Give some examples of everyday vi - m(-3fdbvs6d/y bdtjbrating objects. Which exhibit SHM, at least approximatb3-bfd6t/dsj yv m(d-ely?

Is the acceleration of a simple harmonic oscillator ever zero? If so, wherek r4(xevce 4nia*ol,3?

Explain why the motion of a v(yr;g4gd /r0oyh 5fy piston in an automobile engine is approximately simple harmogyhyo45 /r0ydvg;r (fnic.

Real springs have mass. Will the true period and frequenhe9/j( :a+ d2 ywfimzucy be larger or smaller than given by the equations for a mass oscillating on the end of an idealized m+ya dz(wufi:m2 e/h9jassless spring? Explain.

How could you double the maximum speed of a simple harmonic oslffk0e1ff;an6z)3g i cillator (SHO)?

A 5.0-kg trout is attached to the hook of zxy+f7 nl u l)0lx*er)il*a) z+s*k upa vertical spring scale, and then is ralr uy x+f)l s+n*zkl *zpex 7)*li)u0eleased. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose 3ke0kwgte;5g 2+obsg time when taken to hg0+5eskg;otk 2gb we3igh altitude? Why?

A tire swing hanging from a branch reaches nearly to ti ft4p*2i nhf-he ground (Fig. 11–48). How could you estimate the height of the branch usiptn24i f h*-ifng only a stopwatch?

Why can you make water slawr ni6u0 .tl b*c:wv-osh back and forth in a pan only if you shake the pan at a ci n:6r alw0tu*bw-. vcertain frequency?

Give several everyday examples of resonan1ydk) 5:uf wi4c*i2 kscabxi6ce.

Is a rattle in a car ever a resonance phenomenon? Expla-f6e4 a::c ahx-k. d bl:ctabwin.

Is the frequency of a simple periodic wave equal to the frequency of its source?(axzzz0 h /7rh7 quyo) Why) hx7 hz/ao0rzqyz(7u or why not?

Explain the difference between the sp ,3eak4vvvot0)h0zq feed of a transverse wave traveling down a cord and the speed ooevzf,v3h40 )q ka0tvf a tiny piece of the cord.

Why do the strings used for the lowest9 bt5nfvzy*k (-frequency notes on a piano normally have wiren5 vzb*(kt y9f wrapped around them?

What kind of waves do you think will travel down a horizontal metal r l6vx3 4ke7v mavvm57eod if you strike its end (a) vertically from av7 v6m5e4a3e xkv vm7lbove and (b) horizontally parallel to its length?

Since the density of air decreases wietf* nmg* m,-uth an increase in temperature, but the bulk modulus B is nearlytngu*mf- e*,m independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they travel pxmrt99u ;z6f(rvx a1 away rrax ;u(96xpm1f 9 ztvfrom the source.

Two linear waves have the samue n,j rf1(qpswy93r)e amplitude and speed, and otherwise are identical, except one has half the wavelength of the other)n 3qeup,jy19r w(fr s. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary bfu2 ,mffg7qlsjb3 0w7 1el tt:etween two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and v 0qjtlbf: ems7wu7 tff31l ,2gelocity do change). Explain why.

If a string is vibrating in three segmemk:jwr6e- jo,nts, are there any places you could touchkj- orw :jem6, it with a knife blade without disturbing the motion?

When a standing wave exists on w : 3+5c5l dutnypf9qmhzn;vg fwb( 7-a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed?fmcfd: ntgy7hb zp5n( 9q -53ww; v+lu Explain.

If we knew that energy k262+autb 7fhatqwl2 was being transmitted from one place to another, how might we determine whether the energy was being carried by particles (materw a+72k2h qabu26tt flial bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.1w5w:6h xpkjasc1 m(f+8 m, what is the total distance it travels in one periswpa +:xjfk(h1wcm56od?    m

  An elastic cord is 65 cm long when a weight of 75j zx zrtf:+).v N hangs from it but is 85 cm long when a weighfvxr jz)z +.t:t of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 6s -rr 47znzrf0l0a y-i8-kg driver gets into the driver’s seat. If the car goes over a bump, li-00z4 n ry-rr afz7swhat will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3lakx(7/zod 1e .6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffn/lk7deo a1(zxess 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 f:tda6 wxt/vyppi.3*ed (n8 omass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from it? a :*fp 8p./6ddytex3 iw n(vto   Hz

Construct a Table indicating the position x ofiopq; 8 hq6rs a0lcdza* +9ey. the mass in Fig. 11–2 at times t = 0,t =0q9z h;8prc+i aelaq o6.d s*y $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 webldqyt-,2(2s jjjh h4g vibrates predominately with a frequency of 4.0 Hz.jd2jlh2hqst g y(-j,4
(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 v+hfxe j 1r6ci4 ip.wp9*kwm9s ibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m,whip.x4 pkmr i96w 1 jf9+ce*s the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrate khchbm7xg5 13ng8fq 5s 3.0 times per second with an amplitude of 0.5mgc7bkg3hnf 5xh1q8 13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO halfkk8k6is -l hj)(sqf.zb * td2n the maximum value-k6 ibstjhf)(lk.s8qd2k *nz ?$\approx$    A

A mass attached to thw )mz)b w8rf2ms.tf :wdm)ek;e end of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring is strnb a87 i95ojrbmh68rvpgd: )detched g 58)m6in:odvp7 8jb9a dhrbran additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spq 6 ndkqh9rx cnv9b,5/ring stiffness constant k = 280 N/m and is executing simple harmonqhrqn9kdcx, /n5 vb96 ic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0, *z(8ywbjja . z5jazb.200 m to “load” a z5jwa.by ,jj*8 zzb(a0.180-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 ojcnx emfam6 ,*3mv45jf a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is releamaj x,3ne5 m6fc*4 jvmsed 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 vibratg +)8dlew7c0wgkk y+bes according to the equation x = 0.45cos6.4t where x is in meters and t is in secondly gw+)kb 07k8we cg+ds. 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 +5k zlh lbgx:+ijiaww9 c :s -pw,ec*)half KE and half PE? ± :ic:,l )i+b9z+lk x-jhwwp*sc5 awge    A

  If one vibration has 7.0 times the energy of a secoudyf+gya:z4foq) o 9b1i4ldlih+b3 * nd, but their frequencies and masses are the same, what is the ratio of their amplitudesd9 qulbg+1: 3d fyfoa4bh4l* zy)iio+?   

  A 2.00-kg pumpkin oscillates from a vertically hanging 421sxal it8col 5,wgxlight spring once every 0.65 s8lxwgxst4o l,a 2i5 c1.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs, each* 6ep( ex3mlzydza1 .v with spr61 (*e lmv3xzepa y.dzing stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x cxs,ngsqrdt89 c: 3z 8= 0.38sin6.5t where x is in meters and t is in sz8c:,d8qsxs3g9r tcn econds. 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 s17drb93h1e k8nfuyo 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 = 124 N/m) is swdlk9) 1 ,gdtctruck by )wl c91,gtdkda 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 with spring stiffness constant 305 N/m vibrates with an amplitf p2;ug8qqq3 fudeq q g;3qu28ffp of 28.0 cm when 0.260 kg hangs from 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 po ,,v.yr*xwjxft.-o 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 bl/m: t7kwcvp o.ock attached to a fixed horizontal spring whose spring stiffness constanttw.v/ mo:7kpc 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 reak1*zkc l)u2r. gj8 mhnching his lowest point, he oscillates up and do2. g lu)hnkcm81z r*jkwn, 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 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 ut4 ql :(ts-,ada.gsv -fl j0za/c ie:its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if ugfp *6c:c;u vbp+q+ ab9o0jpit is to make exactly one swing per second?a;ucc6buvfgp p:bj* o+p 9+q0 (That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What id:c+pc9 h;r vf4hur.fs its period on Mars, where the acceleration of gravity is about 0.37 that ov u;+ rdcpf.c4h fh:9rn Earth?    s

  What is the period of a simple pendulum 80 7++ on1l /hemcjlqa8acm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.hnt, zz5p( e.hzwzfku+4)+lt 760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle of 12.0 l4e.hn(t+up k w5zztf+ z,hz)$^{\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 penduluu*ot,m/7zuj+o cngpn+( 5 ewum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendu+ cutwp*o(5mju7gn,z+/ oe nulum? shortened by    mm.

Derive a formula for the maxiykzcmdr;yw0 l: qpzp lvui.eqjd/1;85)v2q - mum 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 lhw+u muh,srt9g c.wa1pj+saj (3, j(d from rest starting a3rh saj9.,jcsp1hum(a+w (,ujt g+ wlt 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 3.0 )rei3fzkt)e/ s. He measures the distance between two crests to be 6.5 m. How fast are the waves travelin t/ izk3ef)e)rg?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 343 zlc 58sc;zt2i m/s Howzcz;ts8 i5l 2c far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencie cf cglb*m0p(le. yi 0x:ot5/ij)c9hd1ej u4is between 550 kHz and 1600 kHz (kilohertz) and tr*ig0 ou:ty eeic 0f9)i4hj5ll1 /c x.p(mbdcjavel with 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 longx9c,yhh2y) .vxe5f li ju,w (bitudinal 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 dense as therbfgrnv,u1.g.;g 2 nf other. In which rod wilgv;gn.1fr. u2 gnb,rfl the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 i((f ,l gscg0r(f ipij-4a9ehm apart. If the tension in the co gph r-c(s,0( iie4jiagff(l9rd is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 62o-;-p hg6 5eufiay 6gc0 m and di 65oc--h af;g6ypiu geameter 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 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 jrjfx*wo ;zsu7q-w; (just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor d qw*z-7( ; jrwsfxj;ouirectly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at d:vhh. z lmo2l fdhvz1zz 7:qyc(wi:8/ifferent speeds, and this difference helps in locating the earthquake “ep:fzlchodzzq:h2/: .h1wym v(iv l z8 7icenter” (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 approximated by a sinusoi*83etw zzmx7wdal 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 begin to leave contact with tzt xw78*emw3 zhe ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a)4j -b0pjq(+nn/ kcxdh the intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 4jnp0bj(/ nhc+- qkxd20 km from the source?(a)    (b)   

  The intensity of an earthquake wave patg*6l, vlo th tyqr2d4/0;n0qaupf 2sssing through the Earth is measured to be ld6t0qn og f0r,/22 tvtl;4 uyha*qps$ 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 sa9zwm;q)8qz.5irm g vkme portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the tw8;mv gz. z5kqiqm9 w)ro waves?   

  Two waves traveling along a stretcheecl*0.s a5dbxa.l 4g cd string have the same frequency, but one transports three times the power of the other. What is50a*c4 el sxl.gbacd. the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is obshg(ighf 8.v jku-xw.lnka;*; erved to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave kjxf8hvg nk( -.awul. ;*;gi hpasses. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch thecn xj*i;ad2c .j+d7m(gx cm5 k shape of the ax2jdgk ( +mc7jn; c*5dim.cxstring at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what are th/:azbj. ft5gq lzes) :e frequencies of the first four harmonbs.qaj:g/l )ef5z: z tics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will i9ibts,so;ws x-j1 i fy++,aj xt vibrate if it is fingered one-third of the way down from the end? (Tb wsa-1xso;sy 9f,tx,ij+i+jhat is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at f:ak;:eep k-14ehvlgd *yti)a frequency of 280 Hz. Name at least three other frequencies at which it wil1ek:f th -gkp ;a:eve il)d4y*l resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s Ivzs lv zj02vhg207ymc 1s, jotl(em4 ;f the frequency of standing waves is 475 Hz, how far apartj j 7v2sezhg0ctolvvm (2;l,0 4s1zmy are two adjacent nodes?   m

  If two successive overtones of a vibrating stringp*u,b 6ht.ntl are 280 Hz and 350 Hz, what istp ut6*l. hnb, the frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distanceao eutrc3+hpd1u 499gh m1hu1 from the bridge to the support post is L = 62cm and the string is under a tension gumau9truh 1 1 dhh p34e1+oc9of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibratekcsre8m-4x(jfqt)b 4efr4a 8 at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the sx8q4) msb4t 4rcfe8(-rjfkea tring be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is me,9e/4 eqwchtg6g,als2 (j1 aayc rf1xasured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correctgs/j 1cer 9qx1w,g(fca y,46l ath a2e the frequency? decreased by    %

  One end of a horizontal string is attached to a smallmlpr u38f/ y2p k1 4uc)hgt:el-amplitude mechanical 60-Hz vibrator. The strin kl p1t /3hef:8rpy4l cm)u2gug’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 strinr,a y7vgyzqai9,n3 i /,pk1k dg may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, howk9,yvq3 /dzng ap,iiar7y ,k1 many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the riw f9c72 rnqyu+ght frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water yu w+9nqc2r7f wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes+j3tv sem- * vw3fp0dm a boundary within the Earth between two kinds of material. If it approachesvvfp j emt-m3w *d+s03 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 velslet+82:8qhg olu 9 0x6u k2-lv,uxzl/rvttrocity changes from 2.8 m/s to 2.1 m/s If the incident wave 8o +2r-rl,uvzx 90l6hv/ u 8lt2g:settkx lu qcrests 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, 46k4x )*xyyc/+zwvrj5z6mp /f ol/azz- jjjj dense air. If the sound wave hits the cold air interface at an anw-/ x rc*k/pvyjfjj5lz o z/6zxm 4zjj4 a+)6ygle 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 oy1pb*bu*z kc0fa2,b u f rock at a bp*kf10b ,z2 abuuy*c 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 ii.v7h1rfck3 jn diameter. According to the user’s manual, the dish has to be pointedh fj.v1k 73ric 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 and velocity 750isk)-pjp ms 8 f ds3s2 rj4cyt.ha0.6j km/h travels across the Pacific Ocean. As it approaches sh .rmiy0ka-s4j 6jfs3p2 jdt s).p 8cHawaii, 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 attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant oftpf30:k /q mbiv)h0nj ly9 q/n 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conserva :h 0y3 tj9iqpf //mln0vbn)qktion of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m beloeqlfgg k w )n rb7628qpyxq4+4w, which stretches the net 1.1 m. Assume that the net behaves like a simple)g2 n 6qp 7xlf4gqqb+e k4r8wy 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 4y+hnljb+6afq4g0v ylh/ v; y3b,yx ma freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the os/f+6b+; n4hgl,ybyvm4hjxal3 0 yqvy cillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. , lcl9uv81koc11–54), compressing the spring 5.0 m. (a) What isku1 8,cc9vo ll the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the ri im4l/ t8mdz*e++e gdcght pace of about 1 step per second, the coffee sloshes more and more until eventually it stat+el/m +dd*zmc ig84erts 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 center of a 33-rpm phonograph fhup p4z57 2t8*y olgmrecord have a wavelength of 1.70 mmt2phuy4g 8fmlzpo 57*. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x -d.qt nn ;m o64sdf6vgis in meters and t 6nmngfs.dd6;vqt- 4oin 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 x+ x,jlkw, wv+k; u*i7iew1 umfrequency if it acceleratesv xuk imlw7wu 1w*+e,jkx+ ;i, 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, i wvy1z-o/hew95u 3 qdit sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a whiq 9d w3h5ze1wi/yuvo-le.
(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 ixnw x4c24e64qbarq06: q pejuq x.jn8nstrument are tuned to play at 392 Hz (G) and 440 Hz (e2 044nrjb jn6q64xw8 xeqq:x aqcp.uA).
(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. 11–3g7sm g/aajr8nq/7:yg 3. Determine a formula (a) for the ratio of the speeds of the:/ g g7qg7/amsj8r any 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 freq21+xeq z3riz5o 2dd mmuency of 264 Hz, and the tip of each prong moves 1.8 mm to eithe e5imxo+mzzd22 q3r1d r 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 oscillates with simple harmonic motion of frequenshrp* 8u9d ;- g;wwqpjcy 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 lose contact with the board during the oss;*-p u8rqwh;d w9jg pcillation?

A string can have a “free” end if that end is attached to a ring that cauas +l9h (;w8etmg5esn slide without friction on a vertical pole (Fig. 11–57). Determinhl9mw8aeg;us s(t5+ee 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-way swsfd46r*y l:t:qjgvo-bf lfikne3) h gw(k*65 ing takes fbyws4gntjgk q 6d):h*:*6f (35kf-lverli o1.000 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 di t)udbofk6ie ndue9 2/,:9ogp rection or can swing as a pendulum of small amplitude, but not both at top,uu bg kd2f d:en6et/)o99ihe 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 pul4 m/;nmtd+* i:hl f(sbrs/o vhse is: mfd+sbt*h /osrv ;(i 4nm/lh generated 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 sprin9d9 a+agxzc lf569 4cj2xjvw mg stiffness 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 of the block? (Assz +4jdf99vl 92gaaxjm 6wcxc5 ume $m \ll M$)

  A crane has hoisted a 1200-kg car s -c0 0e5/hlbbbwe9hhw)ols2 at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 m9-l0lbewhs) hw/2 hs0ec5bb o m. A 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 .t e9u0rfw2 qpym5t p,ypm.,uin 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 th 9fym2.r ,0muy5.uwqtptppe, e 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