Give some examples of everyday vibrating objects. Which exhibitb9w.d zu/7xp u8qlt t: SHM, at least approximately?b89uzp.t/7u dl w:qtx

Is the acceleration of a simple harmo6rnjhm +yn7q0ff9 u7t nic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximatelu 4d3-e) ov- sxnh7gggy simple harmonic.dhg-)3 -vux g7sgen4o

Real springs have mass. Wi2sy7v5i.mri79qso4 t0f,vipz x3zb gll the true period and frequency be larger or smaller than given by the equations for a mass oscillatz r03myvg zx, b os.9sp 4ii57vtf2qi7ing on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonrro+ph+3 eq3yr.8 qjo (ydd5nic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then is rw hc uiamalkzxpx4k/6avki9 2c 7m8)+ h)e04oeleased. Describe the scmx+k7a evho6a0hip8/amwc92uz ))ic 4 kxl k4ale reading as a function of time.

If a pendulum clock is accurate at sea level, willkmcg ihk3*aml 1br-7hj8cr;4 it gain or lose time when taken to high altitude? mki4hcac87j hgr -1; krm*bl3 Why?

A tire swing hanging from a branch reaches nearly to the grounlrfcf f7(xod 0 c-e.qg+2ev n5d (Fig. 11–48). How could you estimate the hefvn0l+( 7d-cg5qe rffox .ce2ight of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you ulorr,3q4dhl*e ) d/cshake the pan at a certa4ruql rhco 3,el /*dd)in frequency?

Give several everyday examples of resoni9 dfp1ok (lp+ance.

Is a rattle in a car ever a resonance phen2 jr*2lwc ol i7j+:5-yaris mbomenon? Explain.

Is the frequency of a simple periodic mvd v3pyjo8 w9w),ufzr4m2 :fwave equal to the frequency of its source? Why or why not,2vmpzruf w4:v)m 98dyfwjo3 ?

Explain the difference between the speed of a transverse wave 7 w w lo7:)edz bt:m:xph;n3bec8ud5utraveling down a cord n u7:em;8:wwud3 7dhbe lt:p xb5)cozand the speed of a tiny piece of the cord.

Why do the strings used for the lowest-fre6an.ev *ks,zdquency notes on a piano normally have wire wrapped around tza, d*nk.se6vhem?

What kind of waves do you think will travel down a hory xc ifh,o6i lcp7o-m8.7nf9vizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its lem ,ho y7 f iic-p8f.onvxc79l6ngth?

Since the density of air decreases with an increase in temty.t;4 9yypti rrt(d-perature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound wavetd t;tpriyrt4y -y.9(s in air to vary with temperature?

Give two reasons why circular water waves decrease in mr : -b5ui5xisamplitude as they travel away from the sourc m:bii sru-55xe.

Two linear waves have the same amplidz*9 l ct d6rdn3utb1h 14,cprtude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more en 9* 3dc4 dt1 6lcr,1tbrnzudhpergy? By what factor?

When a sinusoidal wave crosses the bounan*o rb+m,lr,h sc 68tdary between two sections of cord as in Fig. 118*,hn,sr+r omc6balt –33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places5xplcy4b6v f vpi s:.7 you could touch it with a knife blade without disturbing the s67b ci pv 4.lp5vxy:fmotion?

When a standing wave exists on a string, the vibrations of incident and reflect(z2 s4zw9whvdf4r 4 zyed waves cancel at the nodes. Does this mean that energy was destroyed49wdz4vywf z r2h4z( s? Explain.

If we knew that energy was being transmitted *zd/8) 0k7j3k gbuhqzytkeq; from one place to another, how might we degyk3qj0dz;/buhkk) t8 *qz 7 etermine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what (ty a6o.lz8mhh p :u1tis the total distance it travels ip8t 6t ho1:m(u.ha ylzn one period?    m

  An elastic cord is 65 cm long when a .r0+bnhj +(8.bn)levygcvx z 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” constan.lvxnr(cz)+hv gy+ 8b bn ej.0t k of this elastic cord?    N/m

  The springs of a 1500-kg cahqqml b0efq hfj,*6 sns(k u vz5*i*6,r compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the freqm*(06,ikqj6hs *l 5fz bu ef* hvs,nqquency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cma+0 hpu1h lz5b0 +rutjz 91bji when a 2.7-kg fish hangs from it. (a) What is the spring stiffnessu ++hbipzlha0 1tj1z90 ur5jb 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 n ;gz**l0ild ja frequency of 3.0 Hz when a mass of 0.60 kg is hung nl*dz*j g0;lifrom it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicati0 afgt0 c e4/.hn;hjylufcw64ng the position x of the mass in Fig. 11–2 at times t = 0,t = ;4h u e0/flg a0hc wcnf6t.y4j$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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’sifw) (afru /n60-rz j(-c anjt web. The web vibrates predominately with a n(jntfc w)r irz(-j - 0u/a6affrequency 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 ff6a6zr,lt+v b ev+ak;requency of 0.88 Hz. When an additional 680-g mass is added to m, the frv;vkat+,+ a66zlb fer equency 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 with an ampfm:4a5mern k2 litude of 0.13 m. Dete2 4:rme makf5nrmine
(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 hrpr (b+1 q8xffalf the maximum val bq +prrf(xf81ue?$\approx$    A

A mass attached to the end of a spring is stretche ktwdsf qy;5 gr/rbez35bfu.58u 3krn2w* 1ttd 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 sprin-gfq9-3v h1;fyd k,j)tfyz w;prq/jog 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it tak1g /y-o -p3dff tz9rkjvhqw;;,) jqfye to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness constanu a22pb8gnxy xgmkz:f 32)lh:h1 8o zot k = 280 N/m and is executing simplfm hblx:2:) agohou 8nxgyzk83z212p e harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compr 88.ore :a)z4 a1yxoll5ge2btj0szz zess the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what spe4zox azt.:r yg 1 l50zj82e8aleb)ozsed will the ball leave the gun?    m/s

  A mass sitting on a horizontau4jh3dxbzmc2 4u x8b(bc +-prz3jxo *l, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of whu( od bb8rx32zj3* 4cx4-cu b+mpzxjork 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 in )b3jxz ci8u q3meters qc3bx3 jui8)zand 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 energy of a SHO half KEso*y 3gggba):2+z s jz and half PE? ±sg2*s zg:+ obg3a )zyj    A

  If one vibration has 7.0 j14 d*io6k-/p1i9k qigsnkg ptimes the energy of a second, but their frequencies and masses are the same, what is the ratio i 9s kkd/1o4gpi*-pqigjn 61kof their amplitudes?   

  A 2.00-kg pumpkin oscillatesdj)4u6tgs 8km from a vertically hanging light spring once every 0.65 s.jud)mk4t s 6g8
(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 cx(1q z39rb u k j.;-jh n54lvuf/xoyosprings, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibratif; u9/x3(u qbo.chxoy njv 1z-j4k5 rlon?

  A 300-g mass vibrates according to them4sy d*3swj7:9 bgz y*x) uifffx89aj equation x = 0.38sin6.5t where x is in meters and t is in seconzi8fm s9 djs*7gfu9*ba yxwx3:y )f4jds. 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,i ;760ku:lcoxs xclt .ykm 5o5 labeled A and 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 on the end of a horizontal sprinn:yl )pwj7um zf; 8+;c+k.hg rm8c hqsg (k = 124 N/m) is struck by a hammer, which gives the mass ygc z+)8 hlm:;;hkqs p.cuw 8fm +jnr7an 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 vibrat)+z9dl,o qclr es with an amplitude of 28.0 cm when 0.260 kg hangs frol,+o9qzrl) cdm 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, with spring stiffness constants gcqf/u/(z zh 3w ro30m ,rr4ih+as;od$k_1$ 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) i+4f4 /prgvu dtl n,tb-lg)vm(qb5g 0.600-kg block attached to a fixed horizontal spring whose spring stiffness constq b p 4gtr)vl(tug ,v5bd4-mn /ilgf)+ant 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./w fd-:h t,ciibp0 zbys19a)v After reaching his lowest point, he oscillwbi1czyd:9s,pvtf/ b- a0 ih) ates 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 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 60 sv).d2rgsv : nsg cj(6e. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is tqc7ye2z/(f h yo make exactly one swing per second? (That is, one complete vibrafyc/(he 2qyz7tion takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80(lbsj2o-0r3h u z6y-o v 4vbtk s on Earth. What is its period on Mars, where the accelerat20o3uvb6t4vby zohjk slr( --ion of gravity is about 0.37 that on Earth?    s

  What is the period of a simp,fn 0izy16981w3f baanxu rgule pendulum 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*zb1so9l2dm45sk 05 ix twh1 swpyeh-, the pendulum bob has a mass of 365 grams, and it is released at an a9h25ie1s ydws1z w 40sx-lb*kmto5h pngle 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+z09gm og4jen(nl4o uik0 c 8x the clock loses half a minute per day, how should you adjust the lenlcjxn80oone9 ggzi+0k (u4 m4gth of the pendulum? shortened by    mm.

Derive a formula for the mac4z 3bjgv;h(cox .r-v ximum 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.lpf-dwn ,r 7c9lb txxo: j50q*5 Hz. At it is released from rest s,:px 9wl5 q rtb7fnd-0co jx*ltarting 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 wave crests pass the bow of his anchored boat everyuqmtnt-o85l 9 3.0 s. He measures the distance betweet 9mu5lq-t8 non two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels w n. qx7lftm95; aol;sxith a speed of 343 m/s How far apart are the wave cr;xq aol95 . fxnl7;mstests (compressions)?    m

  (a) AM radio signals have frequencies between cjupum(x 67g r5t5at9550 kHz and 1600 kHz (kilohertz) and trarg6(75ptu cutm 5x a9jvel 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 longitudinpy,wy0 +)w 25c(- 1etpkoxfguzxfn) ual 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 den,hv qdt x;83ezse as the other. In which rod will the speed of longitudinal waves be greater, and by whhtqze83xd; v ,at factor?   

  A cord of mass 0.65 kg is stretvipfspr8i*k:pxlmz6 e;58 1g ched between two supports 28 m apart. If the tension in the cord i1:*sivpk ppmx8z8r5 g6 if; les 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 b fk7-u8mrizo/)cas 53gw- c osy 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. I)fwmck7rsos a5c - 3u/-io zg8t 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 ,a * ;ayk 2xp 4-+ipifxcq2unmjust below the surface of the sea. He hears the echo of the wave reflected from the oce m*xy42u ;xi, iq2 +pafc-napkan floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and th 0,iz1 *2 e/jwpbyx aludl4e0ois difference helps in locat/ pl o 0*ee4ix0yj wzla1,2udbing the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave cxk ol22fb4ev8c.q,h i an 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 xhbq o.kf ,82l 4veic2is 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 intensitozj 189q;aqkb3 ;fkyoies, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two point fky ab qz;913;8jqooks 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to be 1v/u29htk t /l fkdp*ii* l2k1htfk9pud //vt $ 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 portion of thv,,0jfpfjmr oi.2uyl5s ,hp .e Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of tpyf5,r u. j 2v,lhs 0.mp,ijfohe two waves?   

  Two waves traveling along a stretched stu4f7 gz44yx8 nhfms0zring have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitud8 y hz0msff4unxz 44g7es of the two waves?   

  A bug on the surface of a pond is observed to move up and down a totan+a;aey(g:a h l vertical distance of 6.0 cm, yha;a:g(+nea from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward*ts; nfwm, )oo each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shaf *,m otno;ws)pe 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 energy at this moment?

  If a violin string vuplfx6dq-,w0 y py5+q7f1 9f l+lzdifibrates at 440 Hz as its fundamental frequency, what are the freque-l1q 9piu p wfqd6d+0+f5,lyfxfzly7ncies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 2r - cl9td9oe6jlm k6k6 e3c1ds94 Hz when unfingered. At what frequency will it vibrate96jom1t l6k3 -ee9s lrdck6cd if it is fingered 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 fd,l .a 0mfy )yofu22.9abfnd- p h eap.fr2k-aour loops at a frequency of 280 Hz. Name at least thlyr)2dbdan9f . .,af2-0pa.f- faupk ey m2ohree other 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 sta7 p7lpia/d,hvnding waves is 4757 v papil,hd/7 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string x 3n ppduna pwfz3m 2k:q9q(l v5q,84sare 280 Hz and 350 Hz, what is the frequency ofqmp p8 (xzwq4qu2vlk,na 5f3 9np:s3d the fundamental?    Hz

  A guitar string is 90 cm long and has cg *qlso 6g - ae62ckj9(kr4-7kf avoja mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tegjgk cos-97o4qja v-ac6lk *6 fke(2rnsion of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibratewcv7bn 2c 9ep.;bgwl5 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 the three frequencb2 7g lwccbwn pv;e.95ies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but jtt,- *og5eno bu-gq6it is measured to vibrate at 205 Hz. By who -tb5qtg ,ojgu*ne 6-at percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a smal;9rm15z0py7 nq isrhxl-amplitude mechanical 60-Hz vibrator. The string’s mass per50pn9zr7 qy 1s r;mxih 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 cx5a 6yw3x32+ zsvtx)zshu hjfru740 string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different 5hu)h ssw3r+76jav yz z f0xxtxuc 342standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth qs+d/ 2:jlg )w k6gwz 34jmifxin a tub at just the 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.ws)f4/zij3jmglk 6qx2:d gw+ What is the speed of the water wave?    m/s

  An earthquake P wave travet3e +khxsiqta *;9tq )ling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches q9ts ;*hxa3tt+ q) iekthe 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(,m0sb lla61v :dv(p zyvs :bpusm:7q velocity changes from 2.8 m/s to 2.1 m/s If the inpz(qb6 mbl v::p s1s v :yv,m0adu7(slcident 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 hits a layer of cold, dense air e qu e5z+1+wny dcpyclxa38-*. If the sw1n5du qc y-+xep38ea+lz yc* ound 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 tw yaw2 :;+l;rlvpiwt. b (padv6o types of rock at a 32i p:p( yw wl.al+;vad6tv;br8 $^{\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 man uj nmr;xcny+( 7v.xtqx8to:-ual, the dish has to be pointed in the direction of the satellite, but an error of about 7xc.oux8 nv-x ( ;nqjtmyt:r+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 hhyva,2,t/pyjdr* o+ 0vj z-x 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 how much time do they have to run to safety? (In the absence of knowlej2xh ,oaytyrd ,/+h- *jvvz0p dge 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 550 kvn x p+jyz0.+s owzt/7rd:ol8N/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). +z07rs/np:ty8lovw dxo+j. z [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which3v gau(t.jd3a:mk/bi9e )d.cs pwge t6t 8qf7 stretches the net 1.1 m. Assume that the net behaves like)/tj .p7a gcv ee86q3iu gmt.9 t: d(f3wsabdk 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 sa48 kh5mgzcwcd8 jh9 z ft.v7+pring. The mass then falls 33 cm before it stops and begins to rise. What is the frchg 5mv+f zdzh 78jtwc49k.a8equency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fi0l81 s+uablx1mbmzc+ g. 11–54), compressing the spring 5.0 m. (a) What is the spring s1lcz+bxasu m+0 18 mlbtiffness 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)zeu ymy)du7 l;0lmei;m 6;9ao 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 (Fig.ly0;a;mu;d meyu)96z ie7mlo 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonon 9wdn3bow qjpw934*c ssl85dgraph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitted? 8n9c 3l 5ns * 9p3ds4qjwwwdbo   Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t whextvv64lpqu tr8c ex 6m3pl,) w/yp7(xre x is in meters and t in seconds. Determine68,tx vc (xq7/6e txyplvp)wupm 4l3 r
(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 frequency5zby3 w*:h;moschkuo h3b (9 t if it accelerates at 0.50 us ozbbhy5kthh3cw9 o:(;3m*g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-3i9r.b4 naol, qm7 k4e gybg:kkg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps o :4omq4bgbny 9.ag 3iel, r7kkff, 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 39:llb5v by (2enh( 8dru2 Hz (G) and 440 Hz (A) y8 r(edl5lnu:b2vb h(.
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fx +p qjvek;.+zig. 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 x v +pk.;+qzjethe same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and(f1.ubzz xb2x the tip of each prong moves 1.8 mm to either side o xbf(u21zxb. zf center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of fre6oh:gt0 : uoq ;)1xykekjvd +mquency 1.5 cycles per second. qydx)j:+; 1egkvkth0 o6:mu oWhat is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end3t8cx*;h 8k,kzpitp d is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibratiohk d3,*pxc 8t8tk;ip zns of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each onesehnz5zk1 *ym +jd)b* -way swing takes 1.0m+5dbs*1zj *kzn)ey h00 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 sprin fs;gh2v4 gm-7 i:izqmg can 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 horizon :ghmf2iq7isz 4-g;mv tal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretc atl9h :pjj04ghed under a tension of 255 N. A pulse is generated ataj:p9tj0 lh 4g 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 suspepmlq (nw 0) ya6g1,qghnded from 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 stay on top of the bloc1yanwqmg q,lph )(0g 6k? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg grgidqls+ jq;agnb86rw06 3 9car 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 end of the cable. What is the period of the bouncingwagg ;inrl +6jr3g8s9d0b 6qq? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gi;e, djfybjw6+ves 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 6 fdj;b,eyj+wthat the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz