1. The equation of a transverse wave traveling along a very long string is y 6.0
ID: 2074178 • Letter: 1
Question
1. The equation of a transverse wave traveling along a very long string is y 6.0 sin(0.002xx + 4.0 ) where x and y are expressed in centimetres and ris in seconds. Determine (a) the amplitude, (b) the wavelength, (c) the frequency, (d) the speed, (e) the direction of propagation of the wave, and (f) the maximum transverse speed of a particle in the string. (g) What is the transverse displacement at x-3.5 cm when r-0.26 s? 2. A 10 g particle undergoes SHM with an amplitude of 2.0 mm, a maximum acceleration of magnitude 8000 m/s^2, and an unknown phase constant . What are (a) the period of the motion, (b) the maximum speed of the particle, and (c) the total mechanical energy of the oscillator? What is the magnitude of the force on the particle when the particle is at (d) its maximum displacement and (e) half its maximum displacement? 3, A grandfather clock has a pendulum that consists of a thin brass disk of radius r =15 em and mass 1 kg that is attached to a long thin rod of negligible mass. The pendulum swings freely about an axis perpendicular to the rod and through the end of the rod opposite the disk, as shown in the figure. If the pendulum is to have a period of 2 s for small oscillations at a place where g 9.8 m/s what must be the rod length L? ( Moment of Inertia of a thin disk is(1/2)'m'r 2.) Rotation axisExplanation / Answer
given
y=6.0sin(0.020x + 4.0t)
the general wave equation moving in the positive directionis
y(x,t) = ymsin(kx -t)
a) the amplitude is
ym = 6.0cm
b)
we have the angular wave number as
k = 2 /
or
= 2 / 0.020
=1.0*102cm
c)
the frequency is
f = /2
= 4/2
= 2.0 Hz
d)
the wave speed is
v = f
= (100cm)(2.0Hz)
= 2.0*102cm/s
e)
since the trignometric function is (kx -t) , sothe wave propagates in th -x direction
f)
the maximum transverse speed is
umax =2fym
= 2(2.0Hz)(6.0cm)
= 75cm/s
g)
we have
y(3.5cm ,0.26s) = 6.0cmsin[0.020(3.5) +4.0(0.26)]
= -2.0cm
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