n1)-h nu.
(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. ik9a17cpbs*sk 69pjn11–33. Determine a formula (a) for the ratio of the speeds of the 7p9 1bak6 cjpsks in9*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 frequency of 264 Hz, and the tip of each prpc;jaw/:ky4ku7gue-8b,7 :kcx i c a zong moves 1.8 mm to eith,;:aki: 4kec7bka8p x cyu j-uwzc/ g7er 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 witrmzuezz:w r1lv9,yb8g;e- v( 2p rho5h simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble place5(;92zh rberry w -ve:zvp z1m, 8ulogd 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 att:l,q,dhz5 wt 5 tjwgiu*0bb:u ached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the reson 5,iu*:,b: g 0dju ht5qzwwtlbant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.0007 ytzka j(a2xkht0p+w(exhnfx06bq 4 le n/*/ s — each one-way swing takes 1.000 s. +y/ k2h6j(x(x taknn0fw0ezhbe tq ax* /7pl4
(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 sprin lw:6madt4 4 vwl69wirg can oscillate in the vertical direction or can swing as a pendulum of small amplitude, btmlaw i9d6w:lvr6w 44 ut 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 mass 123 g is stretched under a tension of 2dajhvvd-tm10 9(01fb 6l o sos55 N. A pulse is (0v1 -m16svd90otobajf s ldhgenerated at one end, and 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 byv gby1:) ysffry- ;a:c a spring with spring stiffness constant k. fb1sa g:f-)yry: vy;cA penny 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 ax)wrkq+ wyc1mqs32.s 1200-kg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze sta.3r s2cwkx) ymqs+1qwrts 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 (which alsom4xgw id7(dhbhjm6.qe3we, : gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spridh. mqex6 g7i3e ,h: jbwd(w4mng, 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