Give some examples of everyday vibrating objects. Which e,b11y6o *xcz (h,fdbkh 0ymbgxhibit SHM, at least approximate,,m hbfc*yb(1g kyobdh x1z0 6ly?

Is the acceleration of a simple harmonic oscillfm+ms (;nfyy /ator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is c;sl-5zp )psjapproximately simpll5 jsp)zc ;-pse harmonic.

Real springs have mass. Wilq;gdk+cw7iln:zy 64a5 ve no:l the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? ovk5n:+l wq7ceg n da4zi;6 y:Explain.

How could you double the maximum speed of a simple harmonic oscillator (e pm0f,5t +wx)+ht tagv9l tp* qof6exszk;) ,SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, anoxk zjq; ::wev89f 2und then is released. Describe the scale reading as a fun; 2qj8f:xn o:weu kvz9ction of time.

If a pendulum clock is accurate at sea level, will it gain or los(s6n m1z1s vnxe time when taken to high alt svn6(znsm1 1xitude? Why?

A tire swing hanging from a branch reaches nearl exn3i 5at1bsw5y9kc9y to the ground (Fig. 11–48). Hokyxebwi35 9 sat1 5n9cw could you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan om8;r7qxt,cl3*ion rk - gq9ag nly if you shake the pan at a certain frequenct ,q;c ng8li-g xrao37qr m*k9y?

Give several everyday examples of resonanpm+xakjv-g.rk +4g0q+wdfbh t 4 3n7g ce.

Is a rattle in a car ever a 8k22 acem+kmck;tj8 qresonance phenomenon? Explain.

Is the frequency of a simple periodic wad.b t ; )rcxgw68abac6ve equal to the frequency of its source? Why or why notc;6 bdt 6)bwxgacar. 8?

Explain the difference between the speed of a transverse wave tra/r p6j ) 1hspqb peyi5-o24egwveling down a cord and the speed of a tbopqp6)i1/ g2yh- r sjee5p w4iny piece of the cord.

Why do the strings used for the lowest-frequency notes on a pign/soi ,dh2r .j. z1mzano normally have wire wrapped aroun d j 2/mgrnsoi.z.,zh1d them?

What kind of waves do you think will travel down a horizontal metal rod if you 8e- v0,axka;ra2zzyp strike its end (a) vertically from above and (b) horizontally paral8ka0 2 -z xarvep;,ayzlel to its length?

Since the density of air decreases with an increase in temperature, but the bulq:po9r-qll v*-bkqt ;x+q ku1k modulus B is nearly independent of temperature, how would yoqlu +:k1qxk9qorvt q- l-pb; *u expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waveb.q0w5e x2bkcn lsd h4g8a3+5ig(- stw u2tzas decrease in amplitude as they travel away from+ant 3hb0 (wq8gcuk i 5g5-2t.2ebsdws alxz4 the source.

Two linear waves have the same amplitude and speed, and otherwise are idengr e ;imad-5,g1, ofz,js88rtw r fjaan::; abtical, except one has half the wavelength of the other. Which transmits more enerza wraj,d,-f5b8mao e;t g8: nr1fir;j s :ga,gy? By what factor?

When a sinusoidal wave crosses the boundary betfq7)q4 em- rll/o w7ngween two sections of cord as in Fig. 11–33, erq7qg4)l-owln 7/m fthe frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segment-;fygr0u tvz6;)kbn3dg9qubj nbc / :s, are there any places you could touch it with a knife bladen)bz/ gu;9bjkry:q-v guf n3bc ;d0t6 without disturbing the motion?

When a standing wave existsehsn)vhw4 j/x : 3j3en on a string, the vibrations of incident and reflected waves cancel at the 3 4n: 3)xw/eehnjvjhs nodes. Does this mean that energy was destroyed? Explain.

If we knew that enerl,k;:fj t ny7ygy was being transmitted from one place to another, how might we determine whether the energy was being carried by particle,;tjy:n f7kyl s (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distaeef(nisy)-nfi :d4hnz9zy;0nce it travelsze hs9( )0y; ne-y:zini4ffdn in one period?    m

  An elastic cord is 65 cm long when a 58l w/kia kay.weight of 75 N hangs from it but is 85 cm long when a weight of 180 N ha/l kaikwa 85.yngs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car co evla 170 eqzx:kwm*9rmpress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes o: mzrew7ex lka*0q9v1ver a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm whenp6t9kedmq19e a 2.7-kg fish hangs from it. (a) What is the spring stifq9 k 1pm9teed6fness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 k; hx2d(,:qg7r+qgkoic (ikooah+7dr g is hung from it. What is its frequency if only 0.38 kd x7cr+;oqi(g,(hodhk2 i+ gkoq:a7rg hangs from it?    Hz

Construct a Table indic)me h2is4nc*co4lv 2e,i cwu2ating the position x of the mass in Fig. 11–2 at times t = 0,c ie o,2 2ncce4lhsumw4)i*v2t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 * lwu6gn z5mo:gdpnde .,r;;espider’s web. The web vibrates predominately with a freque; zn*wl6gd 5 pm,eu:o gdr.en;ncy of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 4oyyib;z)/*dbp a)3rqugaj m i7n f,( Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. Whaq;myj rn) * g(oiua4i/ bf7)bazd,3yp t is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per secondrjad6b-4w ekfipojib *vus0 2m.ne/63 ) :hve with an amplitude ofpe:v /udnroib.4*b0i - )jam6 vehef2 3wjs k6 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO zc*o-,g*nc qghalf the maximum valueg* gq,n*c-cz o?$\approx$    A

A mass attached to the 2;fyv/0qaxb2a lg; kteie/ d;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 stretc2q l:m1b mr .mbn:/ 3i5)xm hnd;omdauhes a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take tob:r.nmum5mm31b q a) 2hix /m:nld d;o reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with ;7 eojwen aw) m/ muw-kg;)m5qspring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is movin75gqa )w)- /;k; jmem nwouwmeg 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 toy asd0am2gfr ) 9 )flvswqj i rhp;);.j2popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the bal wfa2vq)) ; pss0f2rdj jirm).lg9ha ;l leave the gun?    m/s

  A mass sitting on a horizontal, frictionlespx20 ,vzps +*m+oroaws surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compresse 0wxz , *mar2pposv++od, 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 5+: dvk;ebx tchp ekt*.o;jf*1n0 jopto the equation x = 0.45cos6.4t where x is in oxk :+1 oppe j; *dktfvc bh.5tej*;n0meters and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equil(t :cvjje-emrk l8ku3 pq2s 5/ibrium is the energy of a SHO half KE and half PE? ekur kc 3 : /28spjvl5qme-(tj±    A

  If one vibration has 7.0 times ut-py sl-g+b. hi,c(t the energy of a second, but their frequencies and masses are the same, what is the ratio of thsltc, +(uiby .t-h-gpeir amplitudes?   

  A 2.00-kg pumpkin oscillatesi.e1v7jd r- b0sbv ew7 tgy36h from a vertically hanging light spring once every 0.65 ssbg7i7wrt-yv36v1 0.bde j eh.
(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 tw-vvy*6yq4e lk o identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibrateqv *-4kyylv 6ion?

  A 300-g mass vibrates according to the equation x = 0.38sin6.*. o,awdrn. kfpom-pc5eq1 7m5t where x is in meters and t is in a*f1pe,mod5 pkmcn.7o.q- w rseconds. 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, ldik 5xl9 vinrdt :;n(x-hul2.abeled 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 horizontags2y4,u(y nhts/hll* l spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial spehuy/y*gs2n t, hl(4 lsed 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 stipjyq8q+ee 3ako.3 s6 rffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) wit.o+rq a8e3qy sekj3p6h 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 sj r,lnu 3qy)5z3 tn(x ux3em,uprings, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.6tqdn0+3 -8tu6oq mzxw jky65j00-kg block attached to a fixed horizontal spring whose spring stiffness constant o3zq yd56j tq utwn6 +mx0k-j8is $ 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 mas d q16xaxvh++y jj g/8 tnirq8/x.d+bys 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eightn dj i h/xyqxxady+/68+jvq+ rt8.g1b 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 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 exaww sab-pr9a 97r ehgm3xgz310 ctly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple plvv8jg oc 6p0*endulum be if it is to make exactly one swing per second? (That is, one complete vibratj ov 8v*0p6lgcion takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, 53tum2/3jr ( /f9pwbo *wdlpx i.uhaawhere the acceleration of gravity is about 0.37 jimup ha3a/bxo w5d.upw2rf/93l t ( *that on Earth?    s

  What is the period of a simple pendulum 80 cm long 4e5 pa)nwsp4w
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob h8of* 2rjndyn v: jf6qbwz ,dc2u-+ 6vuas a mass of 365 grams, and it is released *uvffb62q cv jou-6+rjnw d:dyz28 ,n at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length 3oza 5 ow9k8xkof 0.9930 m. If the clock loses half a minut859 3kaowxk zoe per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum sa+ gi tw,)xkl5peed $v_{max}$ 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 f wzu ,-at,3ylxt* pa*2.5 Hz. At it is released from rest starting at an angle of 1,z,y ul *3aftxwpt-a*5 $^{\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 cres7maym,dfk6k l / 55dflts pass the bow of his anchored boat every 3.0 s. He measures the distance belkdfm5f 5/d7 aly6,mk tween 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 34381hxz 2tbf8 qo m/s How far apart are the wave crests (compressitfh12b8oq8z xons)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz ( 06k5)zauejb6ai lv:v1 yde8dkilohertz) and travel with a speed 6k l5euezb6d a1av8)jy:d v i0of $ 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 p+pflb1 -cgiu8y* t1jin
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense 5f1;j aj5q k(7p 20wf/sslcodpb2o9f5qyt b a as the other. In which rod will the speed of longitudinal waves be greater, and1;o/ykf( 5jbcsaj qs5 d9 bqf05op 2 fpl2t7aw by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m a2e1vrk a,9; tgd- a8m*yj /ab+umiunqpart. If the tension in the cord is 150 N, how long will it take a pulse to travel from o+r na au*da,but1ji ;ygk- 2q/m8me9v ne support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 62a,/s x87dcik8dcx2 *;pb inp b0 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wavebnki /pb8c 2xcap*,xs7; did8 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 39e k9zpeb t8hship just below the surface of the sea. He hears the echo of the wave reflected b8e93th kp e9zfrom the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different mgchn w1r1.vxz 2 9x/tptw9suv/v15c , p2o fcspeeds, and this difference helps in locating the earthquake “epicenter” txpnwz,5gm.xfvc vv/cus/w9 1 1c22 prth19 o(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 ,cki5qax hjef+:br ; ng /s8)ocan be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz 8rex q+:fako5;cinhsj/b, g)(typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an earthq cz6w h;x+so)-w 6izinuake P wave passing through the Earth and detected at two points 10 km anwz); xco +hn -iz6i6wsd 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured tohaeph., h0rr3 vm5+/c+ utmo h be o.uh, 0v ph+5meh+ta c3rm/ hr$ 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 7oe .e/znq yv91 0rosesame frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waveeoy 9n/ 1 7vsero.e0qzs?   

  Two waves traveling along a stretched string have the samenr 5if1p.gie ) u petepxr+:,9 frequency, but one transports three times the power of the other. What is tnpex +i)up5.9et, e rg :pfi1rhe ratio of the amplitudes of the two waves?   

  A bug on the surface oflvw8yp 8 6no*8gh -kna a pond is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease ogvn* 8 ha k8-n8pw6lyto 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward er;ifus tsjo c1;r;5 vx)+6oanach 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,fx;stor;)v r io+ n;a5 16cusj 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 frequesrvxy+ 8r.h5 qncy, what are the 8qvsxy 5 h.+rrfrequencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfa (, km3js,d3y2khw (b)pvrq bingered. At what frequency will it vibrate if it is fingered one-third of the2( ,jry3abswm,qbhkp(k3 ) vd way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in fourv rl el9q- dpsjtqgu c+6+74t) loops at a frequency of 280 Hz. Name at least three other frequencies +cjs+ 7rqlv) det9uqlg-tp64 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 9iy /,vz5u44dca;sj9 jg iig- s2m/s If the frequency of standing waves is 475 Hz, how far apart are two adjacent -ugyi9j/a ,szijg4 4i5 vs;dcnodes?   m

  If two successive overtones of a vib(x wkfg1 9zw ,wi;z.(e.kfkoprating string are 280 Hz and 350 Hz, what is the frequency of t 1k;.9fkg w(zz .xw,k fo(ipwehe fundamental?    Hz

  A guitar string is 90 cm longg *y)s)5hgyph+d) edo and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?)h 5*h gyd+gspd)oy) e    Hz

  A particular guitar string is supposed x( lvkc.d8mbxb(c8;k 7f2p atvl pq50 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 the three fl xfc7v.k5c2(lpt0v x;kmba88 bpd(q requencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but w4i 1rbo3npd 8/qa2 lkit is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased byq d8/ ir41owkpla 23nb    %

  One end of a horizontal string is attached to a small-amplitude mecu2grw2a. y/ebyz h1y0hanical 60-Hz vibrator.zr2/1yb hu2y0yga ew. 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 lengp2k5fd z b,a/qth of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wzp2dka/,qf 5bave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back an+(;nqtz2up fl8t6t iad 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 produce such a standing wave in a 65-cm-wide tub is 0auptt6l (8;niz+t qf2 .85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within tp7- qh mi 5rzko(dd8g3he Earth between two kinds of mate h3 5k7dmz(r8-dogipq rial. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity chang kybhtq39a6 )imz r*(ies from 2.8 m/s tkba*h9(zrt qmy6 ii 3)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 layer of cd vs311cfeocud,a*j :old, dense air. If the sound wave hits 1sv:odc*c1f ,euj3a dthe 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.m:/8 qgvweymml6e (i a boundary between two types of rock at a 38 :q(g.vie w/mmley6 8m$^{\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 z5p;ti- 4;6x -tk th0ekz,wz7grrgv wto the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of abowzi;z 5pgw rkgv k4h0zt ;6t--e7xt r,ut 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 anduc:i fg*.n uqq3 f3 dnnx9-w)z velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time nun gzc:.)wxfdui f -*3q3q 9ndo 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 spr zjj. 2 *, f;cu/)gnityehnbqy7wzi09ing 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 (approximately 5 mi/h). [Hint: Uc jt0y;if*ej/nwb97.u 2z )nqizyh,gse conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, whichg;+nq sswp6pta1c/v 4 stretches the net 1.1 m. Assume that the net behaves like a simple spwvc+;n4g p6 /sqts1apring, 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 spring. The mass thenws isp/jrm 3(5 falls 33 cm before it stops and begins to risejrw(/p 3s5 msi. 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), compcun23o zm kg/2ressing the spring 5.0 m. (a) What isz 3/kcg2n2ou m 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 co.eamqgr17m /ck a n 0lkq:1j3msbj2-offee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starca3/sean mmj2ql:gj-1r 7kb o0qk 1.mts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove y:j l*r),*rh3e imzav10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of *z: rrae),mvyi3l* hj the sound emitted?    Hz

  A 2.00-kg mass vibrates accordeukv/s- us6 *ypd4 mu 3.wxn)uing to the equation x=0.650cos7.40t where x is in metersu 4du) w3uvn6k xms *-pusey./ and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. 8 yjapq- /zsf2What is its frequency if it accelerateq8j/ fz2pa-ys s at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg ma 0,i cnoy.k4dun stands on the raft, it sinks 4.0 cm deeper id .ouyn,ick40nto the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instr7xs2, 9 1gqjte0hov*cr4znbu ument are tuned to play at 392 Hz (G) and 440 Hz (At v79jz *uxn c br,102sehgqo4).
(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 stra9h;rbcq1 lddz:*)pxy)r kx 3etched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the 3hk:dqr)ay*xrd; zlb pc1) 9xwave 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 tipq;j nb:s kuf7; of each prong moves 1.8 mm to either s7;bjqkn:s; uf ide 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 simple harmonic motion of frequex)7zesg2 l*iw/gj i g0ncy 1.5 cycles per second. What is the maximum amplitude with which the end of the boalg x70sj ze*g/i)gw 2ird 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 attached to a ring that cvvq31xee:tt ns9, x.han slide without friction on a vertical pole (Fig. 11–57). Determe,:s nx3 1te9 vthvq.xine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exan h2mma))ahhquyz( -0ctly 2.000 s — each one-way swing takes 1.000 m( qmuz0nhh h) )y-2aas.
(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 directiojb4v6)tt:k 2vb 3 lbkin or can swing as a pendulum of small amplitude, but not both at the same time. Which one is lob3lb v)v i:j b2k6t4ktnger, 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 j ww-3e lfe kbq5s:bewf 8:3+xg is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will klfw-+: 3fe3e5 xqj wsb8e:bw the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stiff q 5+ x1v.uqhktl3izr.u-a0vhness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillationslir+uh03qka5xzqh v 1v.. - ut that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 120ka3jxd * k ek:/9zgra50-kg car at the junkyard. 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 the cable. What is:*3 5ra/e9kx z kkdgja 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 o5v7s) gs 41u u2 hp3nzk(plzn)a0fbh(which also gives the dimen4ob n5v7szs) z(ku2uphlnafh)0 g 1 p3sions 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 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