Give some examples of everyday vibrating obufhxa1 h :n7q99qvk/f yxud-3 jects. Which exhibit SHM, at least approximatq -u7x /nq:hf9fuyx19h kd3a vely?

Is the acceleration of a simple harmonic oscillatx 3cnch/qv,7 kor ever zero? If so, where?

Explain why the motion of a piston in an automobile,n4bei( m mfu wvkw2(j r/+0sd engine is approximately simple hnf ds,/m 0 (wwb jv+ermkiu42(armonic.

Real springs have mass. Will the true period and frequency be la:z xup ye1(ui9rger or smaller than givi :eyu1uz (9pxen by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximcse0;s:j xiz5yw5( cg y l-g7sum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of au njbn kyc+c4f /;)9: ccb0wtx vertical spring scale, and then is released. Describe the scale reading as a func4y)ft;wncn0bjcb k +xuc9c / :tion of time.

If a pendulum clock is accurate at sea level, will itq 488h/ptl)ti5 k)uuva(v ic a gain or lose time when taken to high5 iuvlp4h t8)/q8a(cuv)iakt altitude? Why?

A tire swing hanging from a branch reachesxwv ib*an tp fe*y72,;x :)gzu nearly to the ground (Fig. 11–48). How could you estimate the height of the branch usin zgx) aiwp* *bf2;tv7n e:yux,g only a stopwatch?

Why can you make water slosh back and forth in a pan only if youxw8)zg4o+*3y zh1c/gnxlpp/z c,gs c shake the pan at a certaiy,z h /+c3 cp/)c gx1po sglxzg8nw*z4n frequency?

Give several everyday examples of+cu*d03wikvzwc6 p wml. y. sa4 )(yn*o5cdza resonance.

Is a rattle in a car)h 8 dhjg93ckue6 :op3q0vzbb ever a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to tpe2 vw30)e*/ zczjdzhhe frequency of its source? Why wcheze/d 2 *3zjp0v) zor why not?

Explain the difference between the speed of a transverse wave trave)ll.xw9/sc y txw) o0fbp gslpj,+g93ling down a corxww+0,9x o./g lgc ))t3p l9sjbfpsyld and the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally have p 02lwch 8egk7wire wrappedhgkw 7e0c8 p2l around them?

What kind of waves do you think will travel down a horizontal metal rod if youos*p/* 9s i8wfmvk3dz strike its end (a) vertiks*f m*o3is8 dpzw/v9cally from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but qjvkv6/s )b4az*j 3iothe bulk modulus B is nearly independent of temperature, how would you expect the i3j/ vo 6s)jz*qbv4ak speed of sound waves in air to vary with temperature?

Give two reasons why c7kjx hmj.* md1. is+rzircular water waves decrease in amplitude as they travel away fszh.mm x1 j.j+*r7d kirom the source.

Two linear waves have the same/)cm3emvyxaj7 t ts k-+mqp5; amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what ;ej5 v/ mtc73)saytm m+xpqk-factor?

When a sinusoidal wave crosses the boundary between two sections of ccu2,cxmhsp4 up 5it(,ord as in Fig. 11–33, the fr,i,2tx5p ump(csuh 4cequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, ar:zt hht 7fn*w+e there any places you could touch it with a knife blade witwn *+:h ftthz7hout disturbing the motion?

When a standing wave exists on a sg-s-hyq/se* p tring, the vibrations of incident and reflected waves cancel at the nosq*pg sye/--hdes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmittedzn j vmf6 r0xpu9p6++x from one place to another, how might we determine whether the energy 9fv +jpn6xm6rp z0+uxwas being carried by particles (material bodies) or by waves?

  If a particle undergoes S iks1:+* 8efv9 wow-j*na4 7fpgkrxykHM with amplitude 0.18 m, what is the total distance itx g +8kis f* w71 kw9pvj-a:y*4nkerof travels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is :4f1kat fa/ naku* -tc85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastick-tca:1f4*k utf /an a cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm why7e + mwr1et)g2la)rsen its 68-kg driver gets into the driver’s sea+s))7tye rg2arewm l1t. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish ha6u* ut *9 xzvyi7gnyrksy ;1l0ngs from it. (a) What is the springx u0 gy6r*9n1yu y*iz7s vtk;l 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 p r.mdwv+6d s4a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from d6 sr4.dwp +vmit?    Hz

Construct a Table indicating the position x of the massh:7 -5ylxe7d u5cx xv* kwz6zg in Fig. 11–2 at times t = 0,g -wz7:5*xvxhkce7 xz duy 6l5t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 )oh75wcmbyv* 0wh+ge vibrates predominately with a frequency of ycw5 +70bmhog*hw e)v4.0 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 n5du,f; oyw p5a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the freq5po5 ,udyw fn;uency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second wit yviyii cz1,t, )ay*-bo*(iby h an amplitude of 0.13 m. bayzi -y*y)bo1, (icyi*v,i tDetermine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHOl-76hjub :yzlv/4 axg half the maximum valulxlhz4:gb 7j6y-au /ve?$\approx$    A

A mass attached to the end of a spring is stretched a distancr p;ezeco83;le $x_0$ 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. Ifz:asn3*ij3s5 7x xqh m6 j+w,arm2ca f the spring is stretched an additional 0.130 m and released, how long does it take to reach the (n x r+c32nahj ,i :fsw7q asma3zjm*x56ew) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a sjc.zu 75l0)9kpp6ez jig 8lbmq;su t7 pring with spring stiffness constant k = 280 N/m and isj6qpz8gjl7l u ptc u );e9z7.mb0kis5 executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compr m/xi+ 5rxwhl9-m4xkx tx51tj ess the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball let xm xkj/xlm 5+rih-t9 4x5x1wave the gun?    m/s

  A mass sitting on a horizontal, frictionless sur4xm5elugm 90lface is attached to one end of a sel 4glm 0x5m9upring; 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 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 equat8w dsmqn+gz0ulza;w8 6 t(, goion x = 0.45cos6.4t where x is in meters and t is in secon8 ; smg+,q8wzga ntdwzu(o6l0ds. 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 5tqk(j z05 .mt1cro0tgc7qpw 6yy 8a fm3;bnyof a SHO half KE and half PE?yt0 (t51a;cq35opg 8 bwymzrqt7jf y .n06 kcm ±    A

  If one vibration has 7.0 times the energy of a second, but their freqs)zm ltq*5d308qxtm f/km 8vhfdk5c9uencies and masses are the sam9tzdtk)3x *0m5 f slk cv5q8mf8/hqdme, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanahvr kb.zwizb y6 h :s+- d,s0.nl*c:dging light spring once every 0.65 s.6l*a vwhc+y n.bb0:-zskr dds z i.:h,
(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 f- n2cq) .gklq4tg8 0holb+rae(o,wjvertical springs, each with spring stiffness constant k-jr.8 0)tqg ll2ofka (n, gow4cqbe h+ (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t wbpqb0(8p5gfnte 71qlnf5+q6wub b0 yhere x is in meters and t is in seco +l 5q57fp0( fq168ynqgp bbb 0bwnutends. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each,zvhci dgn(oq-3 kg7d m r3/fdd(jh 66/ what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124 N/m) iodj0zyn9 5 gg(bq8qaaj(s,5n s struck by a hammer, which gives the mass an initial speed of 2.96m/s Dete,(sdg0zbyjqa5n qnaj 9 go 58(rmine
(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 stiffn td9 i3-,2d0:*ubz ha1lnkocxeent ;tess constant 305 N/m vibrates with an amplitude of 28.0 cm whe0 e it2zu nntd*k;t,cda1-:oh3e9xbln 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 spring stiffness cog26rdp 941:tyzl)0 bj1ug 4hixuwldgnstants $k_1$ 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 toj an.w*qf2j4xku.in) a fixed horizontal spring whose spring stiffness cj kj4naqufw*.xi.2n) onstant 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 hib8 fivfibho 4- *1zho* m9zj4vs lowest 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 level of the bridge. Calculate tfj1o*4mh-ozb i8fbiv* v9h4z he 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 exal/8kxbf i207lu pi2flctly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exyx2zkq( )cjkhq1x i29actly one swing per second? (That is, one complete vibration takes exack 1i) q kxj2cx2qz9h(ytly 2.0 s.)    m

  A pendulum has a period of 0.80 s on m:rw)mf(. g o2vydoj3a 0gy1lEarth. What is its period on Mars, where the acceleration of gravitygy v:3odrg2m ).omwja ly01f( is about 0.37 that on Earth?    s

  What is the period of a simple pendulerr9 ;w(y m+yxum 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, na ,ed2dmooj5 e* n24ethe pendulum bob has a mass of 365 grams, and it is released a*,5nm2 de2 eooa n4jdet 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 0.9s2e ) qxhxa8 )5zm:.adood;k i930 m. If the clock loses half o)de:5x2km azodi)a;sh q 8 .xa minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speed 9z26 9zmapmoj/-cn gf$v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is released f ;sj ez.)lzwd;rom rest starting at an angle .jsz;d e)z; lwof 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 u 4; 0*syaajbkof his anchored boat every 3.0 s. He measures the distance between two cres*aa; yu04kjbs ts 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 tra 3/m zz:gto9.fiqmak ;vels with a speed of 343 m/s How far apart are the wave ck t;fmmaz3zqg/9: oi. rests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohytizhkr o3aiu :258lejxu-9x 58j fg-ertz) and travel with tz3o5l 9xi8uj-ghk8u ay:x er2ji- f5 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 lj0u3ice:x h: 49 udc -wwpbf*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 -t1agr9 j zwn17d l81xak ge0ais twice as dense as the other. In which rod will the speed o1-dw7 r 1a8 teaj1n0xl 9kgazgf longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the: pti*u9udjp4 tension in t4p*t i9j:upd uhe cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 6k b5z (dyzn;o:20 m and diameter 1z(oz5d: bky ;n.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 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 l ;lzqgvhpx45vp7 8o. osp5 r(surface of the sea. He hears the echo of the wave reflected from the ocean floor 7 l 4pvro5l .xgs8zpqh5o (vp;directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this diffeawg( (yd,ut s4rence helps in locating the earthquake “epicenter” (where the disturbanw,(u4ydg ts(a ce 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 waiz3wrh/p dn jj6 ds9-(ve can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration azpni dj/639s -(jdhrw>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes,au;kwjk +8ys 2 of an earthquake P wave pasky 2ju8; a+wsksing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth ine/-,jgob +vb s measured to be ogn-vb/+eb,j$ 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 the4gam pd9d t8 i63cvtw; same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplit8dw m;94v3tgt 6ipcadudes of the two waves?   

  Two waves traveling along a stretched string have thrtk -v5y4x- qf9yr+zve same frequency, but one transports tv-f- 5vy xkzr4yq+r9 three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up andrnk,sp(f .raa /j tl4cw;i1m8 down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximu(w;.r,ifpckanmla4t / j rs81m KE change?   

The two pulses shown in Fig. 11–52 are moving towariw /soxe7(+x qd each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pas(ex q7i/ox+w ss each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 4 q8n ,odf f(ng*wu1n*by3iy 1d40 Hz as its fundamental frequency, what are the frequencies of the firs 8dyuqd1ofnn*y1w(g 3*fbn,i t four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibratesae ;acv h)aa87 at 294 Hz when unfingered. At what frequency will it vibrate if it is eaa7c h)aav;8fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string bfr+- n d4:mrwresonates in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will resonabr w:r4 m-fn+dte. $f_1$ =    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 wa7.fpk-x(ge6h v4x uap zyx:4ives is 475 Hz, how far apart are two adjacent nodex g ax.pz e7x-(u4hp kifyv:46s?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz,cpj-0a mx;lkm2,*tnfcd3 m m+ what is the frequency of the fundamfmlc,cmxm+ ;2a *-3dkjmpt n0ental?    Hz

  A guitar string is 90 cm long and has lxic rnl;m//8 a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is unde m/;il lx8rc/nr a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string7. up-4dsvvmm(ggvb . 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 uvggdpm.b 7s-m (v4.vthe three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is mr895+ow u ibnueasured to vibrate at 205 Hz. By what percent should the tension in the str 9+r u8boiuw5ning be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude6s. u ft8vxdeu-p .5ce mechanical 60-Hzvfx5d.us6-.e8 t ceup vibrator. 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 string may be adjret(rq(3qwx ;usted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standin3 t ewq;xq(r(rg wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back andc(ofz+qrp2 sn v a:9:e forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to pvae2zs:pn:9of +qc r (roduce 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 ts tr-;vrxb :v r5 7e9muse1q(draveling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incideevx re5bu t7-smq1vs9r r;d:(nt 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 changeao+gn6 gir s6m k8lq m::,va1is from 2.8 m/s tg g rv +oin816a,kla:qim:sm6 o 2.1 m/s If 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 warm air when it hits a lay*)rbco:q+p z rer of cold, dense air. If the sound wave hits the cold air interface a qrr:o*)b+zpct 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 between5290ymq /ch qfhq*tzt two types of rock at a 38 mf0c2z y*h/qt5h 9q qt$^{\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+v9i qwl6x1q k the user’s manual, the dish has to be pointed in the direction of the satellite, but q9 xlw+k 6qi1van 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 velocitym(h1,ifi5zqey: b eu) 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, peophqu5ie() ,fbi: y z1emle have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 imefkj43*20mzyvz,j b 0ps5mkN/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 2m0je3mzs *0,vm5 y4 jpikfbz(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, whii-b.d, x pro(z.,eee n92iuwe ch stretches the net 1.eb(x2pi-,nr zie,. uow9ede. 1 m. Assume that the 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 of a freely hanging srfe rhr -+zog/ wvk7nm ,z17p8pring. The mass then falls 33 cm before it stops and begins to rise. What is the frequgew, o7 h8 +fzrm/knrzrp 7v1-ency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig.b5m p2n jyw03c,jrw3q 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the3 5mwbyj 30r 2jw,pnqc spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right pa2rby1. lra3/kt.uqz ls09 oqbce of about 1 step per second, the cof qtu. 9.rzrlyos2 /1bqk3 a0lbfee 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 10.8 cm from the center of a 33-rpm ph 9qf- )fvy.mq+q og ,6lbvf8hrg8,- kdpg*sp ronograph record have a wavelength of 1.70 mm. What will be the frequency of the sd.pyfq 6 o) gm+q,kqrbp-f- r ghv8,vl*9f8 gsound emitted?    Hz

  A 2.00-kg mass vibrates accoprptoy-p * d (-mk6k*xrding to the equation x=0.650cos7.40t where x is in meters and t ykk(p6p * --prto dx*min 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 its v (i,rvsym:e *frequency if it accelerates at 0.50g (asvi ,yr(m*e v:) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When .bmaa1+p8 z tfa 75-kg man stands on the raft, it sinks 4.0 cm deeper into the watefb z18pm.a+tar. 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 instrhe sxd.i ye* -9sjq n/se/,olm)tjj,g4 -rku;ument are tuned to play at 392 Hz (G) and 440 Hz (A). rs-skts , ylqj/;je4*mo.j ui )g,h e xd-9en/
(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-par;kv3*z xoo z,kslc65e lm bqxu. d/-l3t cord of Fig. 11–33. Determine a formula (a) for the ratio of the sp;/, olb -dv.oulcx3k6s qkxze mz5* 3leeds 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 or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of eachcn rm;r* /f4 guf923 hvzgu.mb prong moves 1.8 9u.fg 3b n*m; c2 furg/4vzrhmmm 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 simplee;qlck lt *8 m71bzt5gsg72r pn; jw+r harmonic motion of frequency 1.5 cycles per second.7 k8tl*q;lrp g7nc b1tz;gwm 5js+re2 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 oscillation?

A string can have a “free” end if that end is at x7dyj zc-u 9wqml(y)1tached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the -w(yjy9xd ulqc1z m )7wavelengths 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-y57mcd(o.e,bhwq r d)way swing takes 1.ow(,rc .)q5h 7mybde d000 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 d , vmj9itdi1i1irection or can swing as a pendulum of small ampli,1m9v i1ijd titude, 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 under a tension of 2wj -,ple 0eju)55 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 first ,p-l ee)wj0j umeet?    m

A block of mass M is suspended from a ceiling by a spring with sq* u fvl*zimd9l r0k/8/q(bu epring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will q vd0i* /9 f/qm lzuuk*(8lerballow 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.ds:*qpj+9 oj2i mupj 0 The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end jod+sp0jij* qpmu9: 2of 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 shown in Fig. 11–58 (whici 7pvshj8an4dh2f et478miv shd6x ,f; 8kdi:h 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 tp4ismjih f2d h dvhv8;ax t:e67n87kis, 8f d4he 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