Give some examples of everyday vibrati xdgryv1up0,4 i zyl(6ng objects. Which exhibit SHM, at least approximateu1vy6,zyg(0r4 ild xply?

Is the acceleration om n8she:kv om**1f3ejtn6iy)n4nuy : f a simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a pis5 p*,cj4utjcston in an automobile engine is approximately simple harmonic. ,sjup 5ct4j*c

Real springs have mass. Will the true period and frequency be larger invm93ck wwuf40yys 1vt ft n;t04w98 or smaller than given by the equations for a mass oscillating on th9fsfwnn4;vkcw0 twvm13 8tu yi0ty94 e end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic os, dlt; 0x)e/ver vv,io2gkao3cillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical s92;cpikk04 yvt v6verpring scale, and then is released. Describe the scale reading as a function of time.ky v90c4ip2v e t;6krv

If a pendulum clock is accurate at sea level, will it gaijdl;v6l.5hc gg7n nce, h2mn 2n or lose time when taken to c2e;lh6lj2cd gnh ,gn 5m7 .nvhigh altitude? Why?

A tire swing hanging from a branch reache,eu3(qgos xm5pc uy 3f a,,5fcs nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only m,o,,u35 (3xfqpgys5 au ef cca stopwatch?

Why can you make water slosh back and forth iul;s*4zygx- cn a pan only if you shake the pan at a certain fs4-ycx *zg;u lrequency?

Give several everyday examples of resabyh od w;ska* i/8f/j3-..zaayxxr2 onance.

Is a rattle in a car ever a resonancm fa eowhuoemn /r/y7 1fi./:7,krc (re phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the uzj -.gf mu eya -oegf0,lpe,qu15j8,frequency of its source? Why or why nog.uaoem u e 01 ,,fqjpz5gjf8ul-e-y,t?

Explain the difference between the speed of a transverse wave traveliqdh neckl j)-(6jx1 u)ng down a cord and the speed of a tiny piece of the cord.) jc(x61q hjed- nuk)l

Why do the strings used for the lowest-frequency notes on a piano 3sb64 ja2v/tv+( c8oyegaz*gwj kp w6df:pz9 normally have z+catvjbpa4:o6e3w(zf / s 8jk9 2dv *gw6 gpywire wrapped around them?

What kind of waves do you thinkrcrp * u5/-ide will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally paralle*-e/r5pcr idu l to its length?

Since the density of air decreases with an increase -n lojb:iq- 4zin temperature, but the bulk modulus B is nearl--jnb4i z:ql oy independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude myjbps *.hl3i;kaxy./ ,jciy z* /j3b as they travel away from the sourcekhz.p blsc jx y/m;i.3i3**/j,jay yb.

Two linear waves have the same amplitude and speed, and otherwise are identi.07l2tbds:rh*kyqsd z 93b y. tf f5sjcal, except one has half the tzbdkjy*s3.bs.f7t0 fy:2 q hrl ds59wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary b;qjmzipx ao g)14l -b5etween two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do 1q5;p) 4mb-az xijg lochange). Explain why.

If a string is vibrating in thre;/q-cs5f lcf9 fpd 2uze segments, are there any places you could touch it with a knife blade without disturbing the m f5dzsuqp29/ c cl-ff;otion?

When a standing wave exists on a spyu a9zu*,.ose*: vh2 fq g/wutring, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Expla.u,/phqs: 9veafo * wy2zugu*in.

If we knew that energy was being transmitted fr) ,ypgcj.6(+yhkwpc c om one place to another, how might we determine whether the energy was being carried by p +c6jkhpw,p)(y c.yc garticles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude cayk xh2vw8 ,6rz(i, ; .spdnl0.18 m, what is the total distance it travels in oxh,8r zk(,wl62.pscv;n id ayne period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it 9 9ifa 5edc0.wu9m :owxwpx5abut is 85 cm long when a weight of 180 N hangs from it. What is the “sprinxdf.ui w99w905:p w ae cax5omg” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg drivemae+ymmq j/q/tem)5 8jv ,(/r(d f kcrr gets into the driver’s seat. If the car goes over a bump, what rqjmq(,cm jm /5/ym dkfve( er8t /+)awill be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2wfn)x6d9 ,zroit v 5h* qzb :geo9pb4;.7-kg fish hangs from it. (a) What is the sprig5t)r6v x,f9ez9z pw*4q :bbodo;ihnng 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 Hz when a qxaw. 9zgebx/ 1l;rxk(ag9 i. mass of 0.60 kg is hung from it. Wha 9wbe(g;/ .9zgka rq1ixa.l xxt is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the posdjp/vw3q - 5pkition x of the mass in Fig. 11–2 at times t = wvqpp-jk53 /d 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. Th(fcm 1kb qr w8iz*:wh+dnq g74e web vibrates predomid hmwq cq7 (w+:zfn*8k4bi1rgnately with 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 * qn ;bmxk/td9frequency of 0.88 Hz. When an additional 6;*tnb9 k/xd mq80-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end mpeaglz7kf *xb2iu 59b6+ )kuof a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Deter 6f u7mb2xpz)l5 ekgau 9k+ib*mine
(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 fros,sh+xm c7dl9w/o m x*m equilibrium is the speed of a SHO half the maximum valuexxhsd /ws +9m,l *c7om?$\approx$    A

A mass attached to the htkp/1 9x099 iyl zohoend of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretch1m wq0h*ehu9ib 0m8joes a vertical spring 0.315 m. If the spring is stretched an additeibo*w 0j8um19 qmh0hional 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 spring stiffness constan4wa0 zs-kbwd b:9k 1lta x:wb9m*yku6t k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed w ykmlb ds9:w-41ktw*u:6 x0az b9ka bof 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 toy popgun 0.20059o efw-kc0yl m to “load” a 00f9 wk5 y-cole.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontaloxetfcdj ,w4xz4 v*4lwe (w*1u .yo/f, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with ,ew1 (oxf/eowz vtw. 4 **ulf4yc4dxj 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 fa p+i: zc pfuyu53*/b= 0.45cos6.4t where x is in meters and t is in sec bz5uc f/fp +yaip*:u3onds. 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 ekaq4s-pjt1 9 wnergy of a SHO half KE and half PE4pjk91qs-wa t ? ±    A

  If one vibration has 7.0 tihe sz7s6ph c/ wlwsa+,+- uhq6gx:dk 6mes the energy of a second, but their frequencies and masses are the same, what is the ratio of their ampli, ac6q ksz:e-spw+x gh7/6hlh6dw+su tudes?   

  A 2.00-kg pumpkin oscillates from a vertically04ae4w- g4 f.agtqz t71tn.2zq nsqfuvd1lk / hanging light spring once every 0a sffn.n 7tu dzk tgvq0/1t24q1a4 -glw4e.q z.65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical;erp4x m)4 aqyof7rx; springs, each with spring stiffness constant k )pa; x4 o7f4q;rxye mr(Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is in meycew 592dos d*ters and t is in *dsw9oeyc2 d 5seconds. 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 Boujv/qpu 0w 85. 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 spring (k = 124 N/eq k ndd fn6.3 ds5mbr0*xv68lm) is struck by a h 0d83*6es qb 5d6d.kxlfn nvrmammer, 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 witm vw6gqh9r,k (trjr, hoix*7 /h an amplitude of 28.0 cm when 0.260 k hg,xv(,r6 m79w/h*rktjq irog 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, with spring stiffness co9sfgegn 1/rd,c6w 5t xnstants $k_1$ 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 hj78; /ituz skkuo y75fixed horizontal spring whose spring stiffness constak 8h/o;uty 75ujs7i kznt 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 reac. ykv*ba2s:x rwic6 h6hing his lowest point, he oscillates up and d*bx .vi6 yrsa 6kh:c2wown, 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 exacmei jmg 0gci,x e1/0(ttly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pen 4qv1*vjy oh/idulum be if it is to make exactly one swing per second? (That is, one complete vibrat1qi yh4*j/vv oion takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mrxvyzf3h zm )7p;kw*0ars, where the acceleration of07ky *xpmwzh ;f rv)3z gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm long jpcv6iy. .n5 l mcbx68
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is uck/r0k 8);p5ke3 ba;z- tlus p,mgln0.760 m, the pendulum bob has a mass of 365 grams, and it is rel,nu0mart;s8ke pp;gkz-5klc) ulb 3 /eased at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clock lopp ( /gbgkq9i 9/k7mvgses half a minute per day, how should you adjust the length of b/p/(gikm 7k 9ggp9 qvthe pendulum? shortened by    mm.

Derive a formula for thepcg(3 .rqc:; hp) bifc 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 releasbznl-h 1mcusu cr:*3: ed from rest starting at an angle of 153clcb :ur- nzuh* 1s:m $^{\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 pa8uukjag47 1 l2cixe scal) /t9ss the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast aail87ugs l1c )ctx/a9 k ej2u4re the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels mp0d*d bca7 nt 0rpb1m1p(vw3 with a speed of 343 m/b *d00p(wt1cv 17mapm npr d3bs How far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600iph t9y pg; t1wagqv4p88)3no kHz (kilohertz) and travet phw)atq81ypp93n4govg8i; l 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 longitudin 1us.v8 (qk :4sz)d *bezbm r2qa.gozgal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as l u8ntq(t4v k/)6cp*aw9vl glthe other. In which rod will the speed of longitudinal waves be greatert t*p v9g )ucl8v4(/allkwnq 6, and by what factor?   

  A cord of mass 0.65 kg is yj:no: +e9 svmstretched between two supports 28 m apart. If the tension in the cord issv:n :o9ym+j e 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 620 m ; k5-c.deoxvvp9)mdv and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sen )me5o; 9vcxpdv vkd-.ds 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 below the surfacd * )m 8q6or; gih0oh0w3 y5(dpxbf m2v9gkigre of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at thi3d6wip;ky9 ()g2m0 dr0ifg mv5hx8 g*o h bqros point?    m

  P and S waves from an earthquake travel at different spdp k86fw+o ,n)csnd k9 2l4cmld+ptl*eeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance +l+kfsdo2l plw,d8k n9dc )4nt*pcm 6took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can by 1mcq1+mo:z j3(v;dcq 4ndtw e approximated by a sinusoidal transverse wave. Assuming a frequency o4qy; +mdc : nzdomvjt 1w3(c1qf 0.50 Hz (typical of earthquakes, which actually 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 injoxle+8;v55s u dp2 k2 oxidy6dxq3f.tensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 2x56lxq2i .dsef+ odyvx82jp5o3 uk;d0 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earthmdbc ) vqwye7:bb6u ,d 0kw)p) is measured to be bqe)b )du0bk7yd ),wp: 6w vmc$ 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 po51op:bbl (9bxq w4dc grtion of the Earth, but one is carrying twice the energy. What is the4q5g w o1c:9pxdl bbb( ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequencyf9+n yp3 g-tkt, but one transports three times the power of the other. What is the ratiot+g3nkfy- 9 pt of the amplitudes of the two waves?   

  A bug on the surface of a pond is observedqq/scs) h0j6u to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest poinqsch/s jq0u) 6t, 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 molwk c*tj61le p7nyd1cj:y85 uving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this momentl7 l*yce :k1jdtwc u 1jn85yp6?

  If a violin string vibrates at 440 Hz as its fundn gv /qqjgx0(-amental frequency, what are the frequencies of (j0x/qq -v gngthe first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. Awrt8w,n(q*(awj/ +ecw qo 7tut what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates t+o(qw wcr7u8j,/w n*q wea(tas a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name at / x0tq7hhtpz-1ckoj (least three other frequencies atjhkp(o/-ch z 71xt0 qt 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 standinzh2j8ck3t j *ag waves is 475 Hz, how far apart are two adk2zcjhj a* 83tjacent nodes?   m

  If two successive overtones of a vibrating strin f:,( vl2qnlbd8q xe:yg are 280 Hz and 350 Hz, what is the freq8 qe:bdx2v nl yq:,fl(uency of the fundamental?    Hz

  A guitar string is 90 cm long and hasld/ 3gofmljh7 b31s: bthd, /h a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?d3sgbhh:t d13,lb f7l ohm/ /j    Hz

  A particular guitar sgp:6nklgf+f99f l cj *tring is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percentf l+j:9pkcn g6g*lff9 should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed tolp)k/bmci)7 ygxa6b7vf, t; x o7:euh 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 hymbo:va6 7f )tb x7,xe)klc/ig 7;pufrequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanioy0qi;wxccs 7 i24s*n+bms- wcal 60-Hz vibrator. The string’s s-snwxq 0ii7wcoc;*m s24b y+ 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 pulley. Ix7.ysshk;p8r f the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be ac.sx;yr7 phks8 hieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a m.anmxxpiu/ y (ki)sa2* ,j4ntub at just the right frequency, the water alternately a2x*mik xi.(panyms/jnu ,)4 rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundark - xyc6-9 mpi vm.3g8;s zul+qdh/x4b:hgvj ty within the Earth between two kinds of materialdy3/cbmx :u .h+ xhskg6z t-vmj-;9ivq84 glp. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an ugni :4bgx62yodxt-v )nderwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make a-g: xvnyxt o 624bgdi) 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, chb u0l;)+myozrut mvd:l/ (2 dense air. If the sound wave hits the cold air interfacmc ub2l +t h 0z)uvr;:(mol/dye 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 typego97oq9owaj+q *ud boa p4;m3 s of rock at a 38bqqoa 4;*g jom+39p da7ouow9 $^{\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 dia7-v67i qzu tzjmeter. According to the user’s manual, the dish has q- 6zi 7t7zujvto be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 kmwg w(lwd z2w7* and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately 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 (dwwlw7 zw* g2stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stpjo.. kzv0j llwd9: 9tiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides wkdw9j .zpov9l.0tjl:ith a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m be.wd 79sgrj oeh(2) . )hrufcxflow, which stretches the net 1.1 m. Assume that the net behaves like a simple spring,xe.79od)jsucfr ()g rf hw.h2 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 ha aq4gccecs(vxlp*l m 8e98/e(nging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillatv98 m*leep(( l8eqax 4cgc /scion?    Hz

  A 950-kg car strikes 8cau +6ym(/ /dyfzf3 uwd*o)z+hh krfs5mo 3pa huge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the spriyusz3yhp/wm/d5 )fk mu6d *f++8o fcz h r3(oang?    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 thecprgiibt 0bfr 069oi(2z4i0/ wcm0vp right pace of about 1 step per second, the coffee sloshes more and grwo49fri0(zc /m0i6 ipti0cbbv p02 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 certainqvo xxh +u,.zpr-u j r(i)1di/ groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sohp.v -+jzirq ,ix1(xurd/uo )und emitted?    Hz

  A 2.00-kg mass vibrates accopl3aao:do6 -,d*)vz gke1v/ 3 vrr pexrding to the equation x=0.650cos7.40t where x is in meters and t in seconds. Determin6pee*a)vprax 13 k lg3rz dd/:ovo v-,e
(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 oscilly/gtb 4bu fphw0, xuv:v517 v:p x9aj kbq1-laates with frequency f. What is its frequency if it accelevj5bvfwbag1ky 0:u1p74,qax-h t9lu vx :bp/rates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a l: 7q7; et iryy.wj6vdlnnsw /3ake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the rqn7wde/jrty .s;6l nv 7w3y i:aft 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 atf6 mk0fw*8lp tsqm/5d 392 Hz (G) and 440 Hz (A). f0m65f*k 8w/stq l mdp
(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 Fig. 11–33. a (n- 6,:hv-uzda py5b r qk6so.wx/bgDetermine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavinvw a6- 5 bzu- op:a(r/ky.dsh 6gxb,qer section of cord or the lighter?

  A tuning fork vibrates at a frequency oe6 s)m tqbs4j(nu*km2f 264 Hz, and the tip of each prong moves 1.8 m)*ut(nqm 42s eskj6b 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 with simple harmonic motion of frequency 1.5 cycleaahu037 c) r1xqys97t bct -tjs per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble pu 1 s7hq9c-ar3)7tcatjt yx b0laced 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 ri 8wvsivzgr9ra6a8 jx7ma6 + o*ng that can slide without friction on a vertical pole (Fig. 11–57). Determine the waveleasg9zwm +6 vjr vr a688a*oix7ngths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 dt p:*5 j ihb*5jmek554f ptkps — each one-way swing takes 1.0* *bpkhji54p 5t5kfj met5: dp00 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical directiolvj2ze+dhet 015 x- tcn 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 osct2ed -l1 ecjvt0+5xhzillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a 1+ef9mre(1 opi 3vf bqtension of 255 N. A pulse is generated at one end, and 20.0 ms later o (f1rmvfpi9eb eq+13a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stiffness q)a dkueom4:ip5 i1)qconstant k. A penny ofqu)opda mi :4ei)kq51 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 block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The dsg+f:0hiq3v steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: fh0gq: 3iv+ dsRefer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. tixmq 3t73vaj. 4n,ph9 ghh3c11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then y4i3ta7 39 qjvcm x,hp.thng3hou 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 jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz