Give some examples of everyday vibrating objepf2 s1.*prlbacts. Which exhibit SHM, at least approximat1f*pb l .a2psrely?

Is the acceleration ofp2 ilzp p(*xp vie395j)0khmr a simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piste d d33 hzg,934fdgjlron in an automobile engine is approximately simple lgdrfghz, 9 3dj34d3eharmonic.

Real springs have mass. Will the true period and frequency be larger or sw4p ixv b.sn5p9du1rhy37ykym,7g 0lmaller than given by the equations for a mass oscillating on the end of an idealizbyyhi ,0 du917w kplvgyxrp. msn 3475ed massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator i),btu em kfax5adk ys32c.:* (SHO)?

A 5.0-kg trout is attached to la2y ,1kao.5os,xkp-- g bnvj the hook of a vertical spring scale, and then is released. Describe the scale reading as a funlo, p kk-ov-xa 5y2b. sjn1ga,ction of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when tay x8ryb ej3i.4ken to high altitu3ye 4xi. brj8yde? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fiyotqm7f c5wfvcm5yb6 5y;/vh* c-l ,hg. 11–48). Howhoq*6 fc h7v-5;yt5/ 5cyvyb,wmlcf m could you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and fortxg(kba41iwug*8a+ yg h in a pan only if you shake the pan at a certabu1a*(xaiw4 8kg g+yg in frequency?

Give several everyday examples of resonanc9* sp:e fz fz4uwebm+j,cy:i;e.

Is a rattle in a car ever4yw+ iee 1yf6q a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the fred9 f b)dtrs:(e ps)c6equency of its source? Why or wp)r9csd e (fb:s6et d)hy not?

Explain the difference betwv2x +n*,y 8fod 5agoeceen the speed of a transverse wave traveling down a cord and the spened+g,*o5ao2f 8cx vyed of a tiny piece of the cord.

Why do the strings used for the lowest-frek*dx+t;a,0ck:paax 7y 4vd kyquency notes on a piano normally have wire wrapp,70a*a: atxk 4d+c; vp ydkyxked around them?

What kind of waves do you think will travel down a horizontal oso4w ;3 l7wmfmetal rod if you strike its end (a) verticalw3 mol o;f7s4wly from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in tempebac/bx0v 2.yjy2v 1ww o3i j0rrature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed bwji0 o 32jv. vbcw/2yryx01aof sound waves in air to vary with temperature?

Give two reasons why circular water wa 1a th/tlkwxqwyq2 /11ves decrease in amplitude as they travel away from the sourcyxh2 qt1 t/wkwal/1q1e.

Two linear waves have the same amplitude and speew5wjq+e50u1aqxus) 6-v ca rtd, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what factor?x e-a qsj0u1wtc55aw +q6vu) r

When a sinusoidal wave crosses the bound2mgn5in9wycz;t hd4 . ary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength w; m25 9ngz.4ydhnitc and velocity do change). Explain why.

If a string is vibratg knz m/u hta)0-;..ioxvlw+ ring in three segments, are there any places you could touch it with a knife ra0m-+ g/;k.v .tinw huz)oxl blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incidend0 df*gmn:lm dwx,,b5t and reflected waves cancel at the nodes. Does this mx,d0b*wfd mn, : d5mlgean that energy was destroyed? Explain.

If we knew that energy was being transmitted from oneriu py,1 bwld*1m1,tj place to another, how might we determine whether the energy was being carried byr,jw mlu,pt d1iy1* 1b particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what,(+m2e56.ghs ro8h: nd6fef 1gs foau .fd wgn is the total distance it travels ingo ga,.5ed16uofwnh se2 dfh 6f s:mfr+ .(8gn one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from i 1 3mf4)0; 0ka51lcvxzvhba: 0timoocp5qrmm t but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elaorm;l xk 031f:)czm5bqhm p aotci0v4va 5m 01stic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg drij8)10v x(sj gsl yv(kyver gets into the driver’s seat. If thsy0)(yjk vlxgs 18(vje 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 hangs frot7,c/ zgmw 8d-io9c79ic hlq em it. (a) What is the spring stiffness zoec9c hm8idi7q- 7w/ , tcg9lconstant $\approx$    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 vibrata/g,bj+f re:8 u0x b3enxno*zuge7 1 zes with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs frozxrje unbza71xe0*o:/gue8bn,gf3 + m it?    Hz

Construct a Table indicating the position x of the mass in Fig. -h(kjgh;j0mxsc0vuqdh.h 4d1q.6 wn 11–2 at times t = 0,t =;( j6dxkh.dw n1m vhqhj cgh-s4u0q .0 $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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. i*e6pv1e ()h l/ sguoqThe web vibrates predominately esqp*v1he /u6(gi)l owith a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibr/wtb 6+-uc xydm mpf6 /oydr62ates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 H6oy-mf r6pb+/6xycdu m d 2w/tz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 t tzfa6*7k:-jgddz(vgimes per second with an amplitude of 0.13 m. D6-tagzz d(j :7 kgvd*fetermine
(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 SHO hn7aj*qh 5y nv-+ s1es0jwnb-d:nu9w kalf the maximum value?qday n9 -hjw nj7 * b:+nsk51-wune0sv$\approx$    A

A mass attached to the end of a springbutp s qt;j+3wo h s7usya-851 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 m. If the spring is stretchlp wcsj5(, /d 4hbqj6sed an addhc j(65sj /b4qdsp ,wlitional 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 sprinsstjai +mm-zt-ue q8g0m2d6/ g stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from it8t- 0+istj dum6gmm sq-a2e/ zs 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 o7sbqrs 1n:cjpnj(+7tlpsq q jt;i8tal- /6h*f a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gun?hstbl s:jq cas *6r7i7tj1 j-qp/ ;8tp(l +nnq    m/s

  A mass sitting on a horizontal, frictionless surface is attacr gpgw uuegfsn01 q 498;2,dmkhed to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum ac g2m,pgdu1;s8q gnre uk0 w4f9celeration 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 tofr72: .pv n+wefzdoj/ the equation x = 0.45cos6.4t where x is in meters and effv wj. zd/r: 7n2+opt 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 fr vzmz2-g h:+xv z6x/bbd2j wm)om equilibrium is the energy of a SHO half KE and half PExj w-/62mzhxm )dbv +z2g:zbv? ±    A

  If one vibration has 7.0 times the energy of a seqnv9 sqdqj q8hg.jp0cm)1. h) cond, but their frequencies and masses are the same, what is thh9sh )0g1qm)qdq qp vjc8. .jne ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertica7p5mjsmcvv eoo47 x.sm33 zq9 lly hanging light spring once every 0.65 s.pzv4 c9m s7sxo m3e7qojv3 .5m
(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 paralbr 2 ahcnlxb:f;0n0f0lel vertical springs, each with spring stiffness constan0affb x02r:n n ch;bl0t k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x isw;)-v w ;3cktxxt cuifg:9 js5 in meters and t is in seconds. Determi:fg;5)i-3 9uwscw;t x kv jtxcne
(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, 87v m :e r m m8n))nk)ra,we;7s 1utlo/hfnnvjlabeled 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 hori6r ,fxytd ;:xzzontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial fx:zty, rd6 x;speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates with anu kdh 6z,3f,) ejqzp2vs9 zdssz(.co5 amplitude of 28.0 cm when 0.260 kg hangs from it. The 6e9sqosz s) k32u zz(zfcvd,p5,jhd .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 constantsa v ru--g+- ynl3h1.4l6tlwzqh cf(bi $k_1$ 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 -zvx lm/cjc- 8a 0.600-kg block attached to a fixed horizontal spring whose spring stiffness constant isc- lcvxj -z/m8 $ 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 kr tq42 u.a-lii3(; 0e9kkdrxw (xq,0xbcpt cp g jumps from a high bridge. After reaching his 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 the spring stiffness constant and the unstretched l l4cu( ri 9i.,xw0-xtecpk qk x3pqar02(dt;b ength 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 k gv2r4fw.x6 :gsc+p wexactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per sec). h.dtl nltx:ie 48rrond? (That is, one complete vibration takes exacr8)r lx nt t4:hlde.i.tly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, where th-mydru94fq,x jp mn) gte 7dwf4)i, 7le acceleration of gravity is about 0.37 that on Earw7 794, )y- gdqm4dlf,f erm)itu jpnxth?    s

  What is the period of a simple m:1eg8wo-boa pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendu srewf)-x1a aw-nrugfj 6jps5s()(e 1lum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at afxrsa-wn 1ra6g fsew(-) 1(p5 j)e ujsn 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 pendulu:d5leemguj/*.v h p/cm has a length of 0.9930 m. If the clock loses half a minute per day, howguv/5j/c m*.l:ehd ep should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speewk/ .:ivbeu/h d $v_{max}$ 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 ste 3l70flt h0released from rest starting at an st07e3htl l0fangle 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 ancho6 y v--yrbau*tred boat every 3.0 s. He measures tha -6-rby*u ytve 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 travels with a speed of 343 m0)(pj.zavz pltl hk3 5/s(l5z3j vzt) 0p.lpkah How far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHr3 *k 0izjxj, uoiocky+..(axz and 1600 kHz (kilohertz) and ix kxri.a3(k j.*ju yz0+ ,ocotravel 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 wavesu g*y) u4zgj:p in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twici c1,;n pzb3i*9 touu 2wrkqm7e as dense as the other. In which rod will the 1 32o r7pi,miq9b;ukt*nwzcuspeed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If th212geeo t+me +*c2t3 dijy kzie tension in the cord is 150 N, hi c1yge e+ 3t2i2zkm+edo2 j*tow 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 byu0)e iol5tc 1dvc0b x. a steel 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 o0c bd ixt lu)v05.1ceand 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 belowszjb 8zo a2(y7 the surface of the sea. He hears the echo of the wave reflected from the ocean floor directz o7zy( ajs28bly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different8xu7o:g 7ritt4 p gzp8 speeds, and this difference helps in locating the earthqu7tx7g8p: 8i tgouzp 4rake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by;h c.*1uae a; adsosjgfy, cuz ;9zx,- a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually incl; . gusxazs 1;zuy cdo;aj*a9,ehf c-,ude 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 intenszi so,r-1p(appu;hs j(py3y8 ities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detec8is py1 ay p pjhs,-pur3oz;((ted at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthqui7k 7 .zl01eo2yiiqc fake wave passing through the Earth is measured to be l c27fioy. e70 zq1kii$ 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 4v 6vgmqn:n7othrough the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of t67n mg:4vnoqv he two waves?   

  Two waves traveling along a stretched string have )saqnhf z (g34 tp ywfd.)pv:5the same frequency, but one transports three times the power of the other. What is the ratio of the amplitu5qapg td4 )s.)(pvfh3nzfy: wdes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total verticaua4 dlp02dyc0 hh9 sl(l distance of 6.0 cm, from the lowest to the highest point, ap h dys0l092 dcaulh(4s 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 other*, )wrzvunt3k+be ;ej. (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,ve3 uw )kj;reznb,t *+ the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental .xo,ce+exo4n; )xw. ap6ba ixfrequency, what are the frequencies of;.,xw. xe)oani4 6bx+ace pox the 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 frequen 49ryn:6igt n0xeg)blcy will it vibrate if it is fingered one-third of the way down from the end? (Thattn60 n 9:iyerx4gb gl) is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loa+ 26not z1hr5rvb6-8 wvaqqyops at a frequency of 280 Hz. Name at least three other frequencies at which it will resonat62 q+-1v6ybanztqrarv 58 wohe. $f_1$ =    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 waves iob2/n 7 zm0ca gfgo0i*s 475 Hz, howfi0ma *0n2gzobo7g c/ far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280am 0 y20g gaup 2vxzhs8ot0l5( Hz and 350 Hz, what is the frequency of the fungz 0 hs0y 8mva20(lu25agopxtdamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distab-xs+u zg )z +3xgnq-wnce from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?gn )s-g+z 3q wbuxx+z-    Hz

  A particular guitar st4zivm;vxq 63 uring is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shoulzui;qvv 4 mx36d the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar stru y-cgu*;a3 lgdo4h m,a(.kdixp u3. hing is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in u d-lgpd4y .(hcgxuo;k iha *3au3,m.the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attache78qjow.b g:f pd to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per uq:p.8 7gfobwj nit 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 l4pb5nj e041k z.w liothe string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave pattikjb45.0l l1 e own4pzerns 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 just the right frequen bf:6i+o k 7lqu 73c-ozw-vhhmcy, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 li-+o uh3:q fz-voh67mkbc7wHz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary3 ywm3;qwg ;7p.*cfzb t ty9fv within the Earth between two kinds of material. If it approaches the boundary at an in;v7mgqz ytfpw w3y*;3ct .9 bfcident 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 velocit(p83 mus4pubo 13zsa dl;;uzfrd2j mt) e x8q7y changes from 2.8 m/s to 2.1 m/s If the incident wave ;u m ;d7 sdjr82 mpa) (ofzus14l3z8qxtb3 uepcrests 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 lay9 l twp4gz)k1 1kscr1qer of cold, dense air. If the sound wagc19rpq1ks t4kwl )1zve hits 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 strikes a boundary between two types of rocktr)fl mo r1ypa9 y;p04m0;cf t at a 38p0fpm; tm )y a4clyrt09o f;r1 $^{\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 abei1k g .7(yewgout 0.5 m in diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an ewi(7gk 1ge.e yrror 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 7uacc fy )o83xvelocity 750 km/h travels across the Pacific Ocean. As it appr8 cy)ao c37fuxoaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumpeea.9j , ttv3ohbd75h rr has 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 (ahe.7hb 39jv5d rtta ,opproximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps f 3e xcnj0m4x n .ik16gtf 4bj.erw)0jhrom a window to a fire net 18 m below, which stretches the net 1ejrint e0 xk 614 jc0g3nb..mw)hf4 xj.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(7rk;xordb dv(b-b)r end of a freely hanging spring. The mass then falls 33 cm before it stops and begin( )7 dxrbbd(vrobr -;ks to rise. 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), compress 7gqsdk j2xvcozg.3ha (jb0 :;b4jmf7ing the spring 5.0 m. (a) What isqo7sc0;zjg( 3vh:4 b j j.gxfb2amkd7 the 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 (diameter 8 cm) atn+s lf+y5lozltd /e7 . just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate te.dfs otnyz+/ l+5 ll7he speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the otgt u/akg-)7 g(t(mo center of a 33-rpm phonograph record have a wavelength of 1.70 mm. o7u)m gtta(- k/(og gtWhat will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is in n5d+l5 aphu3ts99 xkqmeters and t in seconds. Du qs9ht x5k59l +3dapnetermine
(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 wiu(8 luouo*yso3sij47 3m( prr th frequency f. What is its frequency if it accelerates uysu7r* s ooi4 pm83o(u (r3ljat 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake.5mb: h9rsgi t.q+ pdj/ When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the r.9hd/5st igj:+bmpq 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 instrument are tuned to play at 392 Hz (G) and 440teh1m5q*o:l jz/w bn1 Hz (A). : qohbl/tjn5 z 11mw*e
(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-pam tqadrf:hl,e /i e,p*3p* 2wjrt 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 /l2 ,*mp3*q fead,tp: wr iehjsection, 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,0z8al 4,d 7za,izlqjd0aq r+l and the tip of each prong moves 1.8 mm to either side of cza,80+4zdal q70al,rz jdl qienter. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillatese 3my*i :u *.r zghd8jd0y8e 2knzx3wb with simple 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. 11:3ib.80wn*u h8x k2 gzyemrd*yd3jez –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 ring tha5rirsm2qb 9z40g+ijh t can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end hbz95m4g rir2+qs i0jfixed and the other free.

  A “seconds” pendulum has a period of exactlv s8xx2- fr9m;ip5fgd y 2.000 s — each one-way swing takes 1.09f5 sgd2xxf 8 irmp;v-00 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 sk 3o.yxi(u7k vertical direction or can swing as a pendulum of small ampliyks7u.x (i3oktude, 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 tensionpm9 zmo)j 5t(ylx.i+iyj 1qa. of 255 N. A pulse is g.omm. 1+j9lpx(aqyy) jz iti 5enerated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with s vcd, 7csg0m0 )tkedhdd:zr2n0h93zupring stiffness constant k. A penny of mass m is placed on top of the block. What i0 ,dz:03d e9kcr7 ud)2svh0zhdtmgcns 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 junkf9x.rfkt9;zmqc 3 s0g yard. 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 of fqm9f 3 s;rxzck09g. tthe 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 (which also g48 2;d xr32z tu.sywsl7ckv/ wuky w:xwu(7krives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins kw/ vtuk7u(7y.csu8wlzx4w3kxsdrr2; :2w yto 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