Give some examples of everyday vibrating objo0roy z-)zgyrh:v3vvz , tn3(ects. Which exhibit SHM, at least approximatelvv0(3t,ynrvh o ) 3zzgzy-or:y?

Is the acceleration of a simple harmonic oscillator evj;z, bmzrha.:er zero? If so, where?

Explain why the motion of a piston in an automobile engi j0x qku36og9qj+/lditld f f g-,i.2lne is approximately simple .tg /3 29lf0l qoq6fjk, dgldj+uxii-harmonic.

Real springs have mass. Wil8 7 *:fn5hlu3e n7e cyvb9lnjjl the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Explal jj ny977feeh*n:v8b35ncluin.

How could you double the maximum speed of a simple harmonic oscillator (SHO)? ;px 4)1mfuzvs) asmgo4zvbbvam( paq8s;:1:

A 5.0-kg trout is attached to the hook of a vertical(m , mlmudk /ureaik6;8*mdt2 spring scale, and then is released. Describe the scale reading as a function of tilmmt /ddu;i82e 6,u (kma rmk*me.

If a pendulum clock is accurate at sea level, will it gav8ybbgh4d/j v ;1u7uxcbti09in or lose time when taken to high alt;tvyh8jbd b1cu 4bv i9 0gxu7/itude? Why?

A tire swing hanging from 3utl/-/pwi m(bpbzl3a branch reaches nearly to the ground (Fig. 11–48). How couldi-wlu t z3 b/p(l3/pbm you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan oa e yqkyxr4y r7)5+p;r6sawnhq+/n actt78 7knly if you shake the pan at a certain frequencqe y7;rh kac4n7typ7rn5ws)k tr 8x q+6ay/a+ y?

Give several everyday examples of reffe.85pkz-*9w ,qwyd 0iggkj sonance.

Is a rattle in a car ever a resonance phenomenon? Exk+ (:jd5 hvriwh*0qrx plain.

Is the frequency of a simple periodic wave equal to the frezb *zyy76img6 quency of its source? Why or why not?im 6zg67yy* zb

Explain the difference between the speed of a trf f0i)m; f)jvbansverse wave traveling down a cord and the speed of a tiny piece of theij mvfb0)ff) ; cord.

Why do the strings used for the lowest-frequency notezay2b jcd:n/ 3s on a piano normally have wire wr d2y :znj/ac3bapped around them?

What kind of waves do youw3ut3 + jyirc/ think will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its yitc3j wru3+/ length?

Since the density of air decreases with an increase i4 toip ; r6 z1yc m+;pmyovumi:o.n9z9n temperature, but the bulk modulus B zvu:o +p941zy6m.cm iyoo; tnr;i p m9is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude av7+suimhxmou9ny:s4. ax6j y6gv -c+s they travel away from the source.sxvgs6u+ m .n-+6ajy:xyo9c4 iv7uhm

Two linear waves have the same amplitude and speed, and otherwise are 4k )dg ey *3/zkqit)/eho.m,0j kxhblraf8k )identical, excepdt z e34)/8mriqg,o) ebkkyh.x k /jf0 *ka)lht one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave 6 sr+ h(r kzb(3tlwugki5) 4x4r v4jofcrosses the boundary between two sections of cord as in Fig. 11–33, the frequency d gokwk3bht44rzx4u r)lj6i(fr vs(+ 5oes not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in thr2(1n bcnvzt7p ee segments, are there any places you could touch it with a knife blade without disturbing the motion2nc7v (1ntb zp?

When a standing wave exists on a string, the vibrations of incident and reflecvuk 0yvnezlk )i-br7q70ih2- 6t cfg;tef0-kt bg e7-0i6 2uqckzlhvyv7;) nrid waves cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one pl 6wry9tovfmm 3; 1fyz )eq3i1race to another, how might we determine whether the energy was being carried by particles (materia 3wyt rfi;z 13)1qrfeym 6vo9ml bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total wr7sf;c w+p o;distance it travels inc ;;7prw wsf+o one period?    m

  An elastic cord is 65 cm long when a weight of 75 i u bw-ii5s3r2N hangs from it but is 85 cm long when a weight of 180 N hangs froii2-b i 53rwsum it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg (ua ozvq:q yjth3wl0 p (,-zaoa5m 7d3car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goq 35:a-oz(7qu azlov0ahw,( jydpt m3es over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7 mm5jn/ olz(i7-kg fish hangs from it. (a) What is the spring stiffnes mm/z(i7jlo5n s 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 frc. 4ep.yv8qic nnu10i equency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from e0ipn .4u18 .qinvycc it?    Hz

Construct a Table indicating the position x of the mass ilxx -ll ,uvzji*1 (xi,n Fig. 11–2 at times t = 0,t = i(*xlxl zvj,xi1l- u, $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 predomij9mdxswh.a :8wc2t 1inately with a frequency of 4.0 Hz. 1xsdw2h :i.t j9c 8wam
(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 frequencytgd93 a xim +)yy)6acsf2o /nh of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value saxya 6)g3ftd+ 9i )ho/nmy2cof m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per se o8/zd8 3avhoacond with an amplitude of 0.13 m.za /o8d8vo h3a Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half the maxli/w te66b9m9q5i t fryv 0w*nimum valuevf*tw69 6/mii9 bn5qty0r wel?$\approx$    A

A mass attached to the end of a spring is stb9- wx(l)ezhg retched 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. Ifz/ )rl/so z2gwfo35 cnolx9 v,pf5mz9 the spring is stretched an additional 0.130 m and rele 9zxo)3f vmzol/pn,c 5orf5gl ws/29z ased, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness const .bvl/xg k1.kcant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 vk 1x/blck..g 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(t:1vvplz jcbcu8o.g. d3 , ge compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gublc.1o3dgtgc( pjv8,z:e. uv n?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end of at*t n( ewzn1g3 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 frt wnn3(t*gez 1om rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t :.wtr /yxjk 5dwhere x is in meters and t is in seconds./ j5 tyrw.:dkx 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(7va-m a p*x7c+a awp3cq*khn a SHO half KE and half PE? ± (a*a3*c-kc pa qv nwh +7x7pma   A

  If one vibration has 7.0ft a 7f/p,fq0w times the energy of a second, but their frequencies and masses are the same, what is the ratio of their w fpf/f,t07qa amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light wf24g3 xyi2k)a-d fm pspring once every 0fpkf) wy43d i22m gax-.65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs, each h7 mosxu,6vw 2with spring stiffness constant k (Fig. 11–ouwmx v7 6h,s249). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t why+3k npi. aw:fere x is in meters and t is in secondsp .wfny:k+ia3. 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 iso hkgodmy49y4-d4rxq-m s+p -
(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 on1 7apnxy ze,3o the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed pozn 7 3xe,y1aof 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 305f.o.k 4-qm5.rfpnz,o qdd vz 5 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The vmo.zr.k,q odfzpfnd4 55-q. 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,k-k2pz+ 7hmdu- av+bn 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 horizontal sp ieuz6 h6bqmftv h(224l9ncn;ring whose spring stt6 (vluh9e ;n2hqbimc n6fz24iffness 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 fryk k2x2 j)tx7or clx a(css007om 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 stiffness constant and the unstrekr0oj 7 t sxca(2sc)k70l2xy xtched 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, zmw+y*; mhlp-rwi1 fkcd5p4 in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one23u 7tnseae/v swing per second? (That ivtn2/3s7uee a s, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What ik acu /im33vv7s its period on Mars, where the acceleration of gravity is about 0.37 thavkmc iva7u 33/t on Earth?    s

  What is the period of a simple pendulum ip ume8r,( km/80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a massbi89zuag k/8 v of 365 grams, ag889 ui vk/zband it is released 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 clnmae3o e+k 2h/ock loses half a minute per day, how should you adjust the length of the pendulum? shorte+/eak h3e2 nomned by    mm.

Derive a formula for the maximum ssf2y0lj;9/ -fslg ho3i9oal qpeed $v_{max}$ 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 frequencwm*l,vl; qw48qdr h yzb; ):zty of 2.5 Hz. At it is released from rest starting at ;8;wb m)qwvqdy,:hlrtzz 4*lan 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 txrb auyx5t+s1 l)8y6k he bow of his anchored boat every 3.0 s. He meauk6 1yx l +8ytas5b)rxsures 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 frequencmn-d ) 28zfdmbi:eadvdy u h-6ltx r-8 f+bb8:y of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compressioel8 hinmdfbfuyba-v:r:m 2b d8x 6d8t z-d+-)ns)?    m

  (a) AM radio signals have frequencies between 550 kHhui3 +6i ar d1z1gvb(uz and 1600 kHz (kilohertz) and travel with a speed1(zv3ai r ug bh1+u6di 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 longitud x)gj.6c m1iheinal 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 d/q,rxkkff 3.nyeu72 the other. In which rod will the sfr,qnxf 7 ud3k. ek2/ypeed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg -b 3 t0tp/jsisdnn bg2fhsveb ,( ,b.6is stretched between two supports 28 m apart. If the tension in the cord is 150 N, how lp stgi h(etf .nv /dbs,,b-j sb306nb2ong will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected lrgld.vjv gz -2xr+,jsbahl 04x0 9.o to the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable.hl.rarl2l9-dg 4zj00 .vgxs,jbox v+ 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 jiu-bjcdi8hp,o +go/f p msn n0 gz.-8.ust below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s la n/ -mzn.d-hsugpci poi+ o8 g0jbf8.,ter. How deep is the ocean at this point?    m

  P and S waves from an earthquak)i5 kqmd6 w)q:ep96mrcsd wz1e travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbancer1zq kp)ds5q:m ic6e9w6w)m d 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 trapaypaw9+xoz,vvy a1l.p 16 l)nsverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture ofz la,va19.vpp1ox )p lwa6y y+ 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 y sea2p5nofj s( ):i4b(b) the amplitudes, of an earthquake P wave passinj) 2:f(sn 4 ayspb5eiog through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthq6dr/0 h usiy2iuake wave passing through the Earth is measured to be yi s0ui26r/ dh$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same portion5zsspg1vt/zu/(z ea;o9yu 7z of the Earth, but one is carrying twice the energy.ezy7 stz/u; ( p/vua51os9 gzz What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched sj-h w+his7,vs))ot gwtring have the same frequency, but one transports tow,)-7 g+swhsi h v)jthree 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 utt+j eb+qm8lo(c2ctre 5:o m2p and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples e+(m bor2 qmtec+ot5l:tjc82 decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are mov l6-no ypq-m26ysleah 24 ahy,ing toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to ash2h--p2nylmqay4 o6l e 6,ythe energy at this moment?

  If a violin string vibrates at 440 vcqs 0 aazfq *jl,ima69h d*:*Hz as its fundamental frequency, what are the frequencies of the fi*vf0l,daa6j i*qaqm* :zh s9crst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz 5z 3, 4vy gm71dw0b v6uq gfk:.cojuhawhen unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing63cu7w. gf4 yo :dvv,51q 0jgub amhzk wave.)    Hz

  A particular string resonates in four long.88 s+dt (j isg8rcqops at a frequency of 280 Hz. Name at least three other frequencies at wh g +j8n8s(c.gsdit r8qich it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves onynu( u(7lo16huj ;ock a string is 92m/s If the frequency of standing waves is 475 Hz,(nk uou1y( c;j hl7u6o how far apart are two adjacent nodes?   m

  If two successive overtones of yfv ,poq:*1y+l /ksyj a vibrating string are 280 Hz and 350 Hz, what is the frequency of the f*v s: yop +j/1fyk,qlyundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The dist*cl *yfj qp7)rsjaifd 454:nnance from the bridge to the support post is L = 62cm and tf qjfps dirc)y n 47j*5:a4*nlhe string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vm (nrr4tg -vkcc ju(3/ibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the strgc- c/4jk3r (vmt n(uring be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is meas s2rjb 0gd5oja9u5 g; )jzta.eured to vibr0ab9uj)5rjago d2est 5;g.j z ate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal str uorpinw3:2*o ssn+0s;bw *o ling is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s isnp+20;sw*:n *oo 3wslurbomass 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 adjusted by moving the pulley.a7iclt k1pu .0vzf*/.jde 8gv If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varyingtv l701 ckudze/ifg8..v a*jp L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just th8dzq)j -hs rs0e right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wavsd8- rqj sh)z0e?    m/s

  An earthquake P wave traveling at k.0 km/s strikes1or 6gxlwmwjc 3 0/bq( a boundary within the Earth b/b06g mo rxwwqlj31(c etween two kinds 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 chaw /qt;hvbcxr(vvm* )- nges from 2.8 m/s to 2.1 m/s If the incident wave crestqvv*x cb-(v tw;)/rmh s 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 of cold, d.0 d6s j5qmuqmo5f;vx)zr u2kense air. If the sound wave hits the cold air intr 0mq5v)s;kjx.2qf muod z6u5 erface 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 typ,ul3; dnztb; yes of rock at a 38nu;dzly ,tb3 ; $^{\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 atsmvic)m l*r am wf25s11h+0zbout 0.5 m in diameter. According to the user’s manual, the dish has tost1*al)m+ sfvh 0z1i5 mwc2rm be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 25/:tlcuaxdud 8;7 ;/;7 djubr ac jmo6c0 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately h7xduca ct;aco ulrj/b7m d8u:/; j;d6 ow 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 spring sti55e , znruma3rffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1eu5az5 rr3n m,500 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, which stretchesgbx oav4n86 m+ the net 1.1 m. Assume that the ne4 6a8mno+bgvxt 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 sb8-v5qy hjf2h b0 )i bna(n,cvpring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of thhj(a,nv5 n8 y fb02 vciq-)bhbe oscillation?    Hz

  A 950-kg car strikes a huge sprin4hoz ima.t/;i g at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the sprinaz; .4/iotmihg stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the righ;zn.p a/ dgkvjd563klt pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the 5kak zl npg/dv 63dj.;coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 3c.p1hg24jv r f3-rpm phonograph record have a wavelength of 1.70 mm. What wilgj24r 1vch.pfl be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t whx*ppj6trq)t8c4 z0or .axaw1,x /pdd ere x is in meters and t in seconds. Determo8 4papx atx/ pr 6)1rd0zwxd.,*c qtjine
(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 f+cot,-qkwzsbm:. fy 2*9ylsp requency f. What is its frequency if it accelerates at 0.50g (a) upward, : -,ykby2*toq zs+m9.l cw fps    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75)z e .crs 8qwsm+gor+y3d7oh5 -kg man stands on the raft, it sinks 4.0 cm deeper into the water. When g z3deo+yr 5srochm+w.s 7)8qhe steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tun1 d7m2zmcba0 fed to play at 392 Hz (G) and 440 Hz (m fzmd7c1 2b0aA).
(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 stret* wz *k74bfjxgched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is thfxw*z*7 g 4bjke wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz,p sotm+c; 5mis ,4xd y5mzz-/s and the tip of each prong moves 1.8 mm to either side of centp+5 5 izt d-/czyxmmo4s s;m,ser. 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 motifxreq4mz 97h ,on of frequency 1.5 cycles per second. What is the maxirx,9 q hf7mez4mum 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 during the oscillation?

A string can have a “free” end if that end is attached to a ring that can sliw g (3 qobnsr19y93xjfsy l+*dde without friction on a vertical pole (Fig. 11–57). Determine the wavelengt bd y o9srqs+f3l91y3*w (jngxhs of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulumk 5kr-ggo29bs :nfb.a has a period of exactly 2.000 s — each one-way swing takes 1.000okn2:sf.g rak g- b5b9 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring cankz es.ml0s f-9 oscillate in the vertical direction or can swing as a pendulum of small amplitude, but 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 whate.z9 f-s0km sl 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 stretc9+3 gr/xx0s vkbp+gqaz:v, bched 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 oppzcga q,: 3rp0sx+ b/vvxb+k9g osite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stiffnesobtwvnr*ggp 8 )07 o-as constant k. A 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 th8o 0bv- ort awg*gn7)pe block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the nxmzundzs2;f 6i(* i2 junkyard. 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 cable. What is the period of the bouncing? [Hint: Refer *ns nd( 2ifi;2mzz6xuto Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which asc/u ki23bn r1lso gives the dimensions of the block). You push it sideways as shown, and then you let go. The jellrbs n2ku/13i co 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