Give some examples of everyday vibrating objects. Which exhibit SHM, aw: 30w zso gqxnlxq/)8w1v-ypa o-g 5at least approxi3:/xw wqa 15 yv-sp8olz qn gxw-)goa0mately?

Is the acceleration of a simple harmonic oscillator ever zero? dqa+:,x , pmpx -6*,srzcqvv hIf so, where?

Explain why the motion o g5oc2c:oggo/r2f *-vepqm:sf a piston in an automobile engine is approximately simple:og p2 5o-mf/rco : c2s*eggqv harmonic.

Real springs have mass. Will the true period and frequency be larger or1:jr6ji . p;bwoc o1qc smaller than given by the equations for a mass oscillating on the end 61i 1wbojj:p. ;rc cqoof an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator 4c mogfe 2ohz+t8dv-4(SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring be; n+ m-gstg ,pgmuyqj/hb i .8:ph9p8. d4vvscale, and then is released. Describe the td g emb+4p-g vibsp:,/; .m8u9nqyjhpvg. h8scale reading as a function of time.

If a pendulum clock is accurate at sea level, will i+bo,m2h np4 rkt gain or lose time when taken m n+bp42rk, hoto high altitude? Why?

A tire swing hanging from a /ex *qtk-ru/ g0my( yhn)f d6sbranch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using onlgey )/xy h(m0tfsrqn *d-/k6uy a stopwatch?

Why can you make water slosh back and forth in a b1 va6/ yn34pb0rn p8adm;cra pan only if you shake the pan at a a1nv 8;b 3a/r6cba m4n0prypdcertain frequency?

Give several everyday exam73. j(v hnqzr uz.j4+uqjm*vv ples of resonance.

Is a rattle in a car ever a resonance phenomenon? Explveg ey p-kqcg0 kmx)tn .7ay6:v6cp(0ain.

Is the frequency of a simple periodic wave equal to the frequency(ao,kxwo k5m( ) lzp2q of its source? o)p2m(kxolz aq(wk 5,Why or why not?

Explain the difference between the speed of a transverse wave traveli5jcl8bqfd64ss r 17yrng down a cord and the speed of a tiny piece of th6jsf c51 l 8q7rrys4dbe cord.

Why do the strings used for the lowest-frequency notes on a piano norma2wqcbkqic37. lly have wire wrapped aro.27w3qcqc ibk und them?

What kind of waves do you think will travel down a horizont*qrlaf p*q. xkv qu0g0.z +t:aal metal rod if you str0:kq al0qz.xtgp * q*auv r.f+ike its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but the buot1wh5l+q:w mgv824o xlapq8 p6 ug/tlk modulus B is nearly independent of temperature, how m/8qthtxvg 2o15:+ 4p w lg wapou6l8qwould you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular azi.b.x-ss.f water waves decrease in amplitude as they travel awa.fx-siz. .b say from the source.

Two linear waves have the hau84hjnj/e oy+i5gm8a25sl6: auw i same amplitude and speed, and otherwise are identical, except one hasyhwj lj88e2 +a5 usio6ani:5 hm/4gua half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord y5s inv.:ce9oas in Fig.o:ve9ny 5ic. s 11–33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three se- ld) ddf4-eiugments, are there any places you could touch it with a knife blade without distulfdddi)e u-- 4rbing the motion?

When a standing wave exists on a string,-rx +wt a3)g ytmpqu*4 the vibrations of incident and reflected wavea+y4*r tt 3mq )px-wgus cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from on/fdk+x1)i8slgu 5 d j b e)hbq4.kn-one place to another, how might we detn) /hblk45 bxie8oj1qd+ )-f .kdsnguermine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total w)ppo3kdt5t6t9i t*7 nm6k rndistance it travels in one pe6 drk9tp6itt3*omwt 5n7) n kpriod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is kuh+m cbz iorr 1-,;j385 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cou ; 1ic 3,ro+rk-zmhbjrd?    N/m

  The springs of a 1500-kg car compress 5.0 mm v-zp3i )xpc8w when its 68-kg driver gets into the driver’s seat. If thevzx)3cwp-8pi car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3wrqj 8t+e gyc,n.)+ud.6 cm when a 2.7-kg fish hangs from it. (a) What is tdgn ryt e,c 8)+uqj.w+he spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass49: ibrxvup 2f of 0.60 kg is hung from it. What isrivb9fx2p4u : its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating thew55st+sc -.qeh wm mj13eo: wz position x of the mass in Fig. 11–2 at times t = 0,mze3.5jt5h weq- sow+s wcm:1 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. The web vibrates predom35f 1zi i dct*ya5 hee-+rl8wxinately with a frequency of 4ifi5aw3cz*5x1 y - ldr+het8e.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 frequenn4j4vi00tw d,vv (sgm cy of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 H4 vj gviv0m(d s04,twnz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second yxgxt *;v ))sn z ddga bl(gft(,;.bj9with an amplitude of 0.13 m. Determinvn) sxga; jf(b)gxl,d*9gyztb .;(t de
(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 i 38 gpfwmg,rrfp17u: z7 djk;us the speed of a SHO half the maximum value?7mjk u;wr:d ,zpf pgufgr13 78$\approx$    A

A mass attached to the end of a spring is s5 rrgl .n,4sxic,ji- ntretched 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 wibp71zfyjle m/i //t9fwe)4 stretched an additional 0.130 m and releasedf /tfp 19)j bmwi4/zel/eiwy7 , 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 ;/zr1x7lmk rt(g yxt1constant k = 280 N/m and is executing simple harmonic motion. When tk71t;tzryglx(/r 1 xmhe 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 toy popguntfymo 1gjhz6 xv-e+;1 0.200 m to “load” a 0.180-kg ball. With what speed will +m;fot1- gz1hye vjx6 the ball leave the gun?    m/s

  A mass sitting on a horl3 orc( o0bg-nizontal, 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 the spring compressed, the mar-(boolng3c0 ss 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 = 0.45cos6.4tm h hh/ ,2xjx7u9x5mfu where x is in meters and t uhx 2h5 /h fxj7xm9um,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 equiles r3e7m d4ua-ibrium is the energy of a SHO half KE and half PE? dram37es u4- e±    A

  If one vibration has 7.0 times the energy of a second, but their frequdzgix+h.)lwq rgq- . ). 0ruhdencies and masses are the same, what is the rard-q0.d qxu+.h g zhig .l)wr)tio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once everm+zi8wu q7s 9ty 0.65 s. sq789w+um i tz
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs, eaci (m.(mwmp ub2h with bm2.mu( m(p iwspring stiffness constant k (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 *-udwcph 1,od meters and t is in seconds. Deted ,wpo1 hucd*-rmine
(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 SH .t jfwi( mlu.ac;3e8y ,imod3M, 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 th:rs 6dq)yd1fz emow922lk qxgo, v8( re end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determinmyw s(xv)roe1 g69d2q:8fkor ,q2 zld e
(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 e 9s) 9yrjkw1wconstant 305 N/m vibrates with an amplitude of 28.0 jek1sr9yw )w9cm when 0.260 kg 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 p exjf,bbcg5. d+gt(:spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontal spring q+hzteb m )* ,yag7/zbwhoqtg7zh b,* /ezma)b+y se spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reaching his p; hoq:s/q an7lowest 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 lev7:hqqa so; p/nel 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 exactjcoet )gf),mn t6n 3f4hqh.)c ly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per sel,5nro ms e//jcond? lm,/sne/5 jo r(That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is ik x(qxn/+l4jv/t rsa+1engb* ts period on Mars, where the acceleration of gravity is abo*( s1nkatl4jnqg x +/ervb+/xut 0.37 that on Earth?    s

  What is the period of a simplo7ygz8hc j-7uaar l61 e 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, the pendulum bob has a7g5 gg;wnga3b( wdk*m mass of 365 grams, ank(3dwmgna5;wg bg7g* d it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If thzmxi 206aa jdm)n:tj2 e clock loses half a minute per day, how should you adjust the le2i zjam0:d m)xja26tnngth of the pendulum? shortened by    mm.

Derive a formula for thcdu, u .jz5z.gcuhpf0 6/b(j ye 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 oscillatew(wx70 au1hsks at a frequency of 2.5 Hz. At it is released from rest startin01k whaxs (7wug 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 b( 45nk:cgf9w ko qefy7ow of his anchored boat every 3.0 s. He measures the distqckof 5:74n(g y f9kewance between 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 t0o1rajn c:iddtau , 3 -qm,e,qravels with a speed of 343 m/s How far apart are the wave crests (compd cair,0 djm1o,eq-,:3aqtn uressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kiloi 2qrbhi 4m y,)7hg-dzhertz) and travel with4,mdy-ibz g )7qhri2h a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves2/e. 4 jxdhde iij3i:;8 mamuq in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elasz1 bt0,wugq 7dtic modulus, but one is twice as dense as the other. In which rod will ,0wbt1 gduz q7the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two suppodr22*+7iml swdymo0 zrts 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support to the other?*o+2m27r 0dzid lwsmy    s

  A ski gondola is con4ycd.r+s:- z 0 o.rfssof eyu,nected to the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its r us0o:+ -.ys4oes ,rf.fd zrycun, 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 just below the sur/sfa2eddr- r 3face of the sea. He hears the echo of the wave refd3-r2a/ def rslected 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 ear ta+tp1w.jt :gthquake travel at different speeds, and this difference helps in locating the earthquaket.1pj tg:at+w “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 can be approximatedcq*scf+e c9as xm03 *z 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 objects begin to leave c* m9*3cqs xcz sf0ec+aontact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio ofp5w9(n rtba4i (a) the intensities, and (b) the amplitudes, of an earthquake P wait(nbw5r 94 apve passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an o+*l3;s a3s9t6nxubwdubk9hx crc 70 earthquake wave passing through the Earth is measured to be lbo+ntd9ar u xx*7k3 w0; shus36ccb9 $ 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 th6+v mywivl/i; yon( v4e same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two wy;6ni(vloy+v / vwmi4aves?   

  Two waves traveling along a stretched string have the s6mqbw0sz,q l7 ame frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two 6 szqwml0q, 7bwaves?   

  A bug on the surface of a pond is observed to move up and down a total v g+q3-flt81:dtlkof kertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If thekdktltg8+- : qlff31o 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 t2h)nl.473bsk bt s/ :fgbjzc zoward each other. (a) Sketch the shape of the string at the moment they directly overlap3 :)zbthb2/kbzl. s 7fgc4jn s. (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 moment?

  If a violin string vibra4nbjh1fg-l3l ;+ g.owx m0raltes at 440 Hz as its fundamental frequency, what are the frequencies of the first four harnl +h wl0.1m xfr4j-;glabo3gmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequeoz-d uu;g6 9psncy will it vibrate if it is fingered one-tup69sd- u zog;hird 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 joz2/c4d5p v /adgs3 qin four loops at a frequency of 280 Hz. Name at least three o/s 4cjzqd vd23gap5/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 isog ifj/8/ bkq8 92m/s If the frequency of standing waves is 475 Hz, how far aqbgi 8o/ k/j8fpart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350,ksqxk6 e z.z9 Hz, what is the f,xe6 .sqzkkz9requency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The4zpsjn; l*g+x*ma r0 e 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 o+pmzs*4l0ae nxg;j *r vertones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measurehl7oij wj;7 o8j*fm; jd to vibrate at 205 Hz. By what percent should the tension in the string be changed to7*o ;jlw8hm ji;7jjfo correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at , f5,knb8q:o0q- bh4ew vs bow200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension owhbb qbsk:w-8,fo 045 nq,vein the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mec434t*e p jj4r de 9rb;fxz/qnihanical 60-Hz vibrator. The string’s mass per unit z b 4de;4/rjx jt*pri4 qenf39length 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 8ph4wdz/d i+ qpulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L betweei/z d+dp4w qh8n 10 cm and 1.5 m?   

  When you slosh the water back and forth in arbo v*znl f6,9y p/u7v 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.76vz9ly,nubvrp/* f o What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s st+ va22xhv cl+frikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident angle of 42 +2av c+vflhx7 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes fromr8, t ss9)sggs 2.8 m/s to 2.1 m/s )8,sgs gs 9strIf the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in 6vfws/j:j0oo warm air when it hits a layer of cold, dense air. If the sound wave hits the cf6j sjwoov/ 0:old 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 tyxh2hmbk*nm1(xlx eph ;s 4.9o pes of rock at a m .x4n;lbm*o x9heshk ( 12xhp38 $^{\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 diameter3gy )zwex;5g/ffc bt8 pme x+2. According to the user’s manual, the dish has to be pointed in the direction of the satelf 53+z ew2)ytcf bx8xm/ g;pgelite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velfga6 q:n*kgh /b h34gcocity 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 war*h3gk:fcqb /4 hn gga6ning, 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 9r ;rsb/fnnk)stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car,nr;) b/nr9f ks 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.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, whu-femy zt,t 55ich stretches the net 1.1 m. Assume that the n5 mzefut yt-5,et 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.9hw ife-e x8gn :pt*,u/vv3gl The mass then falls 33 cm before it stops and begins to rise.i/v*uxgg3w- p 8e 9:,lte fvhn What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54y4g.wnf9ei8qrnc 15f ), compressing the spring 5.0 m. (a) What is the springy ngf1w4eqn5.89 icrf stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameuxih 5g+,,l ajdyfc* 0ter 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 (Fig. 11–55). Estimate the spy, u * g,x0hjc+5faldieed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center i xrtrq20: h ao9(y ueic1u8u31z*rhzof a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the s1e3ic2u azzrhuh9 q8 oyu*(ri r10xt :ound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t wd5*sv2my6z)c( a:5g h etktr41lk rbehere x is in meters and 5lv s5md1err): ak6hbt g* ztk(c2 ey4t 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 oscillates with frequency f. What is itmb) a;q8cfi3 flt4y0 4xlwn g7s frequency if it accelerates t0bg48im;c73xlqyw faf4ln)at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. Whtwtkm4og7mo/-alat86c+l n.en a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a wh.64noml agk -tot+t8w7/caml ile.
(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 a / ae)nbnvx xbl7o*p*54n ij*3xelv:nre tuned to play at 392 Hz (G) and 440 Hz (A). nxv*5)be*:l nxpenoab3 xj*vil4n /7
(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 travelilog;a4:c kp* hng down 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. Why?) (c) Is the wavelength greater in the heavier sea :*hgoc4;lkp ction of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 H-x8,ng fw,kk kz, and the tip of each prong moves 1.8-g,8,kwfkk nx 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 frequeo, 3(dzh3lc uv*iros-ncy 1.5 cycles per second. What 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 duhvcd-olz is o(3 3*ur,ring the oscillation?

A string can have a “free” end if that end is attacheymkbbvq0wx i1y+i1n b 5f2)x+d to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the w+f2 +kbn)qxy wi1xbvb0 15 yimavelengths 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 s — each one-way sw /a kto0)oqx32c wy4leff/b8 eing takes 1x yae o 2to3/q4fb8wef0k /c)l.000 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 direction or coi.3u ub7:rqpl- 9t) ab,f8k)uqcl olan swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amountto 7l8ubr- ,cq9ba 3. :lulfqpui))k o? [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 3pl2rt;c*4yyc xj/g*fj c:nw123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses firsgc c/c*yyx ;:wn2r fjl* 4pjt3t meet?    m

A block of mass M is suspended from a ceiling by a sprin*ulx 8veosyb*m 1mf7 a(ey ))ig 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 block? (Assu*)elo *i)mbs(aeyyvx um78f 1me $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is 22 cg,pnvp1t .g *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: Rt1gcngpp.v,* efer to Table 9–1.]    s

  A block of jello rests on a plate as s+y-zwmc-o0u - oa3hyt9b-iq chown 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, g3-c- hc io awy--t0zy om9buq+iven that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz