Give some examples of everyday vibrating objects. Which exhibit SHM, at lr w-4zn)ta4xo east approximately 4on4t -zrwax)?

Is the acceleration ieo 38.uwok)( 3xhaku of a simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a -o,b/vooy(k:kjt* rbh ms:z7 piston in an automobile engine is approximately simpl: s,yjrt-(o o:h7kb/vo bkzm *e harmonic.

Real springs have mass. Will the true period and frequency be larger or srjj icayae4 9*j(2 rd l8e22ajmaller than given by the equations for a mass oscillating on ay 4j j ljj e*2e(i2d98rarca2the end of an idealized massless spring? Explain.

How could you double the maximumqv3z)tb,dja)3qv0q y speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook ofni.a/y:;6 vi4raripzv 4q *dn d1t o0n a vertical spring scale, and then is rele .6pd1ya/4iitn04ir:vdq azn;n ovr* ased. Describe the scale reading as a function of time.

If a pendulum clock is accurate ne6xppq:-oqx: 0ffn 9 at sea level, will it gain or lose time when taken fx0q-e 9:6qpf:px on nto high altitude? Why?

A tire swing hanging from a branchgf c28i6wa- nh reaches nearly to the ground (Fig. 11–48). How h268agci -fnw could you estimate the height of the branch using only a stopwatch?

Why can you make water slosh l qx4m4fdug5e2zja n d,.d3 i7back and forth in a pan only if you shake the pan at a certain frjd u gddeq4al5,mi7x2.zf n43equency?

Give several everyday examples of resonani dwo -fj3 gak*k(ohepla;5- +ce.

Is a rattle in a car ever a 18 n/jwxzx qv)resonance phenomenon? Explain.

Is the frequency of a simple periodic wave e g:mkxy;lv3o.qual to the frequency of its source? Why or why n:gxy3; l kvo.mot?

Explain the difference between the speed of a transverse wave traveling down a cxgs4 6h3xny6 eord and the speed of a tiny piece of the x4hsy nx6g 6e3cord.

Why do the strings used for the lowest-freque4hcnwm0(o/tmam 6r:sncy notes on a piano normally have wire wrapped ar r(mc:0 onm s6/mawh4tound them?

What kind of waves do 42enc 1tult h ,:)qhhuyou think will travel down a horizontal metal rod if you strike its end (a) vertic,uc4l e)qh:thtnh1u 2ally from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but the bula.ia pt2 qs6r7n79s iwka*i; ok modulus B is nearly independent of temperature, how n7t*wq2;isk9a ii7.r6ap oas would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplit zrp ju o0sw.wuv;n.1hkne8.ec 6w1k 9ude as they travel away from the sourcenc1ve8o 0 k9 wrwphe1.k;wsz .u6uj.n.

Two linear waves have the same amplitude and speed, and othe b +-1:mhfjwc2o8 mk e;(ovro a7oky1krwise are identical, except one has half the wavelength of the other. Which trano81;- 1:kewhyaofk om v7(2 c rbko+jmsmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between twogdr h vyr*-s0*1 yl4ln sections of cord as in Fig. 11–33, the frequency4v *1hdrnlg0 y-s yrl* does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you euj1lb0 - w5d8r w6gcncould touch it with a knife blade without distu -nruj w5wl08gb6 ced1rbing the motion?

When a standing wave exists ong 9 dwaxa.pd04 a string, the vibrations of incident and reflected waves cancel at t9g0pdxwaa4 d.he nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how *zl 6 2ea1 o/7seghowtmight we determine whether the energy waglhe7z6 / tsao*2we1o s being carried by particles (material bodies) or by waves?

  If a particle undergoes SH *et4p 3x.d-uxmlxu 1 aa,w:rwM with amplitude 0.18 m, what is the total distance it travels in one perl *-w, rax4.xpta:xuuw 1emd3iod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 cmw(ylstc); yi1 dl(ua) lon ) s ;(wluclyy)d1ati(g when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 15009gaqz7k wup*4hx.d5(l f(l tz-kg car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what wilapl zwfg( .dhq5(7 k 4*t9uxlzl be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from i dg0qcyrix419t. (a) What is the spring stiffxi r9y4d01cq gness 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 mass of 0.60 wla7bm:vp5o .8v4es zkg is hung from it. What is its frequency if only 0.38 kgmz487apo:lw5s be. v v hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig.cr7j 1f8px 7om 2qdw;w 11–2 at times t = 0,t =x ow qr1m dfwc7p7j28; $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 ,p)nma i dyr.(spider’s web. The web vibrates predominately with a frequency of 4.)(ani rd.m py,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 frequenav4em e p17uc0cy of 0.88 Hz. When an additional 680e4u1 vpcmae 07-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 of a spring vibrates 3.0 times per secondqb11:so7e x, z f(fgbcxr y2-b with an ampl 2oczf7 b1- bxesrfx by1:(q,gitude of 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibriekxo xwn 6-pem3:m i6)a dhi;;um is the speed of a SHO half the maximum valp;xmn6 i3 io ;:wke6m)-xda heue?$\approx$    A

A mass attached to the end of az1f j0l ff(t(h 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 stretches a vertical spring 0.315 m1b:jggop *-o h8af :al. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium paa : *8-lgjobo1f: phgosition again?    s

  An object with mass 3.0 kg is attac2+u gr*8b (,ry hgvjhched to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m frov8gr (h+hyu ,*r bjc2gm 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 toc0l* i8oq g3iiy popgun 0.200 m to “load” a 0.180-kg ball. gqio i 8i3*c0lWith what speed will the ball leave the gun?    m/s

  A mass sitting on a horizo q4jf1yt +s5s -)ar3s lqom;fevlp .3tntal, 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 .-vfql 3m;+tter5l3ospa4 )qjfsy1sreleased 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 eqm ;nmt+j+2awc9kmbkwk+5*i b6 1kiuquation x = 0.45cos6.4t where x is in meters and t is in secm tmb;k5++2 q*+au1ck 9nkjbmiw w6kionds. 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 enen-v+xcnm 96 wlrgy of a SHO half KE and half PE? n96m-cxwv+ nl ±    A

  If one vibration has 7.0 times the eneqr ( ff5h:tb0ldp r3e;rgy of a second, but their frequencies and masses are the same, what is the ratio of their amplitqpfedfb3 rrh0 (5t: ;ludes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging lig( s0 adbr9f0bxht spring once every 0.65 s. (asrdfx00 9b b
(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 supportni+sc9ks) ,kp+ g -htied by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration? ksnt9hg+)c,k+i - pis

  A 300-g mass vibrates according to thegzo kz-)iud fk ls*-:( equation x = 0.38sin6.5t where x is in meters and t is in seo(ku)* --sd:kzzi gf lconds. 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 nuydif/5o r* 4,*qwu lexamples of SHM, 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 horizonr2 z3.u33x mrh1d kvhbtal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/3bhmk 231.zxhrvu dr3s 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 rdaniqpu.kj2dn 8pg f.6*5n2 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) wiupqjna k..g*i f28r 2d5nn pd6th 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 stims8o: jv1xa* ):7xnoy5vcgcyffness 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 springk1. r)o nu xmttl95m(r whose sprin5k. xtt )onmlr19(r mug 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 fr nsz5a*(n9ybwom a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s.5(anwyn zsb 9* 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 s. W4tc dp6j ify2g:7(r5w ddjt-rhat is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if 6ykjjd6 slc8q vm li7-,*gy5sit is to make exactly one swing per second? (That is, one complete vibration 5d,ljs78jm lg -viyqk6cy*s6 takes exactly 2.0 s.)    m

  A pendulum has a period of fq1 ue1vw (7sadl io(.0.80 s on Earth. What is its period on Mars, where the acceleration of gad(v se1w.7olq u( if1ravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80qkxef +9 uva,xg;jxn+ e;,x l: 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 fok ,s wo18ll;3o;ohoj01 5l *kbipu xpendulum bob has a mass of 365 grams, and it is released at l31lu1lj p5kowox sko o8,h* o;f;i0ban 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 p1ak+5/by ixji4blq* h endulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shortened by*bbixh 5la 4j1+qk/yi    mm.

Derive a formula for the maximum r bq+7b x3odc6speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates n/ lyqdi n2*: n,gck(zat a frequency of 2.5 Hz. At it is released from rest starting atdc: n*2,n q (gkiyl/zn 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 b/07z, mk*lp jejk 4x(w3fynfjoat every 3.0 s. He measures the distance between two crests to be 6.5 m. How ky3k, nfj 4 wf e0mjp(l/x7z*jfast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 34rm40 )/m-; 9we utef)wh smamf3 m/s How far apart are the ))mtewamfs9 ;ruw4m/-0mef h wave crests (compressions)?    m

  (a) AM radio signals have frequencies between /)pfttf)o4 o x3t) dui550 kHz and 1600 kHz (kilohertz) and travel4 o) i)t3d xffup)tto/ 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 zd0e ;/aygi1lof longitudinal 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 dexnjh1(4 c 8u; bee-qstnse as the other. In which rod will the speed of longitudinal waves be greatexs-1b;c(8e4 u njeht qr, and by what factor?   

  A cord of mass 0.65 kgh2 sbw.9gr 2)m o:noon1tcc3 s is stretched between two supports 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)gc1t2.bworsso:3hm n2 o cn9 other?    s

  A ski gondola is connected to the top of a hill by a stee0a+o kmfqo,edxhv - 2s iz 8mvo c0u8m,kk:1,ol cable of length 620 m and diameter 1.5 cm. As the g,som1vk0o f :xqvmha8k,- ioc,0z ke8 +ou2dmondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship jvs* 8xn 8*6kg tnto 145ufkxdmust below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep isuxkgo 68n*td*4 1t 8nv s5mkxf the ocean at this point?    m

  P and S waves from an earthquake travel at different spee73j bzms3u: fp5 vkg.rbc k:e7ds, and this difference helps in locating the earthquake “epicenter” (where the disturbance to3ueck: 7sr 35kj:bm bfzp.g v7ok 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 approximated by a sinusoie.t a(ny -,heqdal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthqu- eye n.,q(thaakes, 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 intensities+(u4/d mzp vna38svon , and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a) ov8/ +4z3d mvunpn(as   (b)   

  The intensity of an earthquake wave passing through thq .hvk7dtko 86e Earth is measured to be kv8to6 7q h.kd$ 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 th,is 9gnik9*.tx(jk r fe same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitude fing9xstr.,*9(kk j is of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but v 4l5mkue( )zymrl45w one transports three times the power of the other. What is the ratioe5y wz (4rvm)54llukm of the amplitudes of the two waves?   

  A bug on the surfaceymeq-e)v9s9o9-khwu 8 d 5u dg of a pond is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, a- g95)vsdyq me keoh9 uuw9d8-s a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each otherrj0poku9 8: bsr6d w4q. (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, uorj04bd8ps6 : 9 wkrqthe string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fund .x: ,ypdg.pb:c akxz*amental frequency, what are the frequencies of thpd.xgz :cxbaky*.,:p e first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency w)fof )uha1z0e v/0n i2:qcdnvill it vibrate if it is fingered one-third of the way down fromnaff0d)vqze:)nc /u1o2vh i0 the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 dss2it)* f*vuHz. Name at letdi vs2u **s)fast three 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 standing wavd5ii9lo3(x. b7 burc mes is 475 Hz, how far apart are two adjacenmb9duir ( ocbl37i5. xt nodes?   m

  If two successive overtones o2 :a r*hck+5hgmg s2ulrd(,wkf a vibrating string are 280 Hz and 350 Hz, what is the frequency of t+gkwuk:c, 2glr5 sh 2arm*dh(he fundamental?    Hz

  A guitar string is 90 cm longp-q* :- ov vhpn)x; bp o-vol;-rpt7zv4du7nh and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a ovzxh)o dp; 4lh p7 -onvvv-p p-:n-rub*;tq7 tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string :cluikp7gt-0eszmt 6xj3p) / is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So thej3 pgs ilt cp6:um-7)/0kxetz three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is mea 0,gohvb4h3 r.quq*gwsured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct th g4u h,hw0g. *qq3brvoe frequency? decreased by    %

  One end of a horizontal string is attached to a smalxq vl0n(1c yx/l-amplitude mechanical 60-Hz vibrator. The string’s masslqx0yn c/1( vx 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 lengcbk+t 7d6zt 7f zeap);th of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L betwe7 d ;+bzazp7fetk c)t6en 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the ri ic;01 hucixv84g/tajyz u(*zw) 7c;vi yy*xtght frequency, the water alternately risvcgiuy c0wx)*jta74 *uyizv1;/ i t 8(;zxchyes 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 boundary withqp6/oks ph2; 5l )wgudcd j72zin the Earth between two 6z w/j2lp7k2u o 5hs)qdd;g cpkinds of material. 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 underwater “shelf” where the velocity j57 ao+l za/pychanges from 2.8 m/s to 2.1 m/s If the incident ja7p+ z5ylao/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*bjqkqq/9 v9av jp1z+ v5br;u a layer of cold, dense air. If the sound wave hits the cold air interfac9qb5vk1/qj vz9ba+uq*pj ;vre at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types of rocw7yn m e87b (kdyld3,hk at aeh dyb3k nwy7 md8l7(, 38 $^{\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 about3s y5*n 3 qvon6;jfch+ zzioa: 0.5 m in diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellitec;izjnof3qa:5z+ v*3 y n6 osh, 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 kx9 hsd p-518frkw u8dfm 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 kn8sxd189pf rh5fuw-d kowledge 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 hae+ fkrs qd5e1 ,r:)zwas a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approxierdw :+krae1f)sz q5 ,mately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretches q ) dtp,3q)gc/eowta ki8my7-the net 1.1 m. Assume that qagq 83p)wei k,o)d/7-y cm ttthe net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of9)1o :cg gugw2+euxhg a freely hanging spring. The mass then falls 33 cm before it stops and begins to 1g weuhog+ :g )cg29xurise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), compr 9:mwpd*t4cxyessing the spring 5.0 m. (a) What is d :wpt*x9m4c ythe spring 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 (diametel6c *b e 799pupg m.,ghe8xqlcr 8 cm) at just the right pace of about 1 step per second, tlc 9ppm7eeb* 6.ulx 8qcg ,gh9he coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.98vnu 35n/nqjmir5/fhgrl/2.zf ml k8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequenc2l.v 5/qmj85zf/ugk 3mrh/ nlnin9rf y of the sound emitted?    Hz

  A 2.00-kg mass vibrates according tot0p g 4kyb 5v+wwq6btmvwa/jf):6 ce) the equation x=0.650cos7.40t where x is in meters and t in seconds. Determine bqkpwm/ t b f:j4c6wa0y) )gt6w +5vev
(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 oscillatt h 1oji1aikrcn:+0 ms7y/vnjca;5s4 es with frequency f. What is its frequency if it accelerates at 0.50g (a) upward, n s +t0ocmaiy;vinc7 kh :j js4/1ra51   f
(b) downward?    f

  A 220-kg wooden raft floats on a m)-w6tznmwd80 -g-rh7 bejfilake. When 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 whilz8m7twg) rj -0-hw b n6difm-ee.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and 4408khxfgo8wi5 n)k*jr 212qbzd Hz ()nzo wg 882 ihrk2k5bx 1fjq*dA).
(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 twwy q mqhg,q5a z)9fu)/o-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 section of cord oq yfwm/z9) agu,)qq h5r the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and thzz53pxeu j 80he tip of each prong moves 1.8 mm to either side of center. Calculaz pu0z 5xh8j3ete
(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 hab;8fp)ja it:7n, adtormonic motion of frequency 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 th: jdftni;,)ap8 ob ta7ere (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 rin5i7p ;ut mtvhsmj63z )g that can slide without friction on a vertical polehj7 );u 53ittspm6vmz (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s zd)+-38 d/0 pwofr qfxc9wuxw 0( bqhu— each one-way swing takes 1.0030d 0h8u ufbz-fw9pxx+qq(cr)o ww d/0 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 vertvl yn-4 uuqr *bha2j1*ical direction or can swing as a pendulu**4a jb q1h2uy v-rlunm of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched undefsgvpmzbn):zgcl, ; ps 9 -*r9r a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse 9sr nb -m,l:psp cz9v;)ggfz* is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended frok h;s*4mdx8 iom 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 oidk 8;hmx*o4sn top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel c denm7;+/u/j unyfhr4rane cable is 22 m long and has a diameter of 6.4 mm. A breeze start/ je4+/yun f7 dun;hrms the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as sho o-wpz-20i, 4zmnc kepwn in Fig. 11–58 (which also gives the dimensions of the block). You pusi0z, cnk-wpo -24mpezh it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz