Give some examples of everyday vibrating objects. Which exhibi y *:v;scox-vqc8zij 5 e;o2vat SHM, at least appjv5c -ez; yx2acq;siov: * vo8roximately?

Is the acceleration of a simple harmonic,./z*gzcomkl;qg :zpf 2i:umox a3+ o oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximatelx cy5x+uepuos /x47+wy simple c+es uyoxux 7+45 xwp/harmonic.

Real springs have mass. Will the true per*hxiincfre/u.n0 ls664 ,woo iod and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized miwoiu* rc6en. of4s,6l0 x /hnassless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillatoay+kq+bee jbi c.+q8boof8a -q z8e7 9r (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scad5lq 9bgod,2wb;w (yole, and then is released. Describe the scale rea5(9wo,b; g w2 loybqddding as a function of time.

If a pendulum clock is accurate at sea level,,z v0mcvn.a,c will it gain or lose time when taken accn mv,zv0. ,to high altitude? Why?

A tire swing hanging from a branch re,,sh- bkdy xf+w 5y3yzaches nearly to the ground (Fig. 11–48). How could you esth wd +, -,ksyfx3b5zyyimate the height of the branch using only a stopwatch?

Why can you make water slosh bacd*0w5 8xcplredi-b :tk and forth in a pan only if you shake the pan at a certain fbtwx*: 85cred d0ipl-requency?

Give several everyday3.5(09iyltp3nsu fhp k 4d3vw pqwwm ) examples of resonance.

Is a rattle in a car ever a resonance phenomenon? Eoq-l- p ehq/4pxplain.

Is the frequency of a simple periodic wave equal to the frequency of itsv co5q g;on8j g7q)l7d source? Why) ;l7 do8vcnj7g o5qqg or why not?

Explain the difference betw euq*blj;mqa(;f +he5een the speed of a transverse wave traveling down a cord an;e um;abq j+hef(*q5 ld the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally 2nq lyohyv0km6eom3nps)gx5w 1q;,4 have wire wrapped arounow042,yo v )lq3q exm;n51npym gk6sh d them?

What kind of waves do you think will travel down k c 60jw0dt4u4sft4pqa horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally paralle4k6tupq0 44 jcft0wdsl to its length?

Since the density of air decreases with an incry0vuv*jz 3;h aease in temperature, but the bulk modulus B is nearly in0auvz;y h vj3*dependent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decreasek e+ f6+kxg6bw in amplitude as they travel away from the so +ebx w6+6kfgkurce.

Two linear waves have the same amplitude and speed, and fd9cxaez1 t; q8k7 uurk; 5lp/otherwise are identical, except onu7re;zpkx kct qa 1l/d59;8f ue has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary bet-er.je37.a ltda: ewzween two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Expw7 .:jzeerl.a e-da 3tlain why.

If a string is vibrating in three s2w3dl6h6w ppc *q0ggjegments, are there any places you could touch it with a knife bladd6lp*63w gj0wq c2 hgpe without disturbing the motion?

When a standing wave exists on a strfpsbcw8 8 lu5:ing, the vibrations of incident and reflected waves cancel at the nodes.8c8sb wfp u5:l Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one p7; +njwh va.zylace to another, how might we determine whether the energy was being carried by particles (matea w7y+.v zhj;nrial bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what isa9ag mpq((,(pjtnu t2 the total distance it travels in one permt j9((ug(aan tqpp,2iod?    m

  An elastic cord is 65 cm lon/o mthu i/m2i+g 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 “spring” consta/ 2+t mi/iomuhnt k of this elastic cord?    N/m

  The springs of a 1500-kg t6p)hz-v v+)-jnetim o*b3 w ccar compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump,z*m)t hoti v6)w-e- jnvcp3b+ what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangse(ta w: f5--mzgea87bmf( iy g from it. (a) What is5wmaem78ag i bzt-fg: fe-y(( 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 frequency of 3.0 ai4;c zblw)k47gi u7m Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs f4;i clbw4 m7zkiau) 7grom it?    Hz

Construct a Table indicez .2*d:ipfxcv:sx0 gating the position x of the mass in Fig. 11–2 at times t = 0,t =z x2psx : cg:iv0*def. $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 vibratesi1t 9b. -k+jgkf6b2nt/gglpjz 8+ m mb predominately with a fk8 lbtjfm.ggbp2bzi9gt n j 1-/+ km+6requency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring 4wke/ c;,udmc vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the kduc, m/ewc4 ;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 times per second:2:gz a:zenrj with an amplitudga:e:2nzj zr: e 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 equilibriu;ziwbo(wr cpjs vn,6 h360. tam is the speed of a SHO half the maximum valuv.sn0w3wj;h(ac6b pio r, tz 6e?$\approx$    A

A mass attached to the end of a spring is stretched a dis1ula z0 p;13n1dbhlm ftance $x_0$ 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 sprnk jermx-cs+ 6 zgh*2 ijr+:3ying is stretched an additio-+ygrne j3i2k:cs hzjxr+6*m nal 0.130 m and released, 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 sprh)m9e*cac n45 ptwft7x jsanb 40x.wogs 4o2 ;ing stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is ) hoaxna2cmw0oe7 pxsjf. n 9t c54tsg *wb;440.020 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 spring of a tot o+93 w.tpijey popgun 0.200 m to “load” a 0.180-ei tow j.3t+p9kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, fricli:6iearn4-l j:m 6zktionless 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 spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maxim6 i:ekrmz l:j -4ai6nlum 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 acroq p) drrlm21sp67e *cording to the equation x = 0.45cos6.4t where x is in meters andr 1mo*7rr2l deq)p ps6 t is in seconds. 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 6h:kwm5xdi5f; zdk:menergy of a SHO half KE and half PE?k; k5h6 5:xdmwfm:zid ±    A

  If one vibration has 7.0 times the energy o4s40t:-/dipvzw yoj:j o7q vof a second, but their frequencies and masses7sd 4 p0/owyz: v4v:jo-t ojiq are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertical b9p4vi(j9sh;q yjobvgsx;.5 ly hanging light spring once every 0.65 s(b;yjvi5h jbgs 9.q9xp4o; v 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 isit jw ij*4d3hw56dt9r supported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. j65hjd dtrtww439i *i 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to th95zulvpa ;ol:xb7pv6e equation x = 0.38sin6.5t where x is in meters and t is in s voluv6azlp b:p;57 9xeconds. 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 a3k09)6/jtvb8mcn:qlpdxa i j nd B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest onorw 8/g:yik4x )9qqyt the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determi8xg)9y qi ok/4r:wqyt ne
(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 wih s( q2g*w6yxeth spring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through x 2 s*yhqe(w6gthe 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 t bx9t(tlsa.fb(( 4usyao5*uwwo springs, 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 ynoyeh14l1 y:z( wu0s fixed horizontal spring whose spring stiffness constant is ez:nw1 s01ylho yy( 4u$ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high b d*xiws 0fwu9-ridge. After reaching his lowest point, he oscillates up and down, hitting a low point0d -fw9*wxsi u 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 6mcwgzg ( i8o;t3;cwkeygt2.. 0 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make emw( )n juhoht,6t cp5t8d)j(zxactly one swing per second? (That iwdzmut8c)) (ph 5,(t hj ojn6ts, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is itse yq:h;jaevuk*0y6 9 c period on Mars, where the acceleration of gravity e:vhj*ey9 0ca;qkuy 6is about 0.37 that on Earth?    s

  What is the period of a simple pendutxnidf 5s m *d*) 6f),7v3sjs8jrwvqxlum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendullr8o vg k cs*9cj:0zd z:m:n+zum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released m r8k0j: z9lzv+:n:sdgc c*o zat 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 th8u7:u xihhx5 0tdvavof /o/*be clock loses half5t ob/v0:h/xax8foi7d uhuv * a minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for thj:vhgc.tl s9l-: -yrvs iz v28e maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is released frovds/e x40,r gwm rest starting at an angle o d/w ,0gxrve4sf 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 anchorz.1h(*g/knb;7 t f 0o/tfmqjz poin*ded boat every 3.0. kdzfnoh*ij0pt1 o( gq;b mt*/ f7n/z s. 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 hl+n o+xv/f1e j3hl+geas a frequency of 262 Hz and travels with a speed of 343 m/s How far a v/h+exf+1n+l ogj3lepart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz9iozu.fthk7 5 (kilohertz) and tra.hkfo 957u zitvel with 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;wca h:p*ja 8x yry1krzod/wd:2y p*j,x+j.y 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 denseel2 ztqj4s4hmo l:r8+ as the other. In which rod will the speed of longitudinal waves be greater, and by what ftoshmqje24z4l: r8l +actor?   

  A cord of mass 0.65 kg is stretched between two supports ,rzfmf5)6mzc - 2ufhg 28 m apart. If the tension in the cord is 150 N, how lonmzrzg fc5 mu)2,f6h f-g 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 d 0oxjcz*:e h3mik hr83)pj5k 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 :d 0rj 8hiz5xh3k3 kmpeo*j) csends 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 belg.toq- ,6 nstb l,rey2ow the surface of the sea. He hears the echo of the wave reflected from the ocean floor direct6nysgq-be., tr2lo, tly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at diffe q( pih i ,uv/zhaa4 :h8oo(.iry0b1c4v/ axtyrent speeds, and this difference helps in lthhv/i , a( :rvo14b(4pziyu0.ih a8/cayxqoocating 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 ws)b:r+ skx b:nabl3 z6ave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actua6rn: :)3xl+ asb sbzbklly 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 au7rx znoilb g..b m-7.8vf. nudjh5. un earthquake.7 nb8g ..n mi. -u xz5.vu7lufodrjhb P wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing throuyh(ptqg(c.wb +9w,/-qhuju ,av:k r*prm9y bgh the Earth is measured to be gy.p ,+w( 9jr qup(abq9r/hykm*bhw -t: ,vuc$ 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 supbpq2kpuh7x-6l 6k 544n ei,qd4nsdame portion of the Earth, butkie4q4 ph lsxqund-p6ud5b6p ,4k2n7 one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but one tro4d;pnzz ekav +d,3ge1ozk9m)6q (it anspor9d4)6z gnmk a(; ed1 zz oeqi3+v,tpokts 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 up and down a total vertical- sz yc,gwj+4vqmz;*l distance of 6.0 cm, from the lowest to wcj * ,-z4 +mqgzsy;vlthe 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 moving toward each other. (a) Sketch th 821wm. jev4 )xsqyzeze shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energys mw8vz2x eq)z.eyj1 4 at this moment?

  If a violin string vibrates at 440 Hz as its fundamep yjd;-(ka x)sxgi+7 yntal frequency, what are the frequencies of th;(- a)xyksdyg+jixp 7e first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will it vd td fc(+0hyg/ibrate if it is fingered one-third of the way down fyd0h +cf/dtg( rom the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in fzki m(yk gq aeg;zca/v: 1y(w t5evpa1gd8/8-our loops at a frequency of 280 Hz. Name at least three other// w5q1 aa8( (kp- gmeac;g y8ty1eid zkgzv:v frequencies 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 frequency of standing 24pepec8ohl ,q9-u)w bf ll(kwaves is 475 Hz, how l8ce2lq4 )kpeh u,(ofwp-b 9l far apart are two adjacent nodes?   m

  If two successive overtones of a vibratin, k3hnf2w8m3ys5xpbn g string are 280 Hz and 350 Hz, what is the frequency of th,3 nw2n5ms8 pbx3 hykfe fundamental?    Hz

  A guitar string is 90 cm long and has s kz8 ng*)jle*j5:jsg a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a te: * jlesnj5jz k8ggs*)nsion of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz,; dj8 nld82eh uft3sfjh6czz2i(9- x a but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three freq;3tz (2xcjahu9-isf zd 6d hnf8el 28juencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar s0euh 5sz/vx:3(wywug tring is 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 correct the frequency? us 3hwgxzv(u/5 : 0eyw decreased by    %

  One end of a horizontal*kdi5k;n d 3el s-+c/r 8m:lcsslx:ku string is attached to a small-amplitude mechanical 60-Hz vibrato8:si:rsxm*- sknd uk3k/+dccl5ll ;er. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string t+w i;-qp ts1 i53x,is- p 4atgyi-juqmay be adjusted by moving the pulley. If the 1j;5s,i+tg-4xwtqq- s ai3u- ptp iyihanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved 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 :m.gqf;w9l nmxf n rk+*x*a2o frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a staofw;x:nx+.ga2 *9fmm l *rn kqnding 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 kp4qa 7v(j-1 mehhgv3b prl 2*r.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary rehp1 bqmh7l 23jr*-ag p v(4vat 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 changes fromn /lqdk r,y*ptw04pd; 2.8 m/s to 2.1 m/s Ifn *p4dy0w qtrld, k;p/ the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it ql*y ww .f*)tqhits a layer of cold, dense air. If the sound wave hits the cold air interf )lww.*q*qtfyace 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 w+d+b,tjrj mu2* yb2kk ave strikes a boundary between two types of rock at a 38 ,k+*tmby2 bd 2jujk+r $^{\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 to the user’s manual )z/+s7mf3imhug1jdmu l 91 lk, the dish has to be pointed in the directionlm 7m f+jiud3 9)m guhk/lzs11 of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 melfha .u-l8h q3 5y;ckm/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded5lh-qhfma;y 3 e. cu8l fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constagplh*-ukae (:p rz );ze8n;ksnt 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 5 mi/h). [Hint: Use )e*la hkn;:z pug s(8z-pk; erconservation of energy.]    m

  A 65-kg person jumps from a window to , zbt +a35tjuv hc)8jva fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves luh,bj+5 tz )v8va3jt cike 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 on1b km-cf41twa the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frat b14wkfmc-1equency of the oscillation?    Hz

  A 950-kg car strikes a huge sp;,,hlbm4 k ch+mal-eg ring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffne, h,cm ;hmkllae4 b-+gss 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 lb .fy ak734lkql4/a+,ivl mfright pace of about 1 step per second, the coffee sl b/ll3 al4,4k .i fvqy+lkfam7oshes 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 grooj)2q5tnwt-en u:5egn ve 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the fjn q uet)5ne :w5n2t-grequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is hx f/:97ioeztbor il8ea5o,-3v o ql8 in meters and t in seconds. De re9l vfz88oto qexl3,/-o ib75ahoi:termine
(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 frequenfmnx:a6 ) zq9bcy if it accelerates at 0.50g (a)fbm qn: x9)a6z upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on ak,5n zr ::psuk lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off:p ks5urn: kz,, 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 to play at 392 Hz (G) and 440 ,-ik z;m7xm hn fp1s5fHz (A7 x;fsm m-1f,ihz5kpn).
(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 co05g ud ent:zx- bsx213jtpq 1vrd 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?) (cnxsxtbjetupdv 35 - :2g101qz) 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 prong movw5 p0obfis 1.ues 1.8 mm to either side of 51f .ps0oiu wbcenter. 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 frequenlpxqu+g4kfvfy3( ;ul: .pq1fq4 qm; j cy 1.5 cycles per second. What is the maximuqmq 3fglf( xq+4qu;fv1 j: p;l4kp.uym 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 r grz2 6vh1a.sping that can slide without friction on a vertical pole (Fig. 11–57). Detzahs6v1pg.r 2 ermine 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:*5z(x7k6hz, cjtd:x x; *ucbgac efn.000 s — each one-way swing takes 1.000 (kc:* xa,f6x:egz t j*57cdcz bnh;xus.
(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 5d5temzbj2e (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 what amount? [Hint: Letmze 2(b5jd te5 $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 i n .zicq*t t ni-iezlt;0fb(r90l (h5N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first m(ir qhb*ii0 ;9 e .-z0tic tntlflzn(5eet?    m

A block of mass M is suspended fromjljc1 wtzl((4 a ceiling by a spring with spring stiffness 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 staj zt(lj( wcl41y on top of the block? (Assume $m \ll M$)

  A crane has hoisted a ras0r,h xz.2 zk5rh mm0r)6q a1200-kg car at the 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 en 0,.qxm)mz2s5r0 ah krr6 hrzad of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11ll*wn h3one66i1z, jo–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 mass vibrating on a spn 6 o6l1 wnoe,j*lzh3iring, 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