Give some examples ofw(a7j +zk gev. everyday vibrating objects. Which exhibit SHM, at least approxikg+a (jw ze.v7mately?

Is the acceleration of a simple harmonic oscil+ bfcq1/pmec1 lator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine i0:wkzag*x7x7 pkyaj j; qv1/is approximately simple harmoni0agja ;/ypiq wvz1 xkjx* 77:kc.

Real springs have mass. Will th86d na ,x/e4my0 irqgge true period and frequency be larger or smaller than given by the equations for a i 6x e4gdnag m0y/8q,rmass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum s + wmafa-wkk z7pcp9zr**5d2 ypeed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical l (87nskp83jvh m a(wsspring scale, and then is released. Describe the sca(jvk ls 38h(na m8swp7le reading as a function of time.

If a pendulum clock is accurate at sea level, will it gainlkum3uj 8dr h d6a 8)gbba/)s7 or lose time when tak hugsd6bm)j3k alda8 b7u r)/8en to high altitude? Why?

A tire swing hanging from a branch reaches nglcy*6n .c9eo early to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stg lcc9e6yo*.nopwatch?

Why can you make water slosh back and forth in a pan only;j+8 ptba*yd ;ulg, do if you shake the pan at a certain freqobgy ;, a8dt;uj*l pd+uency?

Give several everyday examples of resonance.1)ymvq3n fxo 37*slnv

Is a rattle in a car4el oman80j4g5 lc25 +sah yqv ever a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to th tfbs4dao;l ;33kf qu.e frequency of its source?uad .3 bs4k otf;l;3fq Why or why not?

Explain the differencr:.bagm-cqgb*1xc 9 se between the speed of a transverse wave traveling down a cord and the speed of a tiny pie. c*rcm:qb9ggas1 b x-ce of the cord.

Why do the strings used for the lowest-frequency notes on a piano normalli/;mo/)wjs6rjvv9bsc .6z v wy have wire wrapped around themwjwoicvb/vzs9mv ;r6/j s.6)?

What kind of waves do you think will travel down a horizontal metal ro /u .kqbafg( .htzg;r)d if you strike its end (a) vertically fb)qk gh; g/tra(z.u.from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, buvkx1(cfe 8 a2qt the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temper cvx821kqf( eaature?

Give two reasons why circular hq.8(az jbo7m water waves decrease in amplitude as they travel away from.7jzb8h(om a q the source.

Two linear waves have the same amplitude and speed, and otherwise are identical,t 4nw fvs16 z3:ntiz;k except one has half the wavelength of the other. Which transmits 3fzvszi t;knwt :1 6n4more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord as in Fnhst5tmnf d2b6y d .yohr0 7.v9m,w0x ig. 11–33, the frequench2sn y6d7..09h50txw nf ov mt mydbr,y does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in tpf:8lx o:yp;.r ex.b rhree segments, are there any places you could touch it with a knife blade without disturbing lx :xr:; .p 8ryo.bepfthe motion?

When a standing wave exists on a string, the vibrations of incidenta;z rd5137ykfkd7 mb i and reflected waves cancel at7bm35k; 7adyrzki1fd the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmi; eiu;bhw:sg9 tted from one place to another, how might we determine whether the energy was being carr i g9uwe:;hsb;ied by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distancj*-(d9 lz u(n0g*n,3j8e h dbpyrrusbe it travels in one periodsd3h0( b( 9 ebudjnzr- py *l*ngr8ju,?    m

  An elastic cord is 65me:i akf p) rjv0ftoc2l )*t:a gi2e/) cm long when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “sm ft)irgolicjv/)aep:2:at)2ef0 k*pring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg -2fki0b yz:h ww ojbi8 f2,(w wr,te1qdriver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of br ww: wi(,yjfi w ez1, qb-o822ht0kfvibrations?$\approx$    Hz

  A fisherman’s scale stretches 3)8le .:bswy6vorc .,0 vor8lvir/l yf .6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness constalrrswlf0 /,y 8..vycb6)r8evol i v:ont $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 km d u(ay0vfd)ww+8zd cxg*;:xg is hung from itx8 a:mg)du0x (w; wdd+vzy*cf. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at ym/g:- mlazu *lo 8d(ytimes t = 0ldl:-mz *y /(o8ya umg,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web.b v iqe(;x /e1scl/4ad The web vibrates predominated e1vx//il4cbse;a(qly with 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 vib3fvo22hv tu uyl- qc**rates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value t*vuucf3ov2lh q*y- 2of m?    kg

  A 0.60-kg mass at the end of a springmku ty2 2xtl90 -r3jvf-:on4 t n/dnbl vibrates 3.0 times per second with an amplitude of 0.13:bu-tyrf223jtn 0-/mox lkl4v9 tnn d m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibr3 es(+zh.hb ul l77)m;vdpvhmium is the speed of a SHO half the maximum valueh7z3hlmpv7d bh)e;+vls .( mu ?$\approx$    A

A mass attached to th0gwws-hue )m s8 fel6/e end of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. Ibnlrx:3qlr-p r3j5z *ej/.wvg) be0zf the spring is stretched a/ wrgrj)n0jxe rz.3l3vbq * z5pb- le:n additional 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+qa m:ps,zp+ *k bicj( stiffness constant k = 280 N/m and is executing simpl++*a sbp,: i(cmqpkjze 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 compress the spring of a t7yth g/nh 4.xuoy popgun 0.200 m to “load” a 0.180-kg ball. With hyx.4 hg7tu/n what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attp.;zp/fy:jco ached 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 acceleration of ozc;p/.j :pyf 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.465 f c*n*erlxgt where x is in meters and t is in seconds. Determine 5elf6*rgxn *c
(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 ek npp3 5;/gwehh6jtm(quilibrium is the energy of a SHO half KE and half PEh3ht6(j m5kpe/w ngp;? ±    A

  If one vibration has 7.0 times the energy of a second, but their frequenciesivcah 2:qsknr920 pv4 and masses are the scnrqv49sva02p: 2k ihame, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging lighuf; l/gzg-7 n t 9yzt: hi5qaf9)gtwh(t spring once every 0.65 s. 9)izatlny-hg (g7qtt z;:9 /wfug5h f
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs, n9pq2*er8d)tl 0g q s fipqgmn: bm04/each with spring stq*n nb 2 8)mif0:pp4rgq0l mqg/ds 9etiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to thgf c- tz 5y1ozv :3zhtpmj:.l+e equation x = 0.38sin6.5t where x is in meters and t is in seconds. Determinzm:zgtc .jo3h1lpy5 zvf:+-te
(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, wha(doenpxg o 3a79wiq/0 t 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 springaquy/ yaptjfv8f n,+b ma.31* (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96mf tu yn.f j,1p q8aybm/3a+*va/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 stiff+i,cemkdtm hd t7 f) )*b7i:bvness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes thro dctb 77),dhe:b)m+ kmifv*tiugh 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 f,cwz 648lsbcconstants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed jcrt8p,jt4:u odo0-lhorizontal spring whose spring stiffnd tjpc ljt-0:,oo48ruess constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridgmaafw*cug8py71l. 1t*o.w oh;gg(a ee. 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 belo ;agl*ea8t (hwwg. caf.*p11myo 7uo gw 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.hb; j:c2 zc;8 rmna+h-04 zvf sq3qart What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to makee.p9 nl zr 4pjbiob8+. exactly one swing per second? (That is, one complete vibration takes exa p bo8pbilrzjn.+ 94e.ctly 2.0 s.)    m

  A pendulum has a period of 0.80 s on E+n px9*+sw 2f8qujf znarth. What is its period on Mars, where the acceleration of gravity is about 0.37 n92+ qfjs xz*fu8wnp+that on Earth?    s

  What is the period of a si 4jbtd vpsq(k4w+-,edmple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is gaw(i2 pty -c1esd1b: 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle1gey(s-w2 pba :i d1ct 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 cloc3c530niryom m)3f og4xzzp( i9 tw hg)k’s pendulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shortened f) (it3wo)ygpz m 3gzrcnx4 5oi0m9 h3by    mm.

Derive a formula for the maximu( 8q: 0nf +no*eazpwljm 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 oscillatesow lovc /pw+.. at a frequency of 2.5 Hz. At it is released from rest startin./wpov+o l .wcg 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 his anchoretdu/; yh;nj x9ygzq ;9d boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves traveli z;;n tj/ qyuh99gy;xdng?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 3430wt.h m; mg c5vd,z50 azohg;k m/s How far apart are; d 5v5 m,gkz0cmhzt.whao0;g the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHwnz0c kd:wv44ow b3*x9nh ir1z and 1600 kHz (kilohertz) and travel with a speedn bw 1wz3n*i:ko rv0h4c9 4xwd 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 sig) oqc)oxa5 qs1j*+
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same jwzg-5p8rr6i elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be 8w zrr5 pg-6jigreater, and by what factor?   

  A cord of mass 0.65 kg is 9j b3cwc3+gb hc7a-a.fwn0bk stretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support t- 0ca 9jwc37 hbgcb.a3b wnk+fo the other?    s

  A ski gondola is connected to the top ofn25pd9 *feq mn a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run,2f dme*n5np 9q 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 nswcj0iyr* j)t.(1su his ship just below the surface of the sea. He hears the echo ji0ysr)n.ut( * s wj1cof the wave reflected 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 travefcd**eygtqb 8 a9m.8jtzdw4+l at different speeds, and this difference helps in locating the earthquake “epicenter” (whw4 cta j d8qtzyf9d.egm+*b* 8ere 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 ctlt6;10gvxs:v;ve :p :tno-1ej5j hjb0 iwr a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), wha;:-vo tb:6 hx et0vj 1 :0sejt 1nir5;cwpvjglt 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 intensitw5g 9pbyqph (/ies, and (b) the amplitudes, of an earthquake P wave pa hq5p/(wy b9gpssing 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 tz/mmmzuklvr2 )cm6hk1-5skq; wy )bkm;)i -f he Earth is measured to be l-)bc)1zm) 6m ;skz u-ih;mkk2m vmkf/ q5ywr $ 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 i;lt cnjvo () zn+e(5yfrequency travel through the same portion of the Earth, but one is carrying twice the energ cv +le(n;yziot ()n5jy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the saggl;(t2s umvv::lyg4x:gm+f-5 or j kme frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two wa5gyv:-+; mg l4l t( 2:rg ukfjvxgoms:ves?   

  A bug on the surface of a pond is observed to move*xb t2lp g :xq+/nki*s up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passe:iq / *kpxlt x+2ngsb*s. 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 oy4ll v+ gervr +(b7gf8ther. (a) Sketch the shav8 ( vb+gr+e7r 4llygfpe 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, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, 9, nnv2 uq9kxsa.kxw.what are the frequencies of the .aux9,snk.9nxk2qv wfirst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At w v04uxu2ptcu6e z:9 sihat frequency will it vibra6u xu:v 0u2s 9zecipt4te if it is fingered 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 resonates in four loops at a frequency of b /o7trc *ae9j280 Hz. Name at least three other frequencie*at cb9 orej/7s at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of stans u, 6-k.ay-l t.0hvzxsuplf pcy4q 6-ding waves is 475,tzy --xyk. a6hqsc.f-40lusul v6pp Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 35 4dbprz96cir9 0 Hz, what is the frequency of the cb r99p46zirdfundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance frt-ucj*5m vbe.:rv) /fym; kalom 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 anuft:vlk/-5;m mv*rc )j abye. d first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is mebl* p2yohm3 yoor73yw1m8 :wq asured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct theqmm1oo*b38hwyywy p: 3 2olr7 frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is meb 6x ;8-cqgj6h( 5lo5 x;tki,bcty9gms,j j psasured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased bh5 kc,tg sjb95gx,o xcjq 8-(m j;b;ts6iypl 6y    %

  One end of a horizontal strinrl.r. * rowmcoc 6ogwn:4 2yl2g is attached to a small-amplitude mechanical 60-Hz vibrator. The string’2:4.rlw ooc62 .c*nwglm rroys 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 adjusted by moving the jgarb alg)h(8fg42 f/pulley. If the hanging mass m i84afl )/ ga( brjghgf2s fixed at 0.080 kg, how many 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 o cxhacj0 rx :ox;kndw2:,1,stub at just the right frequency, the water alternately rises and falls at oa:sdxx1xncowcjr 0 2 :hk; ,,each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling a-u4gcy;q m ufn o6y.6xt k.0 km/s strikes a boundary within the Earth between two kinds o-4uon 6g.yxquy;6fc mf material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelfy vn /lu9b5md,” where the velocity changes from 2.8 m5dn/ l,y bvum9/s to 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 layer of cold, dense a:8h a/sa 7f3j j56nq q6hvh-ahhqag-m xz15 koir. If the sound wave hits the colon1/-5 zq 8h7:ajqq kjhx5s66- gh mah fhav3ad 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 bet5.yp e39a.vtg0/e ihkfmko .sween two types of rock at a 38 5msi/ka hvfoy0e pkt 9g.e.3 .$^{\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 mqs+yc pq(-bfhk hk 1).anual, the dish has to be pointed in the direction of the satellite, but an error of c)f-h+(h ksyq1bk .pq 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 velwpy+9bq 3 +jbgocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease ofwb+q3j+ y9gpb 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 bumper has a spring sti.cm qnr9rez(7 6h irul cqhw y8l*;.3vffness 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 wycl.z8r(cr qn *l.vrh 9 h3u7;6eiqm(approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18bq -fyq7m628jcz5ex p2:bljs m below, which stretches the net 1.1 m. Assume that the net behaves like a simpp278qx em2 jfzqcbj-s:6 5b ylle 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 spri,0oo6g)0q1 k9cnsbonyyd 2u t ng. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscc962tnkyqnog0boo1 d, 0usy)illation?    Hz

  A 950-kg car strikes a huge spring dd) l p;ypgbp0r5/ wk)at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) Whatw kgp ppd5)/b0 y)l;rd is 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) ae 4+ )6,ezl 611p3hjwutbxj e yls,ax3jugf8mt 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).wl gx8fezej4jy 3uu,h6a 1p)mtb6,3lsj +xe1 Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the cent* 72wn)y:-eqblpgkpg er of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the fw)py- kq2nlp:g7 g* berequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t5sq0cs4cik m+ ha33vu where x is in meters and t inssc3 03 qmvuh4k +5aic 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 frequency if h u/ jhkq;0m jufg07i7it accelerates at 0.50g (a) ;7h/m0j0h7k qfg iuujupward,    f
(b) downward?    f

  A 220-kg wooden raft+e/f znn:y quvs)z(b 4u; .chl floats on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, th bq;n)v.c+(:e zly hs/n4zfuu e 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 (*tvci4z1 g qb2G) and 440 Hz (A). b 2q*t1i gzc4v
(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 cord of Fig. 11–33.x-a2s/ lmne6v Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelx2ma en6 -/lvsengths 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 freq0dbuhoi v(h)g45 sa/nuency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calculateio4s dnghh(5av)/0 u b
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simpl,hd9tu-d3a6ipbn * i2fd+kgie 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 pl6 gih kai3-u*p,t 2ddidbn+f9aced there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” en q*gpj0q*ut 4wnibl.*d if that end is attached to a ring that 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 fixed and the other freeqwg t.il*jb0**pu q4n.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swin. lpx x1pffwq,d 5e70eg takes 1.000 s. pwledf750fxx.p, q e1
(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 t r xs5om sr-a. cc5c)s,3jk*hoscillate in the vertical direction or can swingsm,ahkj oc 5ssc )r5ct-*x.r3 as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what 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 under43((zuj nw kcm a tension of 255 N. A pulse is generated at one end, and 20(k3unmwj 4(z c.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 spring stiffness -:fw- d57v6ued7 fprv qc3ea cconstant k. A penny of mass m is placed on top of the block. What-q d67upff e:vw57ce3d-arvc 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 cabh;: -qi.q facmle is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. -:iqc. hm;fqa What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rest ik 4r*.0h5t7dvwxnr*;gs pxds on a plate as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibxr*5g*wkrd4p .svh x t7d n0;irate. 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