Give some examples of everyday vibrating objects. Which exhibit SHM, at least asa)0*/ (be hz; -byfagb b scsdat2f,9pp0s cs sf)ag (;/ -b2f9htb ,badyeb*azroximately?

Is the acceleration of a simple harmonic osc;,k3 coe9obl gillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximakepahcc98yb6(( ig 8btely simplee (b6hccyib9g k8p 8a( harmonic.

Real springs have mass. Will theyg+oqd;6bg9+kfmr-wgn3p8 aki-: s t true period and frequency be larger or smaller than given by the equations for a mass oscillating on th f ykpo+igtkrqg6gbn:8-w-m 3sa; 9d+ e end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillae9ukj0chz3 /tk*v +( asu2tjitor (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then is , 6yr.tzdrifld4s 7 f/znl5+vreleased. Describe the scale reading +nf .r4dtrlli75zs,d/v f6yz as a function of time.

If a pendulum clock is accurate at se2e dxy5wrqbs;dguty2(c (* 1r a level, will it gain or lose time when taken to high altitude? Whdse; d2 w u25gyrbytq cr(1x(*y?

A tire swing hanging from a branch reaches nea.tn); s. pbhznnx*c2 qrly to the ground (Fig. 11–48). How could you estimate the height of the branch using only x hnnp*t).s2q ncbz.;a stopwatch?

Why can you make water slosh back and f/jq9fu;- f3k pa yl1dborth in a pan only if you shake the pan at a certain freq bpudky9q1fjfl3 ;/ a-uency?

Give several everyday et /h6r)vh eo*ej+d kv9xamples of resonance.

Is a rattle in a car ever a resonanck3-mg gmm+9s1:moaxh e phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its 8uq2ux;xj o*hz:xy -zhgmj 67source? W; zxj: xo-u g8x7my*2hzhq6j uhy or why not?

Explain the difference between the speed of a transver3sq;qd5tpn qe z: 0vq8se wave traveling down a cord and the speed of vq5:;z 0qtdenp8q3q sa tiny piece of the cord.

Why do the strings used fo( q:pvjbl)7 0 *plf/yzl6 wxwor the lowest-frequency notes on a piano normally have wire wrapped aroundz p:l /wl*q6wy7po0 j vf)xl(b them?

What kind of waves do you t ,j.d;1csxw -(*thlo(-c 8p kpdsh iswhink will travel down a horizontal metal rod if you strike its end (a) verticallyd 8(dh,ws p1-o*c -s.jxhi ;ctp (wlks from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temper *51yndj3hricxwlj 02ek (wf:m yk:4k ature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with tempjkw:m5n 1 d*2eix l3f(k40jwc hkry:yerature?

Give two reasons why circular water waves decrea w -jrvg/8hg-ese in amplitude as they travel away from the sour -hvgr/ej-w 8gce.

Two linear waves have the same amplitudeurrv h,1eb5q:b nw(l7 and speed, and otherwise are identical, except one has half t q,5w:7levnuh1 rrb(bhe wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wa ho5fk:.q ufn6,4po*( qhxwyzve crosses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Expwq4h:fo6 .h kxqy(o, fup5*zn lain why.

If a string is vibrating in three segments, are there anyhsz)hjs:vu ( , places you could touch it with a knife blade without disturbing the motionhh) s,v:u(sj z?

When a standing wave exists on a string, the vibrations of incident a8cu /gh)nso0hnd reflected waves cancel at the noosn8hcu)g0/h des. Does this mean that energy was destroyed? Explain.

If we knew that energy was bec y 0c:sv rvlbe:0a,xzc p 8(pp*6mze(ah//ksing transmitted from one place to another, how might we determine whether the ecp/:h k /80ac,( :v*axzmlevyp(sez6bpcs0 rnergy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM wixq ogi)68z +hmxj-o. jth amplitude 0.18 m, what is the total distance it traq .-o jgx)h8i+6mj xozvels in one period?    m

  An elastic cord is 65 cm long when a weight octct1nuw/ :lijkhqy - 6z+ kwcp +u16q0ng/,d f 75 N hangs from it but is 85 cm long when a weight o/cg6ty6:kp z+u-dn1l wnci kuj1h+0/c wq t,qf 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg d;c n;+5h4 h+wpnza/-vkdnaj ariver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of vibratio;5hcv4nn + z aahw ;/akj+-ndpns?$\approx$    Hz

  A fisherman’s scale stretcheshgldyo.393 kbj/utw ) 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness consta/3wy.bk t9od ju3g)h lnt $\approx$    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 0.6 ,;bfo,wdib:hq6 2 lzx0 kg is hung from it. What is its frequency if only 0.38 w;qbz62 o bxf:,l,hdikg hangs from it?    Hz

Construct a Table indicating the position x of the k+-wqez*a6 i kmass in Fig. 11–2 at times t = 0,ike+a- w6q *zkt = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 x f3kj:y te7j1predominately with a frequency7jxj 1f e3ykt: of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. When an n:vwf h9 )*kyiadditional 680-g mass is added to m, the frequency is 0.60 n hv)f*w :9yikHz. What is the value of m?    kg

  A 0.60-kg mass at the end of yohdg9hc+i ,of: u;j;ldw/:nttp ;y1 1st *g na spring vibrates 3.0 times per second with an amplitude of 0.13 1 ;;w n 1/utp*f:dt9oihyn gjdcs th+yg,o;:lm. 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 cr9w1i rove(dc*0ab( equilibrium is the speed of a SHO half the maximum valu c1do0rbvw9icae(*( r e?$\approx$    A

A mass attached to the end of a sprih 8cu -bdvx (c9q.1 x*uh6aii*m4ssytng 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 stretcheu93tux0ko c u1d l5tpb+*v fe*s a vertical spring 0.315 m. If the spring is stretched an additionad13kt c v*ptub5xuo0*u+lfe 9l 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 sti6ul fp 8mcx0jtl6()cfffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving xm )cc(up866 0tflj lfwith 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 sprb/yus;0 1 cd3ak2 ;oipt4aqtx et ).dh2 sg7lling of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what sp)2 dglu tspq3 ykihsa2dc b0/a;x.l 71e ;4ttoeed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is 2szq7 t5xoz 8kattached 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 5s8z2qz7ktx omass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to q:;vxv at 7b72lv 5mxnthe equation x = 0.45cos6.4t where x is in meters and7q; 2a tbmvx x5:vvn7l t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO *34p6 vibl+ ;hrxx+swf/ smkwhalf KE and half PEr p6kwsw4;+hf3+x x*mlivbs/? ±    A

  If one vibration has 7.0 times the energy of a second, but their frequekd- t:bey -pg:-:w dhencies and masses are the sade -w b t-pgy:k:-:hdeme, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once ev 2**ib.k ku8c:yhwrbr ery 0.bcrr*. w 2k 8bkih*y:u65 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 identict.bj +w+- c is,zakzl3al parallel vertical springs, each with spring stiffness constant k (Fig. .sz ,zta +bc-wk+j3il 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 ij.zu*8bdt94yxmrd 74c9 jscon meterstjc7yo9*.r 4xzujs b dcm849 d and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHuc;1o tb7y:cd li 8s8gM, 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 horizontaljd)h8q8s em9a spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial jdms qa8h98e)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 sprina5o1uc ajtd* h.8+ p n1/kgovtg stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs froo tcp58auj n ath1k*d +vg1o./m 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 twd1s.u crpc9; q8h- qnpba0w8o two springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fl u5d7jn+2ujh*ox f yk 2/tq7jixed horizontal spring whose spring stiffness constant ihj2juu j7tqfx 7/n2+lk o y5*ds $ 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 s:l.o:bavt( s;zw to2 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times ins;oo:bzl(t wvt. a2s: 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What isufc1, vscb9px6d vt)s2frh 3* its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simplet y:m2jl8g,zs pendulum be if it is to make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 lt j8,m2 :ygszs.)    m

  A pendulum has a period of 0.80 s on Ear: - bu*0q7vlxkf: ck;utgrlv, th. What is its period on Mars, where the acceleration of gravity is about 0.37 that o; k*,:kft rgbq0uvvcl-lx7 u: n Earth?    s

  What is the period of a simple pendul )mk3+t:m vcz sscc1d+um 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 pendulfrpz3+dt ;cz(1 +tlz5darr 0v w;.xmn um bob has a mass of 365 grf; zv z t+ pm3c+t 5.radrz;1r(0ndlwxams, and 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 the clockmow bd :/ l6f70qepw/j loses half a minute d /q0p: 7blowe6wjf/m per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximu47qj/zg6:efx q3rhqnm z om 4)m 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 i 0: krlt s0riwh)wl,jpj5)2t it is released from rest st)r2wt t,:lhwr0)kii j5s0pljarting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of hiu.2 5ehc wp68l)zzklt s anchored boat every 3.0 s. He m el kt)zzhl .p56uc2w8easures the distance 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 trazhg2 b5hw(3 davels with a speed of 343 m/s How far apart are the wave crests (compress haz dh25gb(3wions)?    m

  (a) AM radio signals have fg 0d y s9b,qh3(h qygq:ig8c:grequencies between 550 kHz and 1600 kHz (kilohertz) agh gcg yy9s3b,q:qi q0d h8:g(nd travel 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 longitudinal waves in ff5h ;p7x( 1dwro qkink).4by
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but lbw 1tvfv;;ui,- mh t:one is twice as dense as the other. In which rod will the speevil-hfm v:tw,tb;1 ; ud of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m aprv u:v ,2p 0)oxyhvniv1d v7b5art. If the tension in the cord is dvhv02) pv:rb uv57nox,vy1 i150 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 ste59jhlw4ma4;qb l.t h+r;qs meel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for 4ha+ tm . 5q;qlw4sbrl;em9hjthe 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 jus5- stffl2k:rpba p:8 rt below the surface of the sea. He hears the echo of the wave rek r:-p5bfar2pts8:f lflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, andeh-ydflik,h)bx1 01r this difference helps in locating the earthquake “epicenter” (where the disturbe1-bhhxi ydl0 ,k)1 france 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 approximated by)3mxxd0og g 4v a sinusoidal transverse wave. Assuming a frequency o3gvg)oxdmx 04f 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 intensities, and (b) the amplitudes, ofo p5a q6j ul1u0xp8hj ;q6-j3:jxqx qg an earthquake P wave passing through the Earth and detected atjp1jgu8-6 qpq:u5jjx 6hx qlo;0 3xaq two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wis nyv -pq/7 8.lmip*dnn0; olave passing through the Earth is measured to be mv lynq*s8/n.poi7 l nd0 ip-;$ 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 travvo 6zr4/cx ;gnel through the same portion of the Earth, but one is carrying twice the energy. W6; o/nzrv g4xchat is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, buf4 pq,)htytw:v*pj c5b(zks1lh :3jxw-v7wut one transports three times the power of the ouy*jptj4zw,wvv 7xs ht() :15lk f3bwh:c-pqther. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to xs+(s t4r 7arbmove up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the rippt s4rbrx as+(7les decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in;e(8cd4vp7ifmaonazg-op8 3* n w m2a Fig. 11–52 are moving 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) -m7*4 v 8daapio;2pfcwag3m8neo (nzIn 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 vibrater1pzy-2bn v o6s at 440 Hz as its fundamental frequency, what are the frequencies of the 1 2bv6 roz-pnyfirst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingad g. b1f(2fst7qin. eered. At 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 string1gfsnfd.. ba(7i et q2 vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name at lenou x-p( r v(jvo1:u)gast three other frequencies at which it will resonate.xoo)(uvp1ugr-:(v jn $f_1$ =    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 wave c-9jy foe6lx9,gprv0s is 475 Hz, how far apart ar-epyr o 9c90x jfgl,v6e two adjacent nodes?   m

  If two successive overtones of a vibra h3q*nt7zmw)w zw7x( oting string are 280 Hz and 350 Hz, what is the frequency of the funda3 m*wnw)hzt77 oxq w(zmental?    Hz

  A guitar string is 90 cmc rdkek0+g zx-e6sx5 y6 4-mnp long 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 tension of 520 N. What are the frequencies of the fundamental and first two overto--xrcdnp6g5 6x y kem+4ke s0znes?    Hz

  A particular guitar string is a(/ o1cbg(r fasupposed 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 freb( a(rc g/1ofaquency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to-ua)vqqp 40j*s 2a8dmqafq 8 z vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the *a4d2 u0zqaq qq sjfv-)8a8mpstring be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude m9-t.k0l qr dmcechanical 60-Hz vibk.ctr0 d9lm q-rator. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the stringl:qibgsf(, k7 3)fakv may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how manykks()3 7ivfaq:b,glf different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at m;nwv/8ka m .1o gihz339fbxfjust the right frequency, the water alternately rises andw znm1v8xab;.3ohkm f f9g3 /i 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 tra pyxse+b: :9ppveling at k.0 km/s strikes a boundary within the Earth between two kinds of mat:pe s: +xb9ppyerial. 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 vel86b-mmok;tp6gdw ms :ocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests mam ms-gk mwt8op6d6b; :ke a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense aib3fa.q7 xuc y3vcp (ei.jiz--r. If the sound wave hits .ec-zv fjb7qxc-( .3uy3aipi the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikesa4q ae. zpwhtzq,. +y0 a boundary between two types of rock at a ., 0t+zpy4qeaw zha. q38 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the user’s manual, tho jk(x8v-u7qae dish has to be p8au (-jxv 7qkoointed 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 km and velocity 750 km/h travel, b pm/yw(jrv(ae(7c ss 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 kresp(vm(j,c /b 7y (awnowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constan 4ue1g(/uznavax,+a u t 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 (approxuxe/auv 41 guzn (+aa,imately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a wsf i)3 wt:n))sqn ;akcindow to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple sprink3tn; :f))wqi nacss )g, 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 placedl c+awdy/ e 9)kt8,jm sv*p*cn on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of w9v m*+8kc/ycan,pldsejt *)the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed4xeb ;k ,2-wtts7n)6dm k q25q ikhpmq of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of th 4qn2,26bts qt5dw pki- he)mm;kk7x qe 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 ;tapnx -1mz rax 4w41rz.ws p1b(k6gecoffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until ep1(e 4mta1xz.b;4nw xpgr6w -szakr1 ventually 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 10.8:*,cuo awn lv. cm from the center of a 33-rpm phonograph record have a wavelength of 1.70nu ,lva*ocw:. mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrad )lx:zoi-*m;a.xo e8yl o0iytes according to the equation x=0.650cos7.40t where x is in edo zoy *iyl;x)o0 al: mi.-8xmeters and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequen6*l/7kaw.+6vxx8j p 5xjrke2uoq fgpcy f. What is its frequency if it accelerates at 0.ekw5kx6v7. 8xp/jf *26rpu+lqa jx og50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floaz8 dh 4rtvkb/9ts on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper int4 r/hbkzd9 8vto the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical j 4ne )zs;mbk096fhfz instrument are tuned to play at 392 Hz (G) and 440 Hz (A). bz 9f4)s6hzf;0km jne
(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 col1p8q/,v efhu rd 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 ratiu,h / vpfq8el1o 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 or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prong mos,w4q-e7w:nizbi 5e p 83zjeb ves 1.8 mm to either side of center. Calculn -7b3wq s4:wez5ijb8ei z,p eate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with sii8zu39d-ukt y+b*jwqt cl f7+mple harmonic 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 there (Fig. 11–56) will not lose contact with the board during the osci8uf3ld+-wz jit *ubt7qy k +c9llation?

A string can have a “free” end if that end is attached ,i1elo / gklc0to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the rgl o/,l0 1iekcesonant 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 sm,me2 11xsto clxi)g-wing takes 1. 1gxcxto, smiml-2)e1000 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 can swi fp ;b0r pj84s, s7br326tiqbkpg3ocong 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, and0b,26 ob;okrj7cgptp8f33 sp r4iqbs 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 aaw98vvcxv74 )mt2 39edvmtq l tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated atc vv4vmmqld tw 2)93a98txe7v the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a sprin- 2*2u pxosh.bip6hb pg with spring stiffness constant k. A penny of mas s u*2bhp-o.h62ip bxps 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 steel crane cable is nn m9x: 5l;e sr u8rfs6viy.i922 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the caf :9m69eul8.sn x;ysi vi5 rrnble. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as s qorgx+vpi2 *a3: pm7chown in Fig. 11–58 (which also gives the dimensions of the block). You push it sidvxa3 q2o:gcp rmp7 i+*eways 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