Give some examples of everyday vibrating object he9dpi q(*v5(k8 a+r5,lac *kbgk ecks. Which exhibit SHM, at least apqvr*p 8g(ke *aeb,c +i5k5ak9k(ld hcproximately?

Is the acceleration of a simj-:ixrh2qd) y ple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximanu+ g 13ebgvx;tely simple hab1vxggne+u3 ;rmonic.

Real springs have mass. Will the true period and frequency be larger or spj2o2fs y)++w w5 +u:w:ctlmisqz+ o bmaller than given by the equations for a mass oscillating on the end of an idealized massless spring? f 5pilc+2s+ wm + bjozqswyo)::w2+u tExplain.

How could you double the maximum speed of a simple harmonic oscillato8uo.gb q,jh *dr (SHO)?

A 5.0-kg trout is attached to the hook of a verti x;ghphz*3z)xgbcnai 5.a h iq)0y)8dcal spring scale, and then is released. Describe the scale rehyq.ig8)z3 *)5 c;x)dnbp0h agza ix hading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lospbuh6ckbsxo :he12p* f 6 )ce:e time when taken to bkec*cop:hp:)s2ue16 fxb6 h high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48z wiiji:wud)2+ckc0 5). How could you estimwzi52 u:i i )k0j+cdwcate the height of the branch using only a stopwatch?

Why can you make watw o- l2a;q(e )d8xadirer slosh back and forth in a pan only if you shake the pan at xol)dqr 8w- ( ;edi2aaa certain frequency?

Give several everyday examples r1ne/ lwewdrh88s 06hof resonance.

Is a rattle in a car ever a resonan ln;p)p.cr+tiq8y-7 o kv7u yvx) -nvwce phenomenon? Explain.

Is the frequency of a simple periodic wave)aih p06ao;r3* q.u jwnxo.wj equal to the frequency of its source?3x )aji6*o;r0pqwwa uo.jn h . Why or why not?

Explain the difference between03arnrp/n x .o the speed of a transverse wave traveling down a cor.ra/xn0 r3onp d and the speed of a tiny piece of the cord.

Why do the strings used for th6ha99m 5e.jskk.rnp x *2 +q)yuegccfe lowest-frequency notes on a piano normally have wire wra9ka2 yp9c*e.fj e+c mguhrk)s . 5nx6qpped around them?

What kind of waves do you think will travel down a horizontal me44vgfz-p r.;p -jbjbh4gzs n8tal rod if you strijj ;fbg--p 48zs.rp4h v4bngz ke its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of a-5cstl,7k ndvqq, 0 xhir decreases 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 wi50 nlsx7tdhq,q,k-vc th temperature?

Give two reasons why ciuq x3*mfq *. mr abx;v 3aio15o7ifl;jrcular water waves decrease in amplitude as they travel away from the sourc* r3f5;io iamo 3ma.u7x;q bvqjf*1lxe.

Two linear waves have the same amplitude and speed, and otherwise are identicaltyd5 dgv;m)/8vwf v05k3yb ls, except one has half the wavelength of the other. W3v;w05ty)/vld5dy s8 bvgmkf hich transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two1ick i2j/-wwwl(t/v/ c oawh0 sections of cord as in Fig. 11–33, the frequency does not change (avwk/ cc(0il1 ww 2owat ih/-/jlthough the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any phxx x jq5vcb z7e+w325laces you could touch it with a knife blade without disturbing7h2z+w c35exxq 5 jvbx the motion?

When a standing wave exists on abeg q,b9dg,ot3:f+ sq string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Ebqgd ,+seoq:3t 9,bgfxplain.

If we knew that energy was being transmitte d+kotno4d8hnm 5npyh+ 4, -gwd from one place to another, how might we determine whether the energy was being carried by particles (material bodies) or by wav g-dmhn5t4yp ho,nw+4n8 dok+es?

  If a particle undergoes SHzfdq9ywxtd; 1 .qwn+)M with amplitude 0.18 m, what is the total distance it travels in one pz;dyd q xn+t.wq1 )wf9eriod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs fromlzllr* nla/ ;; it but is 85 cm long when a weight of 180 N hangs flrl;l*na zl/; rom 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 itsyk ;yyt0 :g2quv jq14u 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the fr12 guy4yqkuq0y v: t;jequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) Wh3 1eh;gp4br r,i 3dass1h1vwn at is the spring stiffness const 31p wihnr4s,131d; bg ahersvant $\approx$    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 jxeaoa4/ vl6o/, /c bpHz when a mass of 0.60 kg is hung from it. What is its freque//j 4ooa,6 abvxlep /cncy if only 0.38 kg hangs from it?    Hz

Construct a Table indicating t9s8lg3ngsg0au hl4s+:j 8 ygthe position x of the mass in Fig. 11–2 at times t = 0,+us3y j4t l8ln9g: ggsgh8sa0t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 pre+2rlgmua.(zg51mcu 1n83kg3 glm k dldominately with a frequency of 4knamm 3 lg+l dl(r gu3.mcu1kg1g5z82.0 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 w/,*ea4s pw6;h geixj3p2f/a srnn b2pith a frequency of 0.88 Hz. When an additional 6s2 ,pf/abp6ejxan r3 nwgp e/; 2ih*s480-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of 1: l/h+jfdfbc a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Det1hbcf+/ j :dflermine
(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 the maximumkgh3q *:d*xqj*yd:y2y h nlj5 valuy 5:qxqgykhdhyl j32d:*j n* *e?$\approx$    A

A mass attached to the end of a spring is stretchwyqj2,)dy l 90sdijy;ed 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 v08f (oi/c: ajtd aptvve0.p0is stretched an additional 0.130 m and released, how long does it take to reach the (new) eqf8ta0:vd 0i.( 0evvop/jtapc uilibrium position again?    s

  An object with mass 3.0 kg is to.nmmv*0knl 8s l//o attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is*l/snon /8.tok vmm0l 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 t2yct nnpi9qm/ j c3x61.k:bhw he spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball lea . 36 tnqy:ijk9x/p2w1cnm bhcve the gun?    m/s

  A mass sitting on a hore-xdl4sv( 6o5yti.f gizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is re.-( ity6eo5lf4 vs gdxquired 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 whu5d wbeh*x35 bere x is in meters and t is in seconds. D uwb5d exb3*h5etermine
(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 m- mwq3xc,ww 8half KE and half PE?xqmww 3,w- mc8 ±    A

  If one vibration has 7.0 times the energy of a second, but their frequenm+;0u fkt ,t9dyt8gh klm-7h)l 9noy tcies and masses are the same, what is the ratio of their am9fhktn+9 7ml, ytk h0o)ulyg; md-tt8plitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spri i 28 e0pswbuw-9ji8vang once every 0.65 s.8sube9i0wv2a8 jw -p i
(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 supportedm y6:zi0ri87p kbd b7m by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibratioy0 7:dzipbk 87mrm6 bin?

  A 300-g mass vibrates ac uy xh jhbj5) reuri,8lz(2-m-cording to the equation x = 0.38sin6.5t where x is in meters and t is u2(iyrm -jh8u),e -h5 xjz blrin 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 tfgc(pw7o2m6:99vnphblt svy:5 b- kSHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124 N/m) jllm,8ylesvo uz-( 75 is struc7 m l v5,(-zuoleljsy8k by a 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 wio)fd3nh 4i p3v3ayn 0ath spring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kgyf hd3p0a3oia 34)vnn 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 constqd nzs(m2wu( fzc q)6)ants $k_1$ 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 r;a fs/ktjg5-ock attached to a fixed horizontal spring whose spring stiffness constant- rs;/gk jaf5t 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 reaching h d t0o26qgfnw39od2t ol:(xvbis 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 spring stiffness constant and the unstretc 92 : dgf0lwtbv3ntoo q(ox26dhed 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 exactly5e 438xvvpau h erys)9 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swinbf8d, (r 7n re7btgee6g per second? (That is, one complete vibration takes exac eg8bndbrr,e7t7f 6e (tly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Ea5uorrgco (v (6rth. What is its period on Mars, where the acceleration of gravity is about 0.37g ucor (r5vo(6 that on Earth?    s

  What is the period of a simple pendul2ink6kibmumbk l09 :q(bf.. ifz7zs4um 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simp-z9y0nj b6;g fehwt 6o98bzurle pendulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it in0bw6r u9zhet8fj; o6-y9g zbs released 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. I7,v-0fxa8+vc gpg f mkf the clock loses half a minute per day, how should yfgfxc8ak+g 7,v-pv0m ou adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximu,x/v idj95pf l18ge mem 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 released fro ,gdt9i6eqtptw113 e h :doo;lm rest e91 pd ;eitt:t3hgoqwodl,6 1starting 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 anchoq,uy.- ;ln+pvoveo.r i,axw5red boat every 3.0 s. He measures the distance between twoy5aeo.-r wv+in, ;o. ,ulvx qp crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels 8zl nkdb-hy mtbd9s:z6j ;q1wrl 0 5u2with a speed of 343 m/s How far apart are the wave cres;1 tr9 unk 0 wqm h56dzlbbly8-2zsj:dts (compressions)?    m

  (a) AM radio signalsog 1v)hxd4x) v have frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a sph4)x1)od v gxveed 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 longitudb /rz;huo1mj9yg x2u5 inal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the sa,ar vw9nl.n f o2a5w8gfu3d+nme elastic modulus, but one is twice as dense as the other. In which rod will the speed of lon v+n. f5wo2g9,wu dalfn3a8nrgitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is+eai q7ip5 tq+a*th x1 stretched between two supports 28 m apart. If the tension in the cord is 150 Nt +i1aqhex*t 7qp5 ai+, 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 hill9px4xiyl* 3*oq whxl em+ l1v( aec4b: by a steel cable of length 620 m *xv ipa1exh*ec+lw4b 3 xlm4yoq(:l9 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 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. *uo;.fg c pygd gh;*o,jv5e/g He hears the echo of the e, vo /;**fo5d;cgj uyhg.pggwave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, andsh)ci f,:hpg9sarc2 ) this difference helps in locating the earthquake “epicenter)fhg pr,ic: hc29ss) a” (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 sinusoidal transmeej5s.5 lkjckx4-k (verse 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 leavesj 5kxj 4kke .m5(cle- contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the i 5v-ld y(v0,rj7ixut 41qhog fntensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and xgjh1v ql40v,7ri (f 5t-dyoudetected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing.n- ql) mlkpn*l+.eld through the Earth is measured to be m *lnld l+pel-.k).nq $ 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 fre:ezpt2.k:z9e +l n ankquency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the e :.+k:nz9e lnpa2 ztktwo waves?   

  Two waves traveling along a stretched string ha:b68vvu+qwl i oambl n0;a9 (yve the same frequency, but one transports three times the powerwi l9+v:aa0mv b68l(;unb qo y 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 .vuem7cw;a aplwk)ys7z/ 9.rup 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 cmyws 7v a p) /z.e.m;rku7awc9l, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 1ql1d7xdos 4fea ./hk91–52 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 m7al k s/fo 1.hqde4d9xoment 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 fundament(d/k5l/euwihfza-x a* smx9k vf 19y8al frequency, what are the frul/f fmw9/ (x5-v19ekzsd8*haiaykx equencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency:l6 dhq ssq,)5qufs6u will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as qf l ) 6q65hssuqd:,sua standing wave.)    Hz

  A particular string resonates in four loops at a frea-w m,*xz(j3 may:dtv ji0ru.quency of 280 Hz. Name at least three other frequencies at rw t .(d*m: 3-jvx,i0jaau zymwhich it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 926 ak+ d-hnzy*jm/s If the frequency of standing waves is 475 Hz, how far a + h6azdky-jn*part are two adjacent nodes?   m

  If two successive overteo *sn1x.dr(gones of a vibrating string are 280 Hz and 350 Hz, what is the frequency of the fundamrx (gde o1.sn*ental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the seuxlh 2 fs6 (hk(ndi+p4o4:fpfx0i 5bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?oi4d:uhp 0xxs l(n f2k5 6p4(ffeis+h    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measured oetr o.k7np0* to vibrate at 205 Hz. By what percent should the tension in the stri*noro tkpe. 70ng 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.1 fh*c/at,xqcclx8w; ef5e( yql lw/ vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By f(/cq . 8lhe*fl5 teqx1aly,x w;wcc/ what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal strin3 y(bt;kabp5w4 w(md yg is attached to a small-amplitude mechanical 60-Hz vibrmd wbyk(5; y4tp(b3 waator. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by q2ek zv d5xw 5(9rgr*mmoving the pulley. If the hanging qwe*9r grmz25d 5vk(x mass m is fixed at 0.080 kg, how 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 ijqc38znn+h:5vg,dc/ sxjz 1/uz(l qan a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the spe8:u ndhncc q vg,x+q/a jjs3zz(5 lz1/ed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundp3 6 i1d9zcx78iktr -hmby8keary within the Earth between two kinds of material. If itpih bxmt-k yc 9k87r1 6e83idz 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 a87.luuf*vemv)n : azvelocity changes from 2.8 m/s to 2.1 m/sl)av.v z :u7fm* n8uae If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, del*,pwiynf5m6 rgd +2 /kj s4xxnse air. If the sound42xnyj6g5*dlkx ws +/r ,pm if wave hits 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 earthquakw:f c9vtn/ (*ppc,cyie wave strikes a boundary between two types of rock at a 3:ivntw,ppf(cy */ 9cc8 $^{\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 dia0goa*x1; yeo kxt1+lie2srb71h 2ba fmeter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, b;+yklehs2 *ixxt1gbob 2afe 0ro17a1 ut 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 wavelengthvt* v5md tku1v els .+;),jojd 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunami*5+ mv ;klj1d e).ud t,svtojvs, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring tvc,5 woit gk ad1pev jd;,a,e8rh0fz16 -md,stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h).d6c;0 h-dgj5ae1avrm,kwet,ioz ,vf , pt81d [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a firjrb:.1q/:hi djh hv *pe net 18 m below, which stretches the net 1.1 j1idbrh.pv hqjh:*:/m. Assume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the v4zrf66qoleg6(e6q i end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillation?zle6 i66(q6g vqo4fre    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), wkdbg2e.h hh-9)df5t compressing the spring 5.0 m. (a) What isdf.d -k9wb 5eh) gt2hh 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 cpen. uy3 cp*g,offee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–5u*np, y3 .cgep5). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a/(tap 2 gaf;m7 uttk7r 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound auk;atfg(/prtt7 7 2memitted?    Hz

  A 2.00-kg mass vibrates acco0.pixrjx 8r* crding to the equation x=0.650cos7.40t where x is in meters and t in 0xpc *r i.x8jrseconds. 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. Wrq2; 8pvh5oy avc66hkhat is its frequency if it accelerates 5qc h;vrh6ky68v 2opaat 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 rafde/t k3b227 t .cn ko+d1jeb:mf (ukypt, it sinks 4.0 cm deeper into the water. When he steps off, the raft d+ :onpy3 2.bt7ue dbf ktm12e/k kj(cvibrates 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 .- ws b1pr0de4pukif1tqj6f3play at 392 Hz (G) and 440 Hz (3 d0 .r-sjqit4 bw1fuk1p6fe pA).
(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. Duzl2r;4, g t - 9nd)j8nnoo, mnyh;ttwetermine 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 thet,n ,9n )mzdl8j;ow;nr oyn 2ugh-tt4 heavier section of cord or the lighter?

  A tuning fork vibrates at a frequenczk+h-)uhd;g q y of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. d+hk ;qz-guh) 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 motio w 4nqamc4ap44n 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.a44pc4n ma qw4 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that 6c( kpyp+bgcz-:a 6ebmz d0iz lc1+,scan slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with oi,:+gak-bscezbpz 61my c (l6p +dcz0 ne end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing takesh22qcgn e423l xrgi,i 1.00rh2q c2ex3g ,inli24 g0 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 gax7,fr, uxzs( uqi03 the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical o, ,zgqxuria(7 3x u0sfscillations 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,9ovdi h3os7 f. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite env os,3fh7oi9d d. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring;6um hv3o0zum9l olh, stiffness constant k. A penny of mass m is placed on top of the block. What iuohl3 ouhm 6v,9m0; zls the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable iz va2jcq uqk,a 7. 4k(rdkv0i3s 22 m 4c a3jq7( .iq,kuvvrk azk2 0dlong 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? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Figlywury )6.sdya 7v w9*. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let g9w6 rvlsy 7 .y*wda)yuo. 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