Give some examples of everch9tjjmrl:i uj*( , k y9+9(uprle6ksyday vibrating objects. Which exhibit SHM, at least approximatelr9kst 6i*cu+j,(e9(u l lkrhj:m yj9py?

Is the acceleration of a simple harmonic oscillator ever ze e 8af.phj(iaw;ow0j/ro? If so, where?

Explain why the motion of a piston in an automobile engine is approximafuv+5z 7ozyob zk3 yjzip y8,-d3p k+2tely simple harmonic.zf5ip-3k+o7pzyk z ,2+oby y d3vz j8u

Real springs have mass. Will the w4jgja/ ,3mv dtrue period and frequency be larger or smaller than given by the equations fo4dj w3ja/mg ,vr a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (SHOafkzjux/nh5 jx.+r:5 )?

A 5.0-kg trout is attached to the hook of a22;toq9r;kmyi mf v(u vertical spring scale, and then is released. Describe the scale reading as a function of tim( ov;;muf mqti9k2r2ye.

If a pendulum clock is accurate at sea level, will it gain or lose time whehc x3p s*tvii:/t1jf: n taken to high altitude? Wh:x:cpt/v s ih*if3tj1y?

A tire swing hanging j 0j nr(9*ehphfrom a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of tnjrh 0 h*9e(jphe branch using only a stopwatch?

Why can you make water slosh back and forth6 jlmt-k68imzj 89wxjeten 8+ in a pan only if you shake the pan at a certain frequ -m8 ik+z te8wxjj8n6m 9ltje6ency?

Give several everyday examples l8em (0xpzbsaq+w d68 of resonance.

Is a rattle in a car ever a resonance phenp2ygq opyezh8 *z6 2- c7fmku+omenon? Explain.

Is the frequency of a simple periodic wavet8f5b. 8x.slen .heka equal to the frequency of its source? Why ne8f8s.ke5x. a.tlbh or why not?

Explain the difference between the speed of a transverse wave traveling down al5s+mfby0 2 vt clvf syb 5t02+mord and the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on :07oeczom vd jdxy ;.0gw; ,aya piano normally have wire wy cd yd;za0om ,vwe g0o:xj7.;rapped around them?

What kind of waves do you think will travel do;k059 iejqee dl.z6zrwn a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its l6ke5rie0 dq 9z;.ejzlength?

Since the density of air decrelofr+ypq+e) lu* skrs -u1 6jopg2; n8ases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you eeo; q+pf1*yl+-sp)u 6ujo 8 rgrsnlk2 xpect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decreasvqxd2 v6letu0 idk;4e 08xl5e. n ;ntze in amplitude as they travel away from el ;ex62e850l dt4dzqnvu0ni.tk xv;the source.

Two linear waves have the same amplitude an .v. mg 71wgkc i95;f7ixznckvd speed, and otherwise are identical, except one has half the wavelexzfcvi9. 1wkmvkgg7ci; .5n7ngth of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses+fac +t 7jxad0 the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do chajtaa+fcd0+ 7x nge). Explain why.

If a string is vibrating in three segments, are there any places you couldwy*k1 i2lcy g. touch it with a knife blade without disturbg*1w.ilyc 2yking the motion?

When a standing wave yz tij(i w(w25exists on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destrotw (52yjii wz(yed? Explain.

If we knew that energy was beinc+b hvhmdw;sk0t 8*cez;d9.y g transmitted from one place to another, how might we determine whether the energy was being carried by particles (materiat e8kb d.vs9*m;;hw dy0hcc+z l bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total 13s5ecw xn1 -9pgcsbhdistance it travels i5h1scce9w -g xs 3p1bnn one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from v o, 6ruo3lsm-it but is 85 cm long when a weight of oos6-3rmulv ,180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm +gd6mt m3umq 6ei81a3 yeho2lwhen its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of vh626 e3tyo1g d8ma l uimeq+m3ibrations?$\approx$    Hz

  A fisherman’s scale strlvj34 /lhy1pietches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness col4 3 vpy/hjl1instant $\approx$    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 wk9:jp 6h/we*7jtax5n w/isxg ith a frequency of 3.0 Hz when a mass of 0.60 kg is hung f7/xn kas*wje9htw5 :g j/p 6ixrom it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the ;14 ogj mqh8whmass in Fig. 11–2 at times t = 0,t =mj w1 o;hghq48 $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 0.2 )bn0zgbx2 rj)5 g is caught in a spider’s web. The web vibrates predominately wz0bnb 2gjx) r)ith a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0qfn(p4h+mfpnv9*x (w1 g 8t* unt*q ffrp8bn:.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of munfbt1: v q mfp**t88f(r*g(fnnq 94hp wpx+n?    kg

  A 0.60-kg mass at the end oqxp. mn bl,.df-:9nzt f a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Determtx:b lpq9ndm.- zf.n ,ine
(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 t g3/kyw+: vz)b/ibqy the maximum valukqb yv3 bw:)ty g+/iz/e?$\approx$    A

A mass attached to the end of a spring isw:gi4o9*)x .psah y xj 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 stretgmed8 qis;w1;ched an additional 0.130 m and released, how long does it take to reach the (new) ;i8ws 1gqe;dm equilibrium position again?    s

  An object with mass 3.0 kg is attached u 4xupa 4cnf*+to a spring with spring stiffness constant k = 280 N/m and is executing simple ha+ xcnu4*4auf prmonic 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 spring of a tonw 0f t h: tq*nykopu+807rj8 xak9yp0y popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the b7 t tkh +u9:oy8nkpq 8 00yf*npwrxja0all leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surfac,fui5(rk,;yt yl4d ure is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of wortf ;kyy,,r( ul dui5r4k is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t where x is i23glcpsm )bhc8 nibw/t3gee . r,n 6:qn meters and t is in seconds. Determ t gqes. /pbeimnrc h8c2l) 3:g6nw3b,ine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half KE atk r n2wyv 0+ r;bxfpo3g0iyk3l 4ic6,nd half PE?4 pkl;o+ri i3 gbwyy2r0fx,vk cn603t ±    A

  If one vibration has 7.0 tbb dq-70 ,vgzv0+ sj*z7ao 0qb9sq eezimes the energy of a second, but their frequencies and masses are the same, wh* bbed9 0vzsbezgqj+0o7 s7 aqq-zv,0at is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging lighd /5+oi5mdkih t spring once every 0/i55mh k d+oid.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 par9lrxqz2;/ 9 ntq5xa;r*mcyj m allel vertical springs, each with spring stiffness constanny*r/j;rqzclxm92 t;5q xa m9 t k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t wher7ulr/ wlfbp z 3 m38dzlu33yp;e x is in metersrlp b8/dm333z3fy lu 7;pwulz and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each,7t1mo:i 08k6emja2efct*;mw onkp - h what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizok.cn u3i2(te y t(wc-q sad3g2ntal spring (k = 124 N/m) is struck by a hammertt23cqg(.c k( usn ay3ie2- dw, which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates xiem n2y3. pzj3:;mz wwith an amplitude of 28.0 cm when 0.260 kzm2x n33zyimj: e;p .wg 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 springs, pb7,tb y h.ol-; f2ss,4wrowe 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 fio2zz tpw(x6ve u+. q9lxed horizontal spring whose spring stiffness constan2te.qux zpw 6(lz9ov +t is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After r jrxz0qb1e, g-vh:5op eaching 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 brq:10g opvxbhjrz5e , -idge. 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 vibge/dsmklk-q ( ukr/p 8n2b::irations 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 ex f703ghs/dzw v+vxt6ge2ylv w pv.2) mactly one swing per second? (That is, one complete vibration dyvvx06lg)s vw7t mh/3pe2 .zwfv g2+takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Eaz srd9tol;, 2trth. What is its period on Mars, where the acceleration of gravity is about 0.37 that on9 2todt,lzsr ; Earth?    s

  What is the period of a simple pendulum 80 cm long grhpr +; arye5x3wf4r9vgw- -
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, tt0. j/dbbn eaae*k*x pok 9d-6he pendulum bob has a mass of 365 grams, ando.9 ee kdka *pjtxba-* bdn06/ 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 ixa9xt/jj- hv;6ev5(jjh f wi)(hlu+ of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shh9jh/ lxjv6ix w 5ieu+(;t)-h v(f jajortened by    mm.

Derive a formula for the maximum speed hd +1lppf h7eh3yk h)4 4lf3th$v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillate +np;l8r8u3 ,j(vjv w huzj/hvs at a frequency of 2.5 Hz. At it is released from rest 8h(w,3u+uz/8rnl jv ;pvjv hj starting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that n/c5(sk5-dd1mp/) pwmcctrm wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests 1)kc dd/ msnmm5wr5(cc/tp-pto be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequen.jpl5 gc .cuzce;: :zfcy of 262 Hz and travels with a speed of 343 m/s How far apart are thez .lp:e gj f:;.5cuzcc wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (av ncrrj/1d-+ jvi*b2kilohertz) and tr-ra+c*bjvr i/dn 21vj avel 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 longit:etd/h.w ,7,/( rbkrcd ab pwvudinal 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 0arm/j qz 8c pm+hu(qnu1/1dr3 mgp3jdense as the other. In which rod will the 3/j 8r0rzu1g3p1 mmcqmn+ap(qdjh/u speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the tens3 xx; wo,zd3ngion in the cord ig; wd,3x 3xzons 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 juv*6mdr kwf9 boc4) 5cable of length 620 m and diameter 1.5 cm. As the gondola cmk j d*f5vr46)wc ubo9omes 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 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 juswm+: f)ehlv6 hz*ah6xt below the surface of the sea. He hears the ech hx6a:6)*m whef+h vlzo 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 dif4u36egt eewoq1 h 4/maferent speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance 6a weg1o4et/4h uem3qtook 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-producey+r+ ha- qw,cxd surface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that oh+axwc+q,- yrbjects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) t *+sefend)i 5nhe amplitudes, of an earthquake P wave passing thro*ifn) + dene5sugh the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Eartht.ri 62vorf/b is measured to be to6fi/2 rb.r v$ 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 tdym1p6he* mh:qhvup4- z -l:bhrough the same portion of the Ea-eh -:*mzu6h hdv14qyplb p :mrth, but 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 frequencycbw 07ks/9zmp , but one transports m pzwb09 c7ks/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 movgj4o 4+hynf+i e up and down a total vertical distance of 6.0 cm, from the lowest to the highest pointn+4jhio 4y+gf, 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 eaw-sz -qzg mlpylk77v; f+w,/ mt7que1ch 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 zm sp1- /7ltw;+u7zf, km qg-lw yq7evstring is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what are thzo z-pmg r6 .nc9et6b7e fgmz- pb9nz 7ce.r66to requencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. Atd.fuzynz-w c+3-mr z* what frequency will it vibrate if it is fingerecdzf--3znym w z*+ur .d one-third 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 280 iv7mz;mm s287n95 l cnsqn6nb Hz. Name at least three other fbq5scnzi n m97 vln;m2ns7m68requencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a stsn;22,mj r rvzring is 92m/s If the frequency of standing waves is 475 Hz, hoj 2vsr rm;2,znw far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 5* zsv:k-pz4pvyb d6qh1i*n fHz, what is the frequency of the fundamenq *nsp-zi5:d*pf vz1 y4kbh6vtal?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance f;cxh,tkph , fy2g o9,prom the bridge to the support post is L = 62cm and the string is und,h tygkp,2 , xchop;9fer a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is dc84u gm:,xoo 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?So u4ocx8mg ,d: othe three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, b13i*k+xucn;m ug/ q qzut it is measured to vibrate at 205 Hz. By what percent should the tension inn;1 iqk*zxm+uq/ cg 3u the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanic+c (vi/v 6s spkavriy07e7hx3al 60-Hz v vvpcsk7eiav (0h3yx/67ri+ sibrator. 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 may be adjusted by moving the pulleyxt;j+ubcg8 5 a5voi+aqz6 1ho. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm tv6bogqo51ah+58 +ac; z xjiuand 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequency, tqj8rk3 * uwxe1t 2 o3up*mi-luhe water alternately rises and falls at each el tr qw1x*e kio3u*mu3-jp8u2nd, 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 strikes a boundary w*x pzrb)l k40githin the Earth between two kinds of material. If it appr)bx*kprlz g0 4oaches 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 o47i,+ f 8fg7fk: weq3mdlmhm “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests ma: k438+hd miq o, f7mwg7fmeflke 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, dense a*z* *j ts,tqorir. If ttt*,s oq*rz j*he sound wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types o-i2 +xizovc(pl t a/y/f rock at a -y/i 2vcizol ap/t(+x38 $^{\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 )ibv sx: g r5jf9f3;las.4xrm user’s manual, the dish has to be pointed in the direction of the satellite, but an error of aboi 9.s 4bar;s35:r xjmvf)fxgl ut 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels5q*6m 0kb 0hdjkqiv w( across the Pacific Ocean. As it approaches Hawaii, people obsehd50kv0wik * m qj6(bqrve 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 car bumper has a spring stiffness constant of 55+e*fyj0wt633i eavyzo 3d ) op0 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 conservation of energy.] z*ta )33pee+d 0vyo ji36ow yf   m

  A 65-kg person jumps from a window to a fire net 18 m below, whicu vd4tj9x6u lo lc8w4w:z+ie 8h stretches the net 1.u48wl8xu j6: wz4oi9tevlcd+1 m. Assume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring)4.,qo+ ervhq h( jjjt. The mass then falls 33 cm before it stops and begins to rise. What i ,.tjv+ejoqhqj)h 4(rs the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54)i );;i 30ug9bhsv *ajclalp 5v, compressing the spring 5.0 m. (a) What is the spring stiffnes pab;ljclvsgvh 35i9;aui* 0) s 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 (dx- a9mar wno22iameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fiaxoa-rmn w92 2g. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a cer+43+mq1t xt2k9mlmqp pe0bkd tain groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What willm2 qe+plb m1+pqm xt9 kt3d40k be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650zyw9uzsl -n fa1.i7 b30btnv5 cos7.40t where x is in metvi.z0u-l s9znb1f3a7bw 5ny ters and t in seconds. Determine
(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 oscillat :2k.c ogypdfgz2ymc3wz8-8kes with frequency f. What is its frequency if it accelerates at 0.50g (a) upwarz8zk yk-2fw cyo8g3gmpc.: 2dd,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stand 8hd 2d4cmwp+.tz(zp vs on the raft, it sinks 4.0 cm deeper into the4 zdp v8.tm+d(whczp 2 water. 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 instrument are tuned to play at 3 ad.+1 tnh5c7fpwr f3d92 Hz (G) and 440 Hz (A a+ 3h.1w5ftrcdf7pn d).
(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 di *z)2qze9 dwgs; :b m4dhjae:own the stretched 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. Whyw;dh 4smg:qad)z:je 9*i2bez ?) (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 prongb3npik90j1q .o e/q/l n qnfwmsb(yj .1r ,r3g moves 1.iq19 wjem1nlnbj/b fqq,.g/p0sro 3rk . ny3(8 mm to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates wiw+*/ms4 1n xz 6ydxat*pag) w,wco)rbth simple harmonic motion of frequency 1.5 cycles per second. What is the maximum w)cp4xd gw y xz)a6*1t* /nro+w,abs mamplitude 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 i9c f zq3zist)qur 8 1r:hlu+i2f that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57).hr9rs1 8q)+i2 t3qzcl u:fz iu 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 exacvje6b4(rdf2 uk-mxs n; g;a *rtly 2.000 s — each one-way swing takes 1.000 s. r6nbsveu(dr m 42;-xfja* ;kg
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction oa rz+z;hs r/a9r can swing as9asr+ ;/zarzh 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: 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 oftew 44oy9oy+n qorfb7kwb1/ ) mass 123 g is stretched under a tension of 255 N. A pulse is generat1ow7wbob k/fn+y ry)tq e o944ed 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 fro.r7 2qf fi.1rsxukgn. yab52tm 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 amplitudr2y5 gk1.7 .t2r.si a fqfnuxbe 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 (: 58x orswu1f2ftyl cthe junkyard. The steel crane cable is 22 m longx ry us1o 8(5lfftw:c2 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 to Table 9–1.]    s

  A block of jello rests onq,ohv(2m k g6sa o/4cs a plate as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of 6s cva,/ o(4h gos2mkqjello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz