Give some examples of everyday vibrating objects. Which ekc3 juqssqz)386;xv lx3 tyz4xhibit SHM, at least approximate68u3tv yx; )lzxjcq334 szsqkly?

Is the acceleration o1a)goxwjf h9 7hd99d wf a simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approx;:ra o ,owf.35dhli rmimately simple hr3oa5 w:.;d, ohmlfri armonic.

Real springs have mass.v.7j r /hs8ucm Will the true period and frequency be larger or smaller than given by the equations for a mass oscillating on thh .s8rmjv7u/ ce end of an idealized massless spring? Explain.

How could you double t2gb.y,ibe)xn he maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then isj,r s c(;gj1xh released. Describe the scaleh, cj xj1s(;rg reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time whenrvm u5mpza) ,2 taken to high alt5pmvza2r, um) itude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fign q8u:1-dql k em5ej q)+7x+qixx f87jyek(cq . 11–48). How could you estimate the height of the branch using onl+n xki x-qq8ue 7lyk+cjqx: )e18qmdje(q5 f7y a stopwatch?

Why can you make water slosh backfv e/)eo2 tsf;who bo,s-)8jz and forth in a pan only if you shake the pan at a certain t8)fojeshosob 2;v f-e/ z)w, frequency?

Give several everyday emi js.(ht o41 -qnc2rdxamples of resonance.

Is a rattle in a car ever a reson.. hd yg8llqz3ance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its source?m;ct si0fw3(o-mo zh c6b6 /ym Why om( zot/ym0 mwfhc6ibs6-c o3;r why not?

Explain the difference between the speed of a transverse wave traveling down sy8lq96jjw, p a cord and the speewjjq8s9ly6,p d of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a;8i8m ntw+d55 lp jzms piano normally have wire wrappetjp5l8s + mmidn5w;z8 d around them?

What kind of waves do you th m-nz7 4-4oygxcjc o ceuec04 4;bthk,ink will travel down a horizontal metal rod if you strike its end (a) vertically ht;44unxk4e7 e m4zc0,bo- c-cycjogfrom above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature 6dzwxelo 00va62 iw1ujr yzce/, e-2d, but the bulk modulus B is nearly independent of temperature, how woule 0i 26/vzwlzcuo 2d6dere1yj,0xa w-d you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decreavz76b-*(h7vxnr oquz anu +h5se in amplitude as they travel away from the souu5*7+v vz (au7hoxnn-qzb hr 6rce.

Two linear waves haveim2cg9 rpv), +qg-dp95 tyfye the same amplitude and speed, and otherwise are identical, except one has half th+) p 9yq2-, ypdgvei9rg5tmfce wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses twd z i.o)-1ydi;y g:akef+d3ohe boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do z-d:a;kdg.+ywo)f3 1ii edo ychange). Explain why.

If a string is vibrating in three segments, are there an y6m)lo; lk1wzy places you could touch it with a knife blade without disturbing the motiz6lwl k my)o;1on?

When a standing wavenkf(+0 dpd y4jwny:p( exists on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was desw0ny( f d4+kjn(d:ypptroyed? Explain.

If we knew that energy was being truik-hu 56 ji:wkb4 6ut/ 0gthoansmitted from one place to another, how might -g /uto6h 56uiktbk0 jw4iuh: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 t/p i/svup.5 pehe total distance it travels in one period?p p/e/u.i sv5p    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from itx,fmx ql5mk- k:0tmc7 but is 85 cm long when a weight of 180 N hangs from it. c :-mlkt k,x05x7qmfmWhat is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm- 6fhmb th2mbk* 7cr.b-vw z;3xyr*ds when its 68-kg driver gets into the driver’s seazwh-*t6 srh2*bkbvmc7. x3b fry-; mdt. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.q ge*zfs;gpw-vcoh unc61s-.9 , ;hr n6 cm when a 2.7-kg fish hangs from it. (a) What is the spring s fg.wvp;c6gr9h; u-,nn so1 -eqc* shztiffness 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 3ggt u8 t(wg6t3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if 3(utgttg w6 8gonly 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass u:otrg u f+3dab+y*yp b.0idav8bh47 in Fig. 11–2 at times t = 0,t =p tu *by0+:a .o8+irgf4ddb uba 3yvh7 $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 19itm0 xsq80h )qtp0b,qyhy w vibrates predominately with a frequency of 4.wx,yiqhq1) qyt089bs00 thmp0 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 vibra ;-p;9xo5jnopbl de:fj3p ;k utes with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the fd;3;f pn 5j9leo-xpjkbuop: ; requency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibri*gob9-b xo r+ates 3.0 times per second with an amplitude of 0.13 9i*roo xg+- bbm. 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 half tht6j chrp -.ss s 7cpyk*67-mxpe maximum valutsy6r7 h 6sp csk p-.xmjp-7*ce?$\approx$    A

A mass attached to the end of 8:f0m l a+lx.bbfcqc4a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring is stretchign:b +9;x nfxm*v2bved an additional 0.130 m and released, how long doesnv *bi2+ nbvxf9 mxg;: it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a sz/) vgg+dd(ne43 7o h(cnwlbu pring with spring stiffness constant k = 280 N/m and is execu (d (b)v7hogwd/+e4uczg3nnl ting simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spgjyn(:u* tkl gc(vl snb08;a jr/.jw) ring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed (*ggjr(ykbclla 0. j8vnw u;n:j/s t) will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface - ydm 6fss0zphzt7s;sh9:yc4 is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work i:htczf7 hp0m6s4ss -z;sy9d ys 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 equation x = 0.45cos6.4ow8gpt3s;/:oht+v ee t where x is in meters and t is in t3g/eswhet+o : 8vp;oseconds. 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 equilibrium is the energy of a SHO hao 1qj79(c dzgzlf KE and half PE? ±gzzo7c 91qjd(    A

  If one vibration has 7.0 times the energy of a second, but their frequencies andu7 bptc+kh1( c masses are the sa t1 (ub7ch+cpkme, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillatesopu- nqc2ndw9/b8n2 t nt7 sv7 from a vertically hanging light spring once every 0.65 ssub qop/w -ncntn728nvt27 d 9.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical-. fq92pc c fymivyexml 49u+1 springs, each with spring stiffness constant k (Fig. 11–49). Wh2f9p ml eic4qxf9.y c mu1-v+yat will be the frequency of vibration?

  A 300-g mass vibrates accord93denjt)t 6 zding to the equation x = 0.38sin6.5t where x is in meters and3t )jdtde9z 6n 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 of SHM, labeled A and B. For each(t97 t+zm qojoh a;m5b, 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 spb8jg3rcjnui3 : n- 9x(twz +rnring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Det9wjbn3xg8z nniru3r + :c-tj (ermine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates with an amdy/ 3z jqewq+:plitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive veloce 3qd/z+wj: qyity 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 speq yj:* +9umccrings, 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 0.600-kg block attached to a fixed horizontal ek,93q :z 2bbz2t1 zx8dhir uvspring whose s,ehvtq :xubb2z1kz idr8 z2 93pring 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 wlmkf+c( jc/ 6 iehs6865.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight mor/6fij w m+chk (c6ls8ee 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 exactly 60 s. What is v(jkoh -nml8y a+ )p-aits
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swin1 lqdupugdb 1sc0 3b6)r;kgn7+axwy 8g per second? (That is, one complete vibration tak013+bwndydxurs8l ugbp 1qkg7) 6;caes exactly 2.0 s.)    m

  A pendulum has a periox7 yih+m-95w h))fvypvq za2v d of 0.80 s on Earth. What is its period on Mars, where the acceleratiy-)i7fhmzv v9y+52)p wqh vx aon of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cmtm/;(dkprjk 8 long
(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 man.d u g a6c;dqft/n3j*ja+gw1 ss of 365 grams, and it is released at an angle ondfa *3j1.+q6atdugc /; jwngf 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. If8om.a ie5h tn.j*is-y the clock loses half a minute per day, how should you adjust the length of the pendulumj*n eismy 5o.ta- i8h.? shortened by    mm.

Derive a formula for tx- iu6ko/zk j*he maximum 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 a frequency of 2.5 Hz. At it is release :.)uliamb.sc2;zy pyd from rest startiyb) .aly2 ;suci: .mpzng at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat every 3.0n wo3,lpz9 v5 tf/fyc( s. He measures the distance between two crests to be 6.5 m. Hoyz(f nf,c tpo/3wlv 59w fast are the waves traveling?    m/s

  A sound wave in air has a frequen, 4ghlrr;,i tucy of 262 Hz and travels with a speed of 343 m/s How ,ih; ug4 r,rltfar apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies betwhe(yotv).(m)mc 9x:j w6 el bzeen 550 kHz and 1600 kHz (kilohertz) and travel with ac:ybm.lto e) (69j)(mv xewhz speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal wave 04awq8 nmd8edh/:h dbs in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twic+ 2c795jle5lzf qksck e as dense as the other. In which rod will the speed of longitudinal waves be greater, and 5k +5 c l9kl7j2efszqcby what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. Ivj+vzig.td d; 9ro( o1f the tension in the cord is 150 N, + 9;otj.d(dv rzg1oivhow long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the toppp rigb / *7p0xyo9u*d of 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 cable. It is observpbdo*0*uyp/rgx ip 97ed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sea. He hea;;shr3cr ch,ani76ql rs the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this poilc sr;i;cq hn3rh76,ant?    m

  P and S waves from an earlhu:yj .re) k7,be5 tzthquake travel at different speeds, and this difference helps in locating th7 eb: j)5.ltekzhry u,e 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 surv m ypu,2/9f,2jtroh l abe-q6face wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of fryhjq,69 vo- ue2 bl2 fta/m,prequencies), 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 earto2 a0am*st7 hui4 ax9ihquake P wave passing through the Earth and detected at twoot i *7aam2sa49ihux0 points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an eair fl0m+eju8 sgs*h 46rthquake wave passing through the Earth is measured to be rsgl+s48j6h em 0u*if$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same 0ag6xda219 rmsd4n daportion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the 2d ms a0g64xd1ran9a dtwo waves?   

  Two waves traveling along a stretched 8fl* zt3wj;p8n(ugwp string have the same frequency, but one transport fgp38l*( ;ntwuzpj8ws three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down aevz9 (38:w*r ramoje4djkpd. total vertical distance of 6.0 a:*pv 9dwkoj 4rz3me( de8.rj cm, from the lowest to the 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 F b) rrpoerojb8ybl46 e*qo-q 41r2w)dd99cthig. 11–52 are moving toward each 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 straight. What has happened to the energy atqyp8 deo9 tl hwe-o9 bo4j4br db*2q1r6 )crr) this moment?

  If a violin string vibrp4uwh2+n ds3 7zfq( uyates at 440 Hz as its fundamental frequency, what are the frequencies of the first four hadp(n2w3h 4u+f usqzy7 rmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequen,hhlpm95e ji8y8 1m gxcy will it vibrate if immx,ehhl5 y8g jpi 891t 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 0e qgvlv*1 12l gfed9cin four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will 9lvve2 dggc*11e q0f lresonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If thet)f; +y po5rgl frequency of standing waves is 475 Hz, how f+)f log;5py trar apart are two adjacent nodes?   m

  If two successive overtones og. , .cbhrwdx4f a vibrating string are 280 Hz and 350 Hz, what is the frequency of the fundamental? xr b..4,gw dch   Hz

  A guitar string is 90 cm long and has a mrocrn-9*j 0)g ageo+ck6(jm lass of 3.6 g. The distance from the bridge to the support post is L (rc*g lr9mkeoj -6ocn +aj0g)= 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 isfx3)++y lx mgp supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shou++pxxl 3f)gymld the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is sug,7; / ,iob; k+xjff n u1enevh;uvg:epposed 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 freffv/;ej; i,bg u7,on kuexv1h; g+n:equency? decreased by    %

  One end of a horizontal string is attached to a small-am: .twc-vvl +i(smjdkr. g-s4 splitude mechanical 60-Hz vibrator. The string’s mass per unit lw(ms. :tl s v-+-jgvcd4.kris ength is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by movi*an:h3nfxj 55/bo kerng the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achire*3x hjo:5k5n/f b naeved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub alii9gg 3,nig0 t just the right frequency, the water alternately rises and falls at each9li n0i,gig g3 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 bo7iw;he6 krisxgtu ;+j09jz 9feq*p7u undary within the Earth between two kinds of material. If it approaches the b k0;f7uu6ehwz 9j7 tjep*ri ;sgq9i +xoundary 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 velocit4j 7uoyv:a n4ry changes from 2.8 m/s to 2.1 m/s If the incident wave cresuaryo v nj447:ts 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. Ile3:7s z:sgfp f the sound wave his:ezsl37 pg:fts the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave qh 1o 6ajd29k zy 3s8:tr *h2yp.:d zjsyuu;wfstrikes a boundary between two types of rock at a 3 s:6 2t9*h:.zdoyy 1jasyjz8p2f kdrw ;u3hq u8 $^{\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 z*o (ltdd5k +pin diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error ofl *5(o+ tpkzdd about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocityu-cj;m.hj pv (xf.0cz 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 have died during tsunamis, some of them attrj0u.h.zpc mjv xf(-c;acted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/+:vpx c b5s2e(vh;gqj m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides cgv+ q5pj xsb2e;h v:(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 str cufn*zqou nsp07-6r7etches the net 1.1 m. Assume that the net behaves like a sisp7*or zq0nf-6 u un7cmple 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 ao vxw t k+(za;o1tj,i/ freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequencyxji tz/;o (a,w1okvt+ of the oscillation?    Hz

  A 950-kg car strikes a hl4wo8cg +n6c kuge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m4c cw6n 8o+lkg. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffpyw2ka 4d;z* fee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventuall*w4 ya kd;fp2zy it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the nb*+ 0vvhk h7acenter of a 33-rpm phonograph rhvh7 b0 k*nav+ecord have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates a lloehea4+amrfp- ;dkn 0*b;.ccording to the equation x=0.650cos7.40t where x is in meters and t in o 0maf nde.l-*kbh +e4;lrap;seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its fryp;+9qoe .wz requency if it accelerates at 0.5roe wyq +;pz9.0g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stanbg w(7i*jz em2 *0oafcds on the raft, it sinks 4.0 cm d*2 *fm(boaj7iz0 ewcgeeper into 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 instrument are tuned to play at 392 Hz (G) and 440 Hm2fqf q1rjp1:z (A). mf 2frjq q11:p
(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 stvf3 nl y gx05j cv1sjwc;k* (ry3d*yq8retched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in tng;y 5*v kr3c(x8j13dlyc0f ysjwq* v he 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 tip of each p5)jb 3ejtb64o .2jx hfvil:ih rong moves 1.8 mm to either sideol3 i jhxt6hbei):2f5v4j .bj 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 frequency 1.5 cycq fy x1u0:; rva p0pwosigh048les per second. What is pua:0 x fyi 1pr4; v8q0og0shwthe maximum amplitude with which the end of the 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 ist yhyf ,ecu,8/v:bp0un7+ z aa attached to a ring that can slide without friction on a au:f,h+ z n7bcvpt8,au yey0/vertical 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 2sw6 q,zo(pp qpmz 5cgmf93-v 9.000 s — each one-way swing takes 1.000 sz- qvp wp9(fo5g3m9s z,pcm q6.
(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 verticall:i t7b;fs :*cex8 clp direction or can swing as a pendulum of small amplitude, but not both at the samlp:7 c*8 biel:stxf;ce 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 mzprjuv:+yb(k;26dv 7rhvt3g is stretched under a tension of 255 N. A pulse is generated vk jm7 vzrb6 du+23;vtyprh: (at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with z93orv4p q9 ztspring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscilla r9ozq9tv34p ztions that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable i,ijq5:5k e/(spwe+y ba rme47un ; wgrs 22 m long and has a diameter of 6.4 mm. (bm7jqki yga5s+ew e /4rep,:nur5; wA breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also3t22t40;yct cy ;tzvyeaq r63kf+cs d gives the dimensions of the block). You push it siecvdtcsq ayc20k2tr + 6zy;t4 3;3ftydeways 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