Give some examples of everyday vibrating objects. Whicn2vopm mn/y aqck r)f11,6nc2h exhibit SHM, at least approximat,)rycv1 nqapom2 mn 1/k n62cfely?

Is the acceleration of a simple harmonic oscillator e- 4ultpd,f s-dver zero? If so, where?

Explain why the motion of a pistonbk w smx,+yhkn,4 +of: in an automobile engine is approximately simple ha+x4 mbofy w,+ks ,:khnrmonic.

Real springs have mass. Will the true period and frequency be larger or small5kg )zdu;pulnikcan d9;vt iv.ws+:0 : ha)(xer than given by the equations for ak p:ahd()+vci d9vt:nnigs;5 )lu z x0.a w;ku mass oscillating on the end of an idealized massless spring? Explain.

How could you double the2ogh*)* hdgf 4uns9yc maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical sprinm pu,+zrl*vw1g scale, and then is released. Descwzmu *vp +,rl1ribe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, wzxu.ym(i a1g 8rlew; r av1cx9ib1-h7ill it gain or lose time when taken to high altitudl-c7 1mu w (ixb;agvarir1h9e.1xz y8e? Why?

A tire swing hanging from a branch reaches nearly to thb+-cun5:us)+blu4 z xa. tqb0 bsq2jve ground (Fig. 11–48). How could you estimate th j u4 )-c tns5qbbs vlx.z+2u0b:+qaube height of the branch using only a stopwatch?

Why can you make water sl6ztpc iaif5)k2 w4:tk -nmz8bosh back and forth in a pan only if you shake the pan at a certain f4c ii2 f k -tnz8)zp5bkwa:tm6requency?

Give several everyday examples of resw -.r . 3ohcdnnyxk1r)61 ;euwl* )(q hdaijgionance.

Is a rattle in a car ever a r w( zlvc*wrvr:c*5y2bk6zmf mow2 )4cesonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequencyhn91jf:djnlfo fuy() pb1z 7c (u(:da of its source? Why or why p9fdnd)hao(nj1 j1((: 7lbf y cu fzu:not?

Explain the difference between the speed of a transv.. sgn2dg(rqen (gz4i erse wave traveling down a cord ange qnn.gs4 i(2.grd(z d the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequ ,+0nknba 1clgency notes on a piano normally have wire wrappekgb +n1l ,0ancd around them?

What kind of waves do you think will travekh*1n 7i9gvqmb;up )rhz7zg:l down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parak 1nguv) 9brzim;7*:zp7h qhg llel to its length?

Since the density of air decrea7sih:k a,x* 7t1e (oeipxc b8ises with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how woux1ka*ehpb(7i se:7oicx ti ,8 ld you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as the t 6 ff:90g( gddcj:dx3p+eoi2jhr)fs y travel awayx(9ji edo 3jrgf cg:fht)0d2:p+ds f6 from the source.

Two linear waves have the same amplitude and speed, and otherwise are identicaxqxu -/9tb; uw s3i2tol, except one has half the wavelength of the other. Which transmits more energy? By what factoqb xws/t u9ti-3 ;uo2xr?

When a sinusoidal wave crosses ty+fd2 11wwb h *oyu cg0j6hcm.he boundary between two sections of cord as in Fig. 11–33, the frequency does not change (alyjwc +ofm6 b1duchh*w0gy .12though the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any placesps7uq d/ee 4v0 you could touch it with a knife blade without disturbing thevesp4q7/ed 0 u motion?

When a standing wave exists on a strivq wp76,y3yc ca/a kn3,e :catng, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed3,a y3vkeac 6:ca tqw,c n7yp/? Explain.

If we knew that energy was being transmitted from onetcu4 13ofppg( place to another, how might we det3 up p14(ofgctermine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHMglm8fp0 c:e5o -r 3joy with amplitude 0.18 m, what is the total distance it tyml5e o:8o -c30j prgfravels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N 2gjv 8 )k .srzc9yvcu/*go1vwhangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elasti8/wcyv k.o gvzc*rv29su) g j1c cord?    N/m

  The springs of a 1500-kg car cm: zren+ zh0tr ks1cgj;1s6+s ompress 5.0 mm when its 68-kg driver gets into the driver’s seat. Ik1 ;rrjg c+zt01 :zses6smn+hf the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs qr4+ytrn -e5nfrom it. (a) What is the s -+teryqrn 5n4pring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.4a,fow + eya,lo3yq- tc2hpj .4*tnve 60 kg is hung from it. What is its w4net.aey,qj ol 2*fyp+t- c o av4,3hfrequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11xo. 1ksjmt i(eh5ta8zh23 d 9c–2 at times t = 0,t = z2mo.th(53 kh 1sat9 dic 8xje$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The w1(dk5yj pkj.1v s 8h6g:ot.d3f wfkireb vibrates predominately with a frequef531jyvh(d .k tf6 jwk: pidogs8rk1.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 Hz.ce9 j:/ 7me6 dkvjl/el When an additiond/ /v eje6ejk lc7m9l:al 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring veg2t xt* wplqbh4i1tbl:m,:ha) l9-v ibrates 3.0 times per second with an amplitude of 0.13 hbt,p2 lb vq-thg:*l9)ie lwx:4a1mtm. 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 equilipf yu p5g((-2olhh db2brium is the speed of a SHO half the maximum valuebhlhyu2g-52(pof dp(?$\approx$    A

A mass attached to the end of a spring is stretched a distance tjjkwx, x.x7;gw /e1h $x_0$ 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: 0 nip/zo9fas)rc.if a vertical spring 0.315 m. If the spring is stretched an additis : cn9 z.fpiafr/oi)0onal 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 ap /jy+ 4)jer7nrntic.jv 7k;q ttached to a spring with spring 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 moving with a spe 7p)7nnk v ejcqj4iyjrt;.r+/ ed 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 popgun 0.201h 1tnow;brj 5k+pq le: v4r8m0 m to “loav5 +wr:k;le41tp1njh qomr8bd” a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end obgbv85 ( k0f;ie/hi 9ion+ihwf a spring; the other end is fixed to a wall. 3.in0g5 +kv ;9bhhf(w eio/8ibi0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equv+d -i;x;)+vr xcp96hp3 bu,v zdewfpation x = 0.45cos6.4t where x is in meters and t is in seconds. Determine 3v6;p9zuvef dhw,rb - pi++cx vp;x d)
(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 e z/xi*g8t1pm.kc -djq quilibrium is the energy of a SHO half KE and half PE? ±pt8*d.ijc-1xzk/q mg    A

  If one vibration has 7.0 timw ooex:5d: 7)kzeak p c)2fv2qes the energy of a second, but their frequencies and masses are the same, what is the rkfeoo:q):5 d2ea wvx2) czpk7atio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a verticm(-;tmpg ,fqhlu, hc +ally hanging light spring once every 0.65 s. , lh,u pghmm q+c-(tf;
(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 vertg0;lvr3uxc* bical springs, each with spring stiffness constant k (Fig. 11–49). What will be3x 0*b;clvgur the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where xk:* zj w5y0e/a,lov2xoi8jmx is in metvyo0 oxwx : i8lk 2jemazj/,*5ers and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples o 6rel6gsza r./f SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizou ;6;k5t bkc8kjhhwz:ice8(xntal spring (k = 124 N/m) is struck by ak8k85k j(cubthz6exi;c :h w ; hammer, which gives the mass an initial 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 wi/d:7acw b5ln612kgw37x jeihhi ,eux th spring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs f 7,:e2wxxb k1luw7 ehaj6d cii3/h5ngrom it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness cons - fu9q3ach 52sbc nhqx4;cbe(tants $k_1$ 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 horizontal springx0 u0sgtiw1;u+v38f 1zu wwc m whosei;3uw0x0 g1+fcwuvt usw18zm spring stiffness 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 bridge. After re* );h zwkhh0xcaching 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 tch0z*; w)xhk hhe bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What is w.wwwg; k6 wpwb r+ pi 8e4*)o8av)jweits
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum b:- ypo fe/vz/oe if it is to make exactly one swing per second? (That is, one complete vibration takeop :oz/evy -f/s exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is,nak n /y. grohc90iqsa1wa 8( its period on Mars, where the acceleration of gravity is about0q8 (w. ac o gnaaysr1h/nk9i, 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm long 2 .ml7mq1mtzc
(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 has a mass of6xve*wzr s,-ab 9 oy8h 365 grams, and it is releaswy 9sh8r*z6 oxvab- ,eed 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’uzo;melsk s7,-g 8 qw2okw:z0s pendulum has a length of 0.9930 m. If the clock loses half a minute per day, how sh su ;8wgsz:z m27,wkloo- kq0eould you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum spihgr2pdys3cw.).ksv b*4 aw)v :2rmkeed $v_{max}$ 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 frequenfm0x-ua :ac 8:ts1pfn cy of 2.5 Hz. At it is released from rest startia-c fa 1u:sn08x:fmtp ng 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 pasm3/: j cq uh.ysb5m,gffxjz 60s the bow of his anchored boat every 3.0 s. He measures the distance between two c.y , 6zjfq0umbm/3scj:g5f hxrests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz andk2oyb;v:do h- travels with a speed of 343 m/s How far apart are the wave crests (compressionoyv-o :kdb2h; s)?    m

  (a) AM radio signals have frequenciek(oe;lz w20yegwx( wn 54w+ zws between 550 kHz and 1600 kHz (kilohertz) and travel w;w0e ww nw yg(4wzex(2+o k5zlith 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 1kfsnf m1+hy kn6 5wm5longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one o(x .zq5k iti 6vld3zl60sj7x is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what fsvi(6j307l qztx k65 x.oizdlactor?   

  A cord of mass 0.65 kg is stretched betweeix8r *lkxsbh:o3v0/f k+vx j1n two supports 28 m apart. If the tension in the cord is 150 N, how long w x1ikkv0x+hrloxv js3b*f 8/:ill it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top o4q2un bwm0x1 df 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, it bumps into the terminal and sends a wave pulse along the cab xqb4m1u2dw0 nle. 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 :8z-pskg *f qj zcsq6-his ship just below the surface of the sea. He hears the echo of tp:zcfj-*6 sqz-qk s 8ghe 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 travel at differe7j8 xscq vzz7 *zh ,g;1g3ebhbnt speeds, and this difference helps in locating the earthqua g7 zh*1 bv s8h3bx,ejqzg7c;zke “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 approxi1blmkyspo0 m5 07p9v kmated by a sinusoidal transverse wave. Assuming a fkpm y57l9bk1 pv 0mso0requency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an earthqu.xb*nap in */bo7:h wurlb/z6ake P wave passing through the Eartr6*x:b/z lnnwho*a /p.bb iu 7h and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave 4bsrr,- ndn8cc yq8;opassing through the Earth is measured to be ,c s- n;q8bno8yr4rcd $ 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 fjy wo5xshm (5lvp5y2 +ize;,wrequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes+wie;,ys5zh2oyw(p 5 mx5l vj of the two waves?   

  Two waves traveling along a stretched string have the same frequenc+7e+pqd v.fo p2qf32gk) lhoby, but one transports three times the power of the other. What is the ratio of the amplitudes of the two wav3 g+v q+.eqk7o2d hopf bpf2l)es?   

  A bug on the surface of a pond is observed to move up and down a total verti)9;lq obtq( i(ldw4( 6 qiatbg e-mf5acal distance of 6.0 cm, from the lowest to thm546l q((fo( )w -eta;q tdlqiibag9be highest point, as 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 eact1x c /uo1ucy.h other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straigcu1o1.ty cu/ xht. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, whatgv2)jobb;y o ;jz- j i,+1q(bvjmw yo- are the f;-j yzi;o-1owjvv)+bbgy,mq jbj ( o2requencies 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 unfingered. At what frequency wmh*d(rc+yd9:t jmu0n2:c: o 0bbmqk mill it vibratt0mnj2qkob:m:* c(d9dhc:u0ym+m rb e 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 ang6mm d5*qx: of 280 Hz. Name at leas*dmnx5qm:g 6a t three other frequencies 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 standing waves38bnqh ye7 09t ejvht;fdt5l8 is 475 Hz, how far apart ar870bh 9t3;hee5vj8ntqd fylte two adjacent nodes?   m

  If two successive overtones of a vibn f+rd9 ,o4w4odbnt*rrating string are 280 Hz and 350 Hz, what is the frequency of the fundame r4dro,df +49tnowb*n ntal?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distan)izpzoa :6( + 3hmciedce from the bridge to the support post is L = 62cm and the string is under a tension o(pzmoi :+i 3c ed6z)ahf 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, bumg ii xk38ejbxyy)bt01s5,za .4ni9y93 frnwt 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 frequen ,e95j0 b x8nkgyyr 3 1zt xa3fs)w9yimi.4bnicies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, bu g .jap gd*n5b3.9rc sos2+cp 3e:fzsut it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the fs. c* ap+ g.fcd3gr ssz b93npo:euj25requency? decreased by    %

  One end of a horizontal string is a-0) b:ce1sdhuxwimso )4e o 7yttached to a small-amplitude mechanical 60-Hz vibrator. The stc4ou )x:s-s b10e)m7iod heywring’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the w +x7owfd48y4o 6e netstring may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many diffex8 twe7do4 6ny4 e+owfrent standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequency, tsxp;qt; rnlk w1huj; (rwlhi3+o9f. e* ,emb1he waterli x;w (orsq 1wp;e9,hf;enh 3jltr .+1u k*bm 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 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundarynf*w/ilhh 2f*vc a -q, within the Earth between two kinds of*qif* hc/ af2nhw-lv, 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 am: s4j58 difuaa wqv,14/ wwpunderwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make 1 swwp a faujw8d/m q4av:5i,4a 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 atg-:s -y8 rnnd layer of cold, dense air. If the sound wave hits the-:g-s tnnydr8 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 waver89yx 2 l/fincy4s(u84 bwq kz strikes a boundary between two types of rock at a( wycl884b xrs9/yf2q zukni4 38 $^{\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 a svhswp/txr: lci* * zm/;u3mm99 zdy(bout 0.5 m in diameter. According to the user’s manual, the dish haupm:/*sr9cs 3tw;/i (*mzl hvzyd xm9s to be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km an-x6:c)z,bq w+li) szuuh /nqkd 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 do they have to run to safety? (In the absence of knowledge and warning, people haves,q:zb /i6xlkcq)h) uu+wzn - died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/m ea+k q8;pei c8 bkk7*eFind the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a spqbe k;+k *i8a78cepekeed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire n+o,w.x o6owwjb y3,af et 18 m below, which stretches the net 1.1 m. Assume tjowa.o,x 3fy+ w6,bowhat the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The mass z5 jf a jstqdo.p uv39h95ue58then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillation? tfqa.hj zsp99u38u 55vd 5oej   Hz

  A 950-kg car strikes a huge spring at a speed of m 7 kg;axpyq97idlu4 ,22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the spring?4,yg;alx d7ui7 pkmq9    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 coffeedk (j-w0g(r it rc3u55ac3bn6 ;dv, zbf5age w (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the r3k rdw6v53 w5-ja n;aebd(tf5g0u ,zgb(i cc top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10g2abi 6zm0 yl2*sg;ya.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitte 2glg0 ; *basymz6a2yid?    Hz

  A 2.00-kg mass vibrates according tie1y xf5 ib*6f-uv py./gf*euo the equation x=0.650cos7.40t where x is in meters and t in seconds. veyuiyix/- 1*u pfb5*6 .gffe 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. Whrh( b6t;.qcb wno2y3wat is its frequency if it accelerat2(3t.y;qb rbn6wwhcoes at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, it s2 rdxbkv qqw;sd2* *sa)xjp1 (inks 4.0 cm deeper into the water. When he x)b(j*p 2rasd s2x ;*k1vwqqdsteps 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 instrument are tuned to play atasr*-9hd ;n sltka0q; 392 Hz (G) and 440 Hz (rhlasn ; -tdka0;*q9s A).
(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 down7nem6wnlh,z2 47xcf q the stretched two-part 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 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 grl h n7nezfcx24,6qm w7eater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of ibs8a 7 be6i.i264 Hz, and the tip of each prong moves 1.8 mm to either side of ce.78s ae ii6ibbnter. 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 si503v(.sg- f2ihk r6qixpln4l9hf- h psk5w dpmple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of hq siw r5hg60pl- p.kv 5p ls4d3hfxkn(-9f2ithe board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is att6/25nf crhwe zached to a ring that can slide without friction on a vertical/zc wh52fne r6 pole (Fig. 11–57). Determine 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 exactly 2.000 s — each one- t9;mlf+ gw(lu pi2yz6way swing takes 1+;2tf(umlpil6w ygz 9.000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or ca ,.kvcvyt0b ) mx rr6w+d:kmm*pf).p cn swing as a pendulum of small amplitude, but not both at the same time. Wb)fm)dxrymkp . p wv06+*c mtrck:.,vhich one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 zl4 uxlza*8 q9el5 zx*N. A pulse is generated at one end, and 20.0 ms later a second pulse is gen*9qau l*zzez 5x4ll8 xerated at the opposite end. Where will the two pulses first meet?    m

A block of mass M iscv0o+) p,1kg s 8gjaqw ndr6;p suspended from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the6wc,sr +nd1pp8g jgko va;)0q 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 jh2 xphdptr8c 95e,m5yunkyard. 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 c95pxpcmr,eyh 5 28htd able. 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 givoj(7a g/ ,wv5tarfv7 kes the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given tha, 5k/wa (ovvj7fg7rt at the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz