Give some examples of everyday vibrating objects. Which exhibit SHM,v.-ar t,ikgx8 wy -x-f at least approximately,t f-gxv wark-8.xi -y?

Is the acceleration of a sim- )z o3fgba0)wpkl6zqple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston i1jjj7q svb1k2 o.h4kin an automobile engine is approximately simple harmo1bqskio27 4j1h .vjjknic.

Real springs have mass. Will tjiqq(vorfj 4faq/f 53ej(91et.m*r jhe true period and frequency be larger or smaller than given by the equations fqqj vq / fm 4er(it1 f5o9j.r(ejf*3ajor a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmon)rq7* u( wt;jbj/m freic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical sr6: jwr t3)l/m q0qv0hjqx 6 (ep(lrxxpring scale, and then is released. Describe the scam6v()j x/ qr3 0jrql: tex60lqwpx( hrle reading as a function of time.

If a pendulum clock is accurate at sea lev48qcpy 6 7hia1 - bjw3dljzdm(el, will it gain or lose time when taken to high 3(li4wqad6y -zj bmjcdh 8p71 altitude? Why?

A tire swing hanging from a branckullmie5rn.fn6 , w- :m4kt3f h reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stonenk rl3um: f m56.k4fi,t-wlpwatch?

Why can you make water slosh back an;i ;bgyav02zi1rta(z o,0 g nud forth in a pan only if you shake the pan at a certa0oya;zn2r(;1 iv gbaz 0uig,tin frequency?

Give several everyday exfw zm4zw(2 aeqcae6g91 ic.r;amples of resonance.

Is a rattle in a car evi)z/;gcgdi9 t er a resonance phenomenon? Explain.

Is the frequency of a s i ffb4kjzs6b/u92-r -tm3uiq imple periodic wave equal to the frequency of its source? Why /uzfjiitmu rf29s -bb 3- 64kqor why not?

Explain the difference between the speed of a transverse wav6 vq*1 c rp*yt ypg.5i9jw*x6nzw3boxe traveling down a cord and the wxt.j5y** bi6pox9 rcq p63v*wngzy1 speed of a tiny piece of the cord.

Why do the strings used for ttsw78 )a0(l d z0xacfshe lowest-frequency notes on a piano normally have w 0 z)alcsa0( 7wsdtf8xire wrapped around them?

What kind of waves do you think will travel down a horizontal mett8) p;nyq r4ymal rod if you strike its end (a) ;n)tyy4rq mp8 vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, buot - upvz:f;p:d4y:ul t the bulk modulus B is nearly independent of temperature, how would you expect the speeduvd:yp ;-uf:zo4tl p: of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they travel ak u1 +(nxyj;pi+q+bugway from th+nib ;jx y u1pu++g(qke source.

Two linear waves have the same amplitude and speed, and otpc1 v20*soiok;a c.q qh mqr56herwise are identical, except one has half the wavelength of the othe;hir*o6savp2 cq.1qcm0q k o5 r. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary eg:p6hq d6l,obetween two sections of cord as in Fig. 11–33, the frequency does not change (although 6goe:dl ,6p hqthe wavelength and velocity do change). Explain why.

If a string is vibrating in)zophy7y (xlsbvqc8 pq yei,*7 2+;ne three segments, are there any places you could touch it with a knife blade without dist, sebhly7q+py7 8 ;oe)y n(*i2pqxc zvurbing the motion?

When a standing wave exists on a string, the vibrations of incident andmjr-cvz i; 334 yq1f nw9q)oqm reflected waves cancel at the nodes. Does this mean that energy was destroyed?ro qq4)1mqv -miwfcyj3 9z3; n Explain.

If we knew that energy was being transmitted from one place to another, how mig:xq2k0u 3+iimg p5nghm)lf4 dht we determine whethek +g4m0 u5nl2 gd3fq)hm:pixir the energy was being carried by particles (material bodies) or by waves?

  If a particle underg0ak7 6 6zhv5/rzb(djk so l,oyoes SHM with amplitude 0.18 m, what is the total distance it travels in o(6zds5bk67 lh y oarvz,o0kj/ ne period?    m

  An elastic cord is 65 cm lonmmn-5xsh 4f. a*3d mieg when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “springm ma*4d.ih-ef nxs m53” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver getgqoe5w w m ;9.jkbr.r8s into the driver’s seat. If the car goes oveoqre9 wwg jb.rm 8k;5.r a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs frun) p eg o93m6aob.ox7om it. (a) What is the ogobxaon)3m.up9 e67spring 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 frequency of 3.0 Hz when a mass of 0.60 kg iq/) -mj+ v;cqu yoc.mts hung from it. What is its frequency if only 0.38 kg hangs fro ; )qtc yu+-vqojm/m.cm it?    Hz

Construct a Table indin /z-6ja+v2 o9a zipoxcating the position x of the mass in Fig. 11–2 at times t = 0,t -a x9vz+ 6n/ oajpoi2z= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 a8gg ) sgk-xsum6l n7e9u r:;wsdp2dj2c- c pk/ spider’s web. The web vibrates predominately with a;s/w mndk9kd -gu8:p s2l 76x -)jg pru2gscce 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 springb/1 kl7pyty ; 8 ui19g0;xdpdc.gsmsk vibrates with a frequency of 0.88 Hz. When an additional 680-gy 9udpitkm 110dxs7g/8skg;.b ycpl; mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 ti rcaa0z. ;;f-bzrmm9imes per second with an amplitude r-0c;9rmzm i;ab fa. zof 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 609vmxxp pc110vlbtm+ch ab* SHO half the maximum value1 lcxm01+9cp*6mxha vbvbt0p ?$\approx$    A

A mass attached to the end of a spring is soch:(xn o. r2dk.k)zstretched 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 0.3;o2piq 5;fan h15 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium posi;i 52; fnhoaqption again?    s

  An object with mass 3.0 kg is attached to a spring withqdnte*3kcjb y+fn6( x 3g.a/x spring 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 with a speed of 0n6.jft+qda n e/c kbx3*(3xyg.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 comprepv oo58/bsquv1b, c28ec +hsk ss the spring of a toy popgun 0.200 m to “lous5bk 1s /hvbc v8,oe28co+qp ad” a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one en rv010x6fanr(q; :kwqsnqjfj .um 8i/ d of a spr v(j1:qnwn6uqfrr 8;im /x 00kj. fqasing; 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 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 = 0.45o/2 ectm,r5+uym pojh;6dpc8s z3 u s5cos6.4t where x is in meters and t is in seconds.cj 5m 5tp yc,z oh/6ur sm2spu+;d3e8o 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 half KE and halfa l*6j3uq5t6+i xvk) pj i6dde PE) 65u36xk6idpeia*djqvlj +t? ±    A

  If one vibration has 7.0 times thh k,4ktoo0ng)+z rx6mght*(b e energy of a second, but their frequencies and masses are the same, what is the ratio o)nkgmtk(t r,gb *h4o0+6zh x of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light sprq:kbm5 y;s2ddjzv / i-s1ncggf8c- 4 cing once every 0.65 s. -j ksdv;g2dzm-ybc8q i: /41cnsf5 gc
(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 :h9i m5hip1qgsprings, each with spring stiffness constant k (Fig. 11–49). What will be the frequg1ip5h9 q ihm:ency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38s gtxv2m ;2sw;pg7dofs,q *. anin6.5t where x is in mete.wdgv7qts2*fo2 g; nmsx;p ,ars and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. Fs .;n2rpeeudw) od*:aor 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 uy nw6t8 5to*k= 124 N/m) is struck by a hammer, which gives the mass an initial sonkut 6 w58y*tpeed 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 sti:a )-,l ;xapy8hdkiagffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positx:,p- k;)g adyi lah8aive 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 sprq )f9;u6q sws rrld6rbw8 )qg3ings, 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 to a fixed horizont,dg7kb md5*hz c6bix)al spring whose spring stg)c 5bh b7x*kzi6d dm,iffness 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 65.43xwbm75audj)9gsw a ola;ot6 4d a,l0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiu4 owml5x;ta ,gaa7j sd34w 9odabl6)ffness 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 fhw38r4mf79w sb yfev;n,c m0exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to q3gxank9p:2 9 +t+ tyhwvuf4i make exactly one swing per second? (That is, one compl + +ayf3k29hwxv9qttg:n i up4ete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What iomt /l33y qi/vs its period on Mars, where the acceleration of gravity is about 0.37 that /ymq/o l 3t3ivon Earth?    s

  What is the period of a simple pendulum 80 cm long 7; ch ,bjy 7ka5ziy6,1x(pzp awkh r+d
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, t5w-yzm tq(ts 8he pendulum bob has a mass of 365 grams, and it is released at an angle of 12(ztq 5sy8mt -w.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 clock loseml0 *+fx37dadhfykl z qtej10r ,17w ls half a minute per day, how should you adjust the length odllema7rx,0jhf01l3q tf z7y 1*kw d+f the pendulum? shortened by    mm.

Derive a formula for thjowdc 0/ksw.beyy*+-s2b blik42qee b g+2p- e 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 at4 vtk,; ;kmcht a frequency of 2.5 Hz. At it is released from rest starting at an ang m;c, ktt;kv4hle 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 3.0i1599uer jjmi/7fprs rui9rj7i5 1se/ f9pjms. He measures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a r;)j :bm+z xca oler+0frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the w0xzbeo +;: rmcra)+l jave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 knnt sz/:*l.8g h xydu+p77wc pHz and 1600 kHz (kilohertz) and travel 8tx/nu7c+d p g nzwh*ys.:l7pwith 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 longitudinal waves in pcg d7(i )(gudq:4 7ife;aqer
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic myc7ksy6;s wsxc( 4vg7odulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves7ck xs6(;7 gwycvy ss4 be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 1ycyqxbo*c/3 28 m apart. If the tension in the cord is 150 N, how long will it takey*xc/ob1 3qcy a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by v:;(j zvld z4ga steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the(l v zj;zv4:gd 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 belo;7;o mk9kfu/kv 8pjtzw the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly bej 9zkvo7k/tpk;8f;mu low 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at dif8uckxun6bl.q mh+d/: ferent speeds, and this difference helu/xlq:c nkh u.68b d+mps 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 sinusoidev0v2 p.qtv(h + ;fi(n4expuoal transverse wave. Assuming a frequency of 0.50 Hz (typical u+e0q;xp e v((.2ofnh i tvvp4of 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) the amplitudes, of an e 305iwwyv3ca earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from wa50ic33e wyvthe source?(a)    (b)   

  The intensity of an earthquake wavetaovc,3b fcg z;lde5g(3 d2v; passing through the Earth is measured to be g o(gd,v d;cc3z 5;ef tlavb23$ 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 theofn)z8b6wl(*- p vek9) qy qqb same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitud8py6nb* 9)wqe)f q qzbvo-l(kes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but uh2w-x , ,6pdcnlqix;one transports three times the power of the other. What is the ratio of the amplitudedp-q 2nx hux6 ,,ilw;cs of the two waves?   

  A bug on the surface of a pond is observed to move up and down sa41 0rftjd4xa total vertical di40t 1dsrajf4 xstance 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 does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are ma a.pwfxf,)mdp4(ke 6oving 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 h6kdeafaf m.4w) xp(, pappened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what ra ;htv hoiy1: v76*tgare the frequencies of the fiy7ivohtg t1a6; h:*v rrst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At whu;6;p0v ga 1ijbkw.wxat frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, onugpi; j ;x wv01kawb6.ly two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of ) 8z8r-1oraq klgexb6+ stp 6j280 Hz. Name at least three other frequenciespk1b6e)al js8-6ox+q r8rg zt 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 freque*x/ yjid6 as-,)chbnzlc)e,ency of standing waves is 475 *lh b - 6,e)zj siyx)c/c,ednaHz, how far apart are two adjacent nodes?   m

  If two successive overtones of ay.pw r j.valwjc+6t5dy*a(8 q04cji e vibrating string are 280 Hz and 350 Hz, what is the frequency of the fp 5iq.ctw cy yw486+e*rj. 0d(j valjaundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The dista1 6uahwj)p ijpi q.0 zzta0)8jnce from the bridge to the support post is L a1j j00i6wau)t zipq pz).jh8 = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is5wxuka))f.lxolu vs 92wo( g1u6e +ve supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the s6ogu52 u1+lwv 9.e(o )af vexl)uxwsk tring be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is mrz* *w -w1w/v rncxh+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 cwwrr -h cz *+1mv*xwn/orrect the frequency? decreased by    %

  One end of a horizontal s,5c yuv 8aqbimstxc .y8f33/string is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit length is /ivq8csx8. amb, tcf3y35y us $3.9 \times10^{ -4}$ 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 otsb;-xt 9x)+v5; /ixgaqe u dhf the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns ma gq+9b-x5 ae)ut/itxhs; ;vdxy be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the wfv+bmwkzf9 /3ater back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaininfmb/kw3f v+z 9g relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave trau6z(7i1u lqj.p5bigbveling at k.0 km/s strikes a boundary within the Earth between two kin 6i(iub p1bu5 gz7.jqlds of material. 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 ch6;)1 ekecg h,td aoud-anges from 2.8 m/s to 2.16edc u1tko- e;d),g ah 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 travelqhhkng7bf5s(h.1rx)z (on3f *pr /w ring in warm air when it hits a layer of cold, dense air. If the sound wa/z(nhr phb wk ox1 5h.3r7f rnq*(fs)gve 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 earthquake wave strikes a boundary between two types of ro 6i+e)4ch8aa pw*z ggqck at a q8 6 awgpezgc+)*h a4i38 $^{\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 diam ri.uo eah3n.2eter. According to the user’s manual, the dish has to be pointed in the direction of the satelliiou3 2an.e h.rte, 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 velo-n94-vpcpj 3 enyd 0cbcity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approxima -cj4nyd9vn0pbpc -3etely how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a sp l x659w 80,lb.a onw1 ;amfcjhoapz)kring 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 (approximately 5k,l.)x89 lzah m5w bap61aoj;o n0fcw mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to gd(z)n q +jpe,a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spring, npq,g( d+)je zand
(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. The mas 0cj,5fle gd1is then fag1fd ,lceij0 5lls 33 cm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a spmk*v4x(zdk t0 eed of 22 m/s (Fig. 11–54), compressing xtvkkz4 m0*d( the spring 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) m q98g/bu f6.q u+gzpfat just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill ofguqqm /8pg6fz9 .ub+ ver the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a cerwf16n/iq tm+ atain groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of th + twi61qfman/e sound emitted?    Hz

  A 2.00-kg mass vibrate89z6,ek1 buuix ekaa5 g*x s7fs according to the equation x=0.650cos7.40t where x is in meters and t in seconds. Determikag6b u*ee189ufx skx,7 5a zine
(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 h sn mm;vut7b(g.lk/p;e -3hhf. What is its frequency if it accelerates at 0. hkvutnh3p.;glh-;msbm(7 /e50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft flouuxm *q(t.a )kats on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he stepq (.um*axkt)u s 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 lll ,j5/f:(8 r xo.s6m pzzrzyto play at 392 Hz (G) and 440 Hz ( 5(xlzz,6f:rplm8rso.ljz/ yA).
(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. 11gn1y z 4m/vqe4 *ac+xf–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 razx/nf4gav1* q ycm+e4tio 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 freqspq4murrb 3)t01n u*4ix+ pejuency of 264 Hz, and the tip of each prong moves 1.8 mm to4rp1 jqtxn imr4+p0 us*e3 )ub either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic mro01 (oau;d)ag fg ra0oxg4nne9qm 50 otion 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 placed there (Fig. 11–56) will not lose conta0;9ua(o xga)mgnq r1fgo0e a0d5r 4noct with the board during the oscillation?

A string can have a “freehf46 qxoo; j2dtvh /1c” end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57).d o2vo;h xt4 q1/jh6fc Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swin.szl 4fvrf3yvn+j o 06g takes 1.000 3foyn0j f +zr.v4svl6s.
(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 direction o+r4aob k/vojs9qhlri +,;v+ vr can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillationvo/lr+r9vob ++hsk avqij ,;4s 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 12-: ,l alqio1yh ,/uch7mjc)aw3 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the oppo,wl qyc)/ h1 a,7 lc:ohm-juaisite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring c .bo+)bwf n ow3r;g.owith spring stiffness constant k. A penny of mass m is placed on top of the block. What i+fn.r bo3;.cw gw)oobs 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 jucyj1i *9(1wrdan ,uognkyard. The steel crane cable is 22 m long and has a diameter of 6.4,inojaw 1gur 9cy* (d1 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Figq1vw/v j+typqjwb4m :y+u,n.. 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. In analogy to a m+yy,q:nvvwu m jwj41 / t.+pbqass 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