Give some examples of everydayl9ddb**+4 nq:yrv q6ou k r7xh vibrating objects. Which exhibit SHM, at least appro dlhx*b49r*r n+ 6uqvqo 7dky:ximately?

Is the acceleration of a simple harmonic oscillator ever zerog2u z. hal;sy67 5dti (gidd3d? If so, where?

Explain why the motion of a pz4kvf;ro) ry+ iston in an automobile engine is approximately simple harmonicrfr+ 4o yv;z)k.

Real springs have mass. Will the true period and frequency be larger orb1 z8vtw6ax wnq (2m3v smaller than giveawvnm wq61x2 tvz(8b 3n by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the mala(z pq:mmm4.-td o3.oj t4a sximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook om: yfwfs y4;7wf a vertical spring scale, and then is released. Describe the scale wf;s4:fm7yyw reading as a function of time.

If a pendulum clock is accurate at sea level, will it gaa0jdn jz dy* vlz;u5zv4.xf86in or lose time when taken to high altitudejdlf vzz0.z;n46x5j8u ay* dv? Why?

A tire swing hanging from a branch reac kafpf8m,ln ps,fi*49hes nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwatch?,9f f8 4ak*pnlsifpm,

Why can you make water slosh back and forth in a pan only if you shakeershi29 rz*8jz7a k;b rkgmnc80j,r 3 the pan at a certain fr2z9 rr*iej;b8,hgackmkn s30zrj 78requency?

Give several everyday examples ottiy8 fwwq6q 7ibz 1l*4+ nh8wu3 +ibkf resonance.

Is a rattle in a car ever a resonaay tjss)i9rxd( fqkr8 u6;;g 6nce phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its sourcemfj 2aq 6l5prs2vhu 1;? Wh rm12q vfhu; jlsp26a5y or why not?

Explain the difference between the sj c*s.,-jf i 1buj1emtpeed of a transverse wave traveling down a cori* c., 11tefjmubsjj -d and the speed of a tiny piece of the cord.

Why do the strings used for the lo6:q8g :fco7gjqo90 (kpyq odtwest-frequency notes on a piano normally have oct qogy:d6(q07fkg 9pqj 8o:wire wrapped around them?

What kind of waves do you think will travel down a horizontal metal rod if you i.e,6+pj0poc tyz+vlg:yv/f strike its end (a) vertically from above and (b) hyj+.,0:/vcplt y6v+ezif goporizontally parallel to its length?

Since the density of air decreases with an increase in temperat,empg,ecr4 u1hno/6 b ure, but the bulk modulus B is nearly ing m,4/n, chrebope6u1dependent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why crns;cf43xsfyo2 zgj 8i wf4p /fr38z:ircular water waves decrease in amplitude as they travel away from the sourcew;/z38fxpso 84rfffsync2z :jgr3 i4.

Two linear waves have the same amplitudp* m0.0h zbghoe and speed, and otherwise are identical, except one has half the wavelength of the other. Which trmghbop0.z0 *h ansmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord at8 mso ;ci6ipjk;4et9)mv h1fs in Fig. 11–3ip19 kv6 hct4t s)om;ij m;8fe3, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrat wd8 tuykeb9sen- k3:1y;tkz-ing in three segments, are there any places you could touch it with a knife blade without dist31 bewu se ky nyz;kd:k-8t-9turbing the motion?

When a standing wave exists on a string, the vibrations of innj (m0ey9k5ej mid ;nkz 4+:eocident and reflected waves cancel at the nodes. Does this mean that ener(kmdjj9y i+zon eme4 50: ;enkgy was destroyed? Explain.

If we knew that energy was being transmitted from one place to agqx0 b*k t0/( hi:mmrwnother, how might we determine whether the energy wasiwbq/0t (g0kh *rmm :x being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total d2bvk axm p1; :rtl,vcdxrb7yhj. 3o 97istance it tr m13,c k2r.vjoh vd9ba ;xypr7x:l7tbavels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 c9fn(ydk/ fs zm l(1t28mb8 zvN hangs from it but is 85 cm long when a weight of 180 N hangs from iy 8 dc/fbklf(t(9 zmzv2n81sm t. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm wh t lgbf4:w1o5g4gek.c en its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the gt4geo4.gw1b:f k lc5frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs sd2/(ql p pkv8x7vzny- h) d7pfrom it. (a) What k v s(27zd vp8 xqhdpl-7n/yp)is 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 fr, omczmsojh/ 6(3i+-qhw2kq e12 rzmpequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency o,s qprk3 zwhmqc+j2eh( m/z2io61 m-if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x 82y1ild7xvz v of the mass in Fig. 11–2 at times t = vilydvz 7x1820,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrates prbegf3:r0k0ky.uz .; cc ncx 9kedominately with a frequency of 4.0r:xc ;kf.9.c zbu3e0nc 0kgky 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 t,fsybyriet8o6-/-xp x r- 5ap sr-n)additional 680--),8ibte-oxns pstyrarr p6x-/f-5y g 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 timesjbpc .hr afd3z7+( * ipdm(/nw per second with an ampld m3fdn*p+rhaw i7bp/j.zc ( (itude of 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO ha9p0kiq7ht(k bm wl++ k;)u ezglf the maximum valueh7 ( w0qikl9u;+tbekkz gp+)m?$\approx$    A

A mass attached to the end of aqa fx. a*otoc.d ;7c;n*.cf zu spring is stretched 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 0.315 m. If the spring is sjng45h i(k/(ncp( y mitretched an additional 0.130 m and released, how long does kinhmg((j/c5 4 yip(nit take to reach the (new) equilibrium position again?    s

  An object with mass 3+5hg1 n r;t f+u;o.4udi bfzck.0 kg is attached to a spring with spring stiffness constant k = 280 N/m and i+g. r;;hc4futno1 id+kb5z ufs executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the sprlb)-b oq,espg q * lg,lu5t)r+ing of a toy popgun 0.200 m to “load” a 0.5gllo)p+ rbq)eq*s,b ,tlug- 180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizobsnnpb; ss6 ,e 3os-u8ntal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spri b 6ps -3ssnobnus,e;8ng 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 hs pwql 6i64 j;si*az,= 0.45cos6.4t where x is in meters and t is in seconds. Det6pis a; ijqs4h*, z6wlermine
(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 o , i9e5)tb c kl2um.wx2av1axof a SHO half KE and half PE?u2ivweo1km)5 92x aa, tc.blx ±    A

  If one vibration has 7.0 times the energy of a second, but their 70-c(s lgw4 n gg;in(nsqsf5t2qvn e )frequencies and masses are the same, n i0-qlnc(5t n4(ng)g 2sfvs w;geq7swhat is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vwe, 4j 15aqh8a.tiybz 54/h, twpvaluertically hanging light spring once every 0.6l.a5hz/1i,8 ,vab4wua w e5 yqj4 hptt5 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is suppor; qx mj-z1ppl9ted by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49).q;p19xmjlp -z What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is i ps.k4*x64 a lfw0 ha-:yztpymn meters and t is in secok aya4 x-y .s4tml6:whpf 0*zpnds. 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. For each, what is yvi;empm6 27m
(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 = )5yu9 30zm+cc8j/t zk fsct rd124 N/m) is struck 8sjr/3t0) d+ mkzcyu9zt5c fc 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 stiffny0pu .x)7vdo b2fahs,ess constant 305 N/m vibrates with an amplitude of 28.0 cm7. ,aovbdx0u)p2hys f when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two spri0 wlux .sc1byy9: tye(ngs, 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 ak*epv0,)ufj ;st nokh.9 ma 4ettached to a fixed horizontal spring whose spring stiffness constanv he 9s*)nj0,ke.tuf4kmpa; ot 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 vq,c )) wmrdl*u lq );jkpdi+7jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hittingiq)mvpwdkd q 7;)),+*jull rc 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 6 6)6 lvwj6j 4lo ttcepzs1+n7e0 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum ,kpw46cmcgd6yz c.l d)c + :efvuvl60 be if it is to make exactly one swing per second? (That is, one complete vibration tak. z, uw:dc)gvd0f c+6v ll64emckpy6ces exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its periodtd; x7 rtp3c k2tyg 9fmj35dq) on Mars, where the acceleration of gravity is about 0.37 that on Earthd25;ytc 3 fkjq tgp7rt9m) d3x?    s

  What is the period of a simple pendulum 80gw-nidof+kdcsx6;of;z p / xu wxq.4 b 3:,0ib cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple penldme)z1y+mthdm08b , 1l rt.xdulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is reem)hd0y t1mr1lb+l, d8zx.t mleased 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 se)0m)g*lg ug5vv ;dp’s pendulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shortened u gdv)pgs* 05g e);mvlby    mm.

Derive a formula for the maximum 8thzu /4j*w wztga) /lspeed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is relet 3b:, ,z/rzaq0 v(a k00kvcxnu4ztsxased from rest starting at an angle of 15 c/n t r400t,3z(x kvaqb,:aus0xkv zz$^{\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 evb t4/x(0 avdpvery 3.0 s. He measures the distance between two crests to be 6.5/ bpx0v4 dt(av m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a s jcsy,1+sj0fi peed of 343 m/s How fjc+s1i0 jyfs, ar apart are the wave crests (compressions)?    m

  (a) AM radio signals z0-+waz; nrbsx l:js*have frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with asa0-s b zw;lxr:*jn+z 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 h7 7)7fmh cop(j7ngnr of longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as the o4 xk /oty9*nc4m g6lixther. In which rod will the speed of longitudinal wave/yl*tm9ngkix46 4 x ocs be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the mlq5zz-ba +o5d3 c:watension in the cord i w+5 mc3:lqaazz-d b5os 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 of lhh;, ,pp orimt.mh95w5 (u1e azev* dvength 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse mr,5hh5p9.( eehpudm i*z;1ow vav, t 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 beob2r gi)-2g z0 u.z -ykrhmo;glow the surface of the sea. He hears the eczo)rz.r hiym2gg o0- u-b2g;k ho 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 thi32b.bd9of le rs difference helps in locating the earthquake “epicenter” (whe b 9odb2.3lfrere 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 cp42 ymrutw.3fan be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actuallum324t w.pf ryy 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 amplitudeswfk e .,2)tz2lc*7rhdrpw d -c, of an earthquake P wave passing through the Earth and detected at tw-w *f)r h2wd lz.k7cpt,rec 2do points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to be 2vt*6;qceut5 v0unlr25cuql 0v * tn;ve6urt$ 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 thrp1jahgt dzx99wrst9)l) r0* yough the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudz0sw)9h*rp lr91jxdy g9)ttaes of the two waves?   

  Two waves traveling along a stretched string have th cb (hhw;n94oce same frequency, but one transp ob9hcwc4(;h norts three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move ( t:42+unsfo. xcfbtu up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE cf2o+tbutx :n4f.(csu hange?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch tmcm38 xf *-vwbjj(h3w 7 o0ktthe 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, th0-t8fmwmbjk 7wj( c*h v3t 3oxe string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as itsd:5 jc7uer wa; fundamental frequency, what are the frequencies of the first w;ar5d7 c:ju efour harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfinyuwi,i+-u)t k gered. At what frequency will it vibrate if it is fingered one-third -wiu,u+t)ki y of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of t3 ,,op6o cqwij7 jf0q*w,yec280 Hz. Name at least three other frequencies at which it will resonatoc tp,*qeqo3,7fy j 6,cjww0ie. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of s/dqs9fy/z:qp3g r v (u:xem0standing waves is 475 Hz, how far apart are two adjacent :/ su:yrp( zems9g 3/vqx0dfqnodes?   m

  If two successive overtones ofnd jpl fk4j**: acg)q/ a vibrating string are 280 Hz and 350 Hz, what is th *j:/pkjnlq)gd*fa4c e frequency of the fundamental?    Hz

  A guitar string is 90 cm long and haf,cdc(6txwy ; q 2ii3ps a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is uc,tq ;y 3pfw2( cixi6dnder a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed tnj35)dj: fudp o vibrate at 200 Hz, but it is measured to vibdju3n5d):fp j rate 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 supposed to vibrate l85 n+u icaso,t* hu/xdb.qc4at 200 Hz, but it is measured to vibrate at 205 Hzuan +/tc 48clhi xbdq *,5uso.. By what percent 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 ab.*mj-+ d5yuxi2a x nmechanical 60-Hz vibrator. The string’s mass per unit j2 yx a.-+i*xudnm5a blength 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 adj ;p+lnp4v;w55;0fqolrszyg f3 m a,q ousted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieve0;5l 5 p ypq;wngf ram+3o,o sz;4flvqd by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequency,7lkk;r1 mg sz4 the water alternately rises and falls at each eskm1kg rl7 z4;nd, 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. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strike,zy0 ch6u.n/ f6 ob1,lfyyjgvs a boundary within the Earth between two kinds of material. If it approaches the boundary at an iof yvyf6uh,y 1 jz0l.c/n6bg ,ncident 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 4k/ smvj4h( o+rerl mno txg((o ;d(x6underwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests ro;hodx r+t( x( (mkv4s(6/gjleo4nm make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer qan py g80+ycal 4.*fbof cold, dense air. If the sound wave hits t 8b0y n*q+4g.lfapacy he 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 boundaryrw*s8486w-lrsqmd ch27nc7x ;sgwwp between two types of rock at a 38 7rqm p4ds6c8n s sw7g cl;ww r*-x8w2h$^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According 8*qyds*oqwm* hzkn -*4d fihwb6f/4qto the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of about di yobh4z*4w/*h* d qf sw*6q kq-f8mn2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 w-xi2fx ce81 zl (inul+w7yv*jr37cm km and velocity 750 km/h travels across the Pacific Ocean. As it appr+culr*l2138 mi7xf yxz nwie(-c7wvjoaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing carutzqj+cl*us64zoq fk2zg4 1 + bumper has a spring stiffness constant of 550 kN/m Find kl4*+ zsquju o4 z+tg2 6qzc1fthe 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 energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, whibkdd.svsz +(a+av(6hpd a6 u3r(lydp a3 uc4 6ch stretches the net 1.1 m. Assume that the net behaves like dppa(z b(. +r6uu(ad34skydvsda6+hl 3 6 v caa 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 2cf0 auv ewv8-gb45hx on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillation?xcgewv40u -8f2bh5av    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 8;mmi z xs /xs6we1a*kku.vk)11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant ofs 6.vakmkk1 e xm;wuix* /zs)8 the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the r26j 6dn-mm97y tdu as8lbz t4dight pace of about 1 steplnm9 zb28-dt u64datms6 yj 7d per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain ge/ o,,lb bjvlt ,j7nhe :fma*3roove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.73v mjb/7,nl:t,fbelo,hae*j 0 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7qf3l)6dz nwn 7.40t where x is in meters and t in seconds. Deterd 63nw7 qlznf)mine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency i63isg -z ktiqoqv dm9 c5h7:v2f it acceleratmzt:73hsi9g2 6 i-q oq vdckv5es at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, it out+t g(: r8adsinks 4.0 cm deeper into the wate ut+:t(o 8rdagr. 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 instrumentng8w1,b zhncd. e+ *qifb6)ml are tuned to play at 392 Hz (G) and 440 Hz (A). zw.clnm 6bqg+h 8ei)d,b*n f1
(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 travegmm hdq; 0of)7ling down the stretched two-part cord of Fig. 11–33. Determine a formula (fhmqod7 0g );ma) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the 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 li 6 nxzi1w qkpajv66r4rg5p s:. h6y)prong moves 1.8 mm to eit p4wx nlk6a6: rgqz. 15yr6ivhjps)6iher side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frerb(0rr sw y0oj *t3gh0quency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board du0wjhyrt r o( 300s*rbgring the oscillation?

A string can have a “free” end if that end is attached to f qw(l*+szz1m5xu b+/5pplbn a ring that can slide without friction1 +sxz5lp b+m/ plzb5*ufw( qn on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way r/yzr2j enjpbx4xn9,n sg3(8swing takes 1.000 s. bgx,ynj j/3pxr8nr2(sn4z9 e
(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 intqlew,c ) g-xfv;u sobnw1 01xrc/e. 1 the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, thv)1 xw-r/t1.l ;bfeqco 1usne 0 wx,cge 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 12zb y ura8yl r./)8h1bm3 g is stretched under a tension of 255 N. A pulse is ge)8m lr a.hrbzyyb/81 unerated 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 by a spring with spring stltno0*1r 3c itiffness constant k. A penny of mass m is placed on top otc1r*3il to0n f 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 8bn+ar6 5okl5f tm2b:z:xg3) f 9yb v)hyajjqjunkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cgb5 aqh ta2 9bj:k ovj+y:6 x3)fz8bmf l5n)yrable. 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 (whichywaa 68w57 ovl also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jella w yo685vlaw7o springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz