Give some examples of everyday vibrating objects. Which exhibit SHM, at leandu 0;m8 pgxr6st approximatel8r m60pun;gdxy?

Is the acceleration of a simple harmonic oscillator ever zero? If so, where?x.qf,yg 9 nr.o

Explain why the motion of a piston in an automobile engine is approximately simr2 r q46iqc+kdple harmonicc 42rrqd6+kiq .

Real springs have mass. Will the true period9v)zn4/drn 7; gdyou xs8sww4 and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealiuy gr )z/4ss7d o9d48;wv wnnxzed massless spring? Explain.

How could you double the maximum speed of a simple h9l;,t:p h4fo y;ogemixfd 9q/armonic oscillator (SHO)?

A 5.0-kg trout is attached tm4j *rfy2:ssq o the hook of a vertical spring scale, and then is release4r qyjss *fm2:d. Describe the scale reading as a function of time.

If a pendulum clock is accurate me9hv ov-noj7(4y ku7at sea level, will it gain or lose time when taken to hig-9u 7v( he4mjnv7yokoh altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig.9y*eocz+di(v o4u59uskdkzj 1 q(9h t 11–48). How could you estimate the c+d15skuy9vz zt(4(k*uji o9 qdh9oeheight of the branch using only a stopwatch?

Why can you make water slosh back and fb7r pwwh:bq j,( mbh03orth in a pan only if you shake the pan at a certain frmrw0(b bj3,b: h7p hwqequency?

Give several everyday vnaf9 h) .ey;y vvovunt;1b5/e-)kf mexamples of resonance.

Is a rattle in a car ever a resonance phenomorrbvh( ct gk,/h 1k31enon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of c.7)emflmcg wbf3 -l; its source? Why or.gl 3)fc7 e;-cm wmblf why not?

Explain the difference between the speed of a transverse wave traveling down ai1)d8oh9-zqz b b* 3p fcyo+ix cord and the sp b9 )h 8c-bioi3fozpdyxq*z+1eed of a tiny piece of the cord.

Why do the strings used for the lowestv*aa7xnjq k( ,-frequency notes on a piano normally have wirej(*a,qk nvxa7 wrapped around them?

What kind of waves do you think will travel down a horizontal me3q j(v-d:/lbrf ds :gr; n-o-pr)cwyetal rod if you styd3 sjrd og q -rr/-::plenwvbc(f; )-rike its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air dee90)vtcz-vez47 o lmccreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperaturetle vo9z vc)m7zce40- ?

Give two reasons why circular water waves decreh ./, 7k ipz rqcpt-gn)q3qs:iase in amplitude as they travel away from theq.q /iqhnk g-c:z7) pt,3rp si source.

Two linear waves havea1 qk,eh5we e9 rpb k1ya;o(x3 the same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which tran1qrk(e a5wxh ap; ekob9e 3y,1smits more energy? By what factor?

When a sinusoidal wave crosses the h/gmr)bz,su2 eb(.w-guuld jg:7wd/ boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Expub.:gurdu, -)/ es2z/g j7dwgmwhlb(lain why.

If a string is vibrating in three s6m*hib*dd. .p,onm ui egments, are there any places you could touch it with a knife blade without dio. *d u.n*,dmmpb i6histurbing the motion?

When a standing wave exists on a string, the v8iy/ak .s 60x 6pa;r,c00/seked txtijq6yi oibrations of incident and reflected waves cancel at the nodes. Does this mean that energy wact d0ijex a.it, s 8kr6exy/ipq6o6s/k00a y; s destroyed? Explain.

If we knew that enervqq oy,i6d92oxia. 9vgy was being transmitted from one place to another, how mighto .a6i9qdi9v2vo ,y xq we determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the totay:fc( ye74 o)c e+k rxgvld7.xl distance it travels in one period?+k 4)r ce y.d(exy:7vx7of lcg    m

  An elastic cord is 65 cm long when a weight of 75 N hangs f7hgg9kusw,9zd l,:w mrom it but is 85 cm long when a weight of 180 N hangs from i,h9 g:wlszgd9, 7u wmkt. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when d+*g40hn xc ghb.jc:e its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be +b4xcgjcg0 *:hnhed .the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) W4d9 odq )c+iwl6ndewr;sm6 (w hat is the spring stiffness constanwd)w;m9wq e4d d+6lsic(r no 6t $\approx$    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 wit70gdrsk )3,frp z 5s2dj2fw uhh a frequency of 3.0 Hz when a mass of 0.60 kg is hung from hpgu ,k5df)w2sd2zfr3j0 rs7it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x8f/p n:uxwl x k08d*ln of the mass in Fig. 11–2 at times t = 0: 8pn0ldlnkwxu/*8fx ,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. The web vibrates predom4o2nn ur*i/ox 68w -a:dz wrdvin wrv* 6 zi2rdd-u oxo4/8naw:nately 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 vibrates with6ps/sn jwc e63zp*v.8mch8kcd+w r-z 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 valuess68hdz -cncz *e+vw8cpj p wkm./3r 6 of m?    kg

  A 0.60-kg mass at the end qfukayto+r:-h-)t:5. ow eedof a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Deter+tykd:q:owho5fe )arut- .e -mine
(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 eqzjsi,9qrgg g 1tj;/ s usn3a.:uilibrium is the speed of a SHO half the maximum valgzs 9j1 quan,/.s;gs rj :3tigue?$\approx$    A

A mass attached to the end of a spring is stretched a di 5aw9ca)j4jhp xo 5o3rstance $x_0$ 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 verticqo gri;iz)gl+5u y1h) al spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium pos) ryqh1;uz)5g iol +igition again?    s

  An object with mass 3.0 kg is attached to a spring wuzb8b hx9.zj-1*xcg x,1 ,o. wocfckqith 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 witbqw,bu*cz ,8kzgxo1oc 1c.9-fx hx.jh 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 t ,ni)o(pwg:,*rbt s bto compress the spring of a toy popgun 0.200 m to “load” a 0.180-kr,)bt, :t*i spobg wn(g 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 o2wd d.g0 l5siff a spring; the other end is fixed to a wall. 3.0 J of work is requirlwsd0. i 5fdg2ed 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 equation x = 0.45cos6.4t where x is i ,b(b8 cxg+mxyv6thaox *0zv8n meters and t is ivv +bxmxcg(ha8t* 08 ,xzb 6oyn 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 equilibrx w3s+b28uya ww;doj:m y *2fbium is the energy of a SHO half KE and half PE? ± 3u y2fmsb;:d*xa ww +o2y8bjw   A

  If one vibration has 7.0 times the energy of a second, but their fq97f:a azf y k0o))uu jtj6fm.ran)3 wrequencies and masses are the same, what is the ratio of ra)f:7)a93qtm f ujf 0az.oknw y)j 6utheir amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging lige hcatq;jhm yhj ((+*,ht spring once every 0.6(haqct*jej+m( y, ; hh5 s.
(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 pa)-tm0mmkfxkl9x kpqk)+w,jym 8f3 3 nrallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of+))yn,8jkmp fm9mxtk3- l fkwxqmk30 vibration?

  A 300-g mass vibratesmayh)1 b +c/is according to the equation x = 0.38sin6.5t where x is in meters and t is m+hs /ay1)c ibin 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 of SHM, labeled A a1m )2yzai4q6gxb dye6nd 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 horizontal spring (k = :pkyfs3 / 8 hwc(uar-g3nb h//kp yu w8qen;2r124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s /a/r3:w(fn gr8pe83b;w q yk 2/ uhshy-kpncu 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 sprind+s ta2:f1vjbighj a2+; 0 sxbo, hjo0g stiffness 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=j bh+t 2 ;:iovg2o1sjdbah x00 fja+s,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 stf:i+3 cxy ie2qp+bd(m5*a atk iffness 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 0.600-kg block attached to a fixed horizontal sprin ni v8p0q4sd2nak/dl 5g whose spring stiffness cqn4l adp/8s2 0inv5dkonstant 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 rni hqt48*.w4ndpu 4(q zr6jhdqa,j9 reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the su4h dq,8rqrd qz*6tp44( wnnjj9 .ihapring 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 ua0*gykez,2-*y fgeu in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make e lingckbl+:ql (j-*rh dx):;hxactly one swing per second? (That is, one complete vibration iln- j:rghq:l;khc( + lx*) bdtakes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earttu-3 asrb(y i/hw0hy3 h. What is its period on Mars, where the accelety/rsa ih0ub(wy33 - hration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm 7p/ : w )jbdas m-7tnf 8o*xbaarq(zq0long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simp3.knl9qv,k9-( hf yca -+/aqs hvigd gle pendulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released,yv9anh 9s-qik+.(vh /-gfq3g dl ack 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 of 0.9930 m. If;4 j g7mipp+yaqe -ry(x8wvd- the clock loses half a minute per day, how should you adjust the lengty4vxqiymjwa e;-+ (d7pgp8 -rh of the pendulum? shortened by    mm.

Derive a formula for the maximumr)7 6q liw4awz 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 oscillates at ax qzpim 5-jtb7v50 to6 frequency of 2.5 Hz. At it is released from restb0 5m5tiqzjx6vpo t- 7 starting 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 cz/ryw h;xc57 78 lg/ei5apz pprests pass the bow of his anchored boat every 3.0 s. He measures the distance betwei py/ z577xcw l8;ph5 zae/rgpen 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 an0 ,f i,ugwt7zj0l xs7gavw)g*d travels with a speed of 343 m/s H0t z)s7w,wx i, fgvau0j7lg*g ow far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies betwl,hz a7psypw rf ./)q-een 550 kHz and 1600 kHz (kilohertz) and travel wi).7-,psflqar hw /zyp th 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 vz2mp/dw. .mdvd* hkku (8 3nhlongitudinal waves in
(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 deo no 7 ya9n7tt:i,bhj2nse as the other. In which rod wio 7otina9ynjthb: 2, 7ll the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports rk3ovb* o(hy -rzvem2*er - 27kzll2o28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one suppo 2( *2 l-ylerrvb7em -3hrko *vokz2zort to the other?    s

  A ski gondola is connected to the top of a hill by a steel cablel3/mgb 2, bt6/zreiaa 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 cable. It is observed that it took 16 s for the pulse to /a/gmz e r3 babl62t,ireturn.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the sq1a:.vnz lj 0eurface of the sea. He hears the echo of the wave reflected from the ocean floor directly belownl1: eqjz 0v.a 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake traveljj7;t. d-,+sgmu2w bf7 oramq-nzzs4 at different speeds, and this difference helps iq n7z 2msm-wbfgt .;r 7s ,-zu+oj4dajn locating the earthquake “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 approximat e*q-*ovs l5koa qz5n2ed by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects beginq o5 alkve*s -2no5z*q 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 earthqjsp2d uei6xt vqed,e* c;-9h n5e(l*nuake P wave passing through e92-t5euxq e *nid ;s6,d *elvhn(cjp the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an ea8q7jryxf 7,4 mqm1z jarthquake wave passing through the Earth is measured to be xmzfm7 17qrj q 4y8,ja$ 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 frequencyui(hu n (h1ji2 travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio (iihhun2 1(ujof the amplitudes of the two waves?   

  Two waves traveling e h wy;6og+-zfalong a stretched string have the same frequency, but one transports three times the power of the other. What is the ratio of oe6-g ;yzf+w hthe amplitudes of the two waves?   

  A bug on the surface rw d 0ru:o.*gm(vo q;fof 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 to 4.5 cm;oo: gw0v.rmqf*(rud , by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 a47omii (looc-re moving toward each other. (a) Sketch the shape of tio74 lm-(ooiche 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 frequency9pc0o e+2wiph,fb q *z, what are the frequencpp *0z 2ewqboh,9+ ifcies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hzjo+8y h fhiz3df0/z b6 when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-fid8foh0j z3/+6h y zbthirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequenxc6 *fkq:l e+f, s7emucy of 280 Hz. Name at least three othe qfs:x7k,l mfeu e*+c6r 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 in, yl1/zv1 aupp lx 5ikr,xw4,b0r-pus 92m/s If the frequency of standing waves is 475 Hz, how1 knv,w4u p/xl lrbipapz,ux15 0-,ry far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what is l ,lsrx9fzr 4-rt*cg1i5det 4 gl is4crr t*l1,t zx 5r-9de4fthe frequency of the fundamental?    Hz

  A guitar string is 90 cm long and hasdls+j2sb- 4+it2ov oq a mass of 3.6 g. The distance from the bridge to the support po sosb24+v t-oidj2lq+st is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 d3/ bk(wbg-- qdb5vi cghjv93Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency3 chgi d(-vw9gb d5v3/bb- kqj?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 isf n1 f idzxnj/,10j9 q7cbuj*m measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to jj9ud0ib qzf1 7j,f x*/cn1nm correct the frequency? decreased by    %

  One end of a horizontal string is attached to a sagdky/g-0v+niqtngy o5o4 x l9r7b,j+ov v - 1mall-amplitude mechanical 60-Hz vibrator. The string’s mass per unit length g- vbnja 4ntyy v+7-dv+/5x0o1ioo g lr,9kqgis $3.9 \times10^{ -4}$ 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 strinzxta .y1t(vk1 gg(0 dug may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieve0 t1(gzdx ka ug(1.tyvd by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the n:uc)biu mv75right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose thuni)u7 cbv m:5e 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 boundaf) etv8fm/f nhtxp04dy, *vf :ry within the Earth between two kinds of material. d ,ev*0fnxtyh/f4mv )ff8t :p 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 changes from32 d3jmxe*uhx*y : hmo 2.8 m/s to 2.1 m/s If the incident wave cr me:h2hx*3x3ymo jdu* ests 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 air.52d:fmlbh 1ld,hw 60 mamtm0x If the sound wave hits the cl06 w5fthbm1m2m a,dd0lhx: mold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types of01k+* as:xwxcjfug 0ssy i65 f rock at ag6yufsxc:j5 x iwfa+k10ss* 0 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 about 0.5 m in diameter. According :q kj2g9l ,pzuo5bqos(ir f3es (-k -ato the user’s manual, the dish has to be pointed in the direction of the satellisb3ks:- f5( j (2ro-9zi kqp,ula oqgete, 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 jn;favbirc y7e ya0453ci+, gand 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 ruj; nf5ei r3aa icyg7c,b4v0+yn 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 buoyw3d;- afs)u mper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500yfu;a w3-) ods kg, collides with a wall at a speed 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 net 18 m below, which stretches tf(suyu d2rma87w7 ds+.t 8tjbhe net 1.1 m. Assume that the net behaves lb 2 8dj+a7 7swdr8tf(t ysum.uike 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 frk*.ymzh :6tko eely hanging spring. The mass then falls 33 cm before it stopzt*k6hy. o mk:s and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes50t lmrm 0j8gq* u)nik a huge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiff )u5mgj8* l0knim0qrtness 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) at just the right pace of +rmz e e vy lhv/1u6ir74xg/zrxl2:x:about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coyxl7uzer::vz 6 +xr4ivm e2 g/x rl1/hffee.    cm/s

  The ripples in a certain groove 10.82r a fdq9smu:u 92ttwv)6/by/o)qn dl cm from the center of a 33-rpm phonograph record have a wavelength of u9tl6 f wdqas2oum/)2 /tyn9qvbdr):1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrakr1u/b5s81j7o bg82jmyb tju tes according to the equation x=0.650cos7.40t where x is in meters aomtj8/j811r2bgusk 5by b j u7nd 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 freq7 i(:snv t+uo5zmb a;duency f. What is its frequency if it accelerates at a:z5u;tsi 7b(d nvom+ 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on am*t lks q:kbhw*h s:(j7ll+ .w lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft : m*l tjqhkshwlblkw+* 7(.s: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 r lidi309(mjp,r1ytlil/s +a instrument are tuned to play at 392 Hz (G) and 440 Hz (A y/i,l+arr s30lp j91imlid (t).
(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. yt8z(c ud1w3hDeterz1 (hwy3c u8dtmine 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 greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 26c* x0j p vp;)x)mw 9dfqhz5v5n4 Hz, and the tip of each prong movesq9*)w0cjz5 p)5dxf ;n vxmp hv 1.8 mm to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscill p 9md631hvujuates with simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not losehmj1pu 6 9vd3u contact with the board during the oscillation?

A string can have a “free” end if thatc:my0p k,4eezq/ sno:6-w bil end is attached to a ring that can slide without friction on a vertical pocemq:kz4biw ly s6o:/-pne, 0le (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 ons3i)/iwa5 ah; -efjoqe-way swing takes 1.000 qw ;/ae5 ha) 3iofsi-js.
(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 directiogby)cd.. yq k+8axdm:n or can swing as a pendulum of small amplitude, but not bot8 +c.) kg .ybdyxq:madh at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A pulsj aah:xagqxsa1 /yf ) co 0dr8;jul51-e is generated at one end, and 20.0 ms later a second pulse is generated at the opposite h /la- q caof)da:5rxg s0;8j1jxy a1uend. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stiffnessfqnsz4a m6j 9z ny;a): constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top asj;f4:an 6yz 9qznm)of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel csi wez-,y z-7z ww;fl4qa3c ,;c:w6ol-hdngprane 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 the period of the bouncing? [az-slc- cynwl,wi,eo647gzqh : z ;p-wd ;wf3Hint: Refer to Table 9–1.]    s

  A block of jello rests on a q:h1 rv+yzqb4stg0 h 3/e: ysv ge-b.pplate 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 vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the sh: -sgq +eybvg.vrqp 3e :b4tyshzh1/0ear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz