A sinusoidal transverse wave of wavelength 22.0 cm travels along a string in the
ID: 1628435 • Letter: A
Question
A sinusoidal transverse wave of wavelength 22.0 cm travels along a string in the positive direction of an x axis. The displacement y of the string particle at x = 0 is given in the figure as a function of time t. The scale of the vertical axis is set by ys = 2 cm. The wave equation is to be in the form of
y = ym sin(kx - t + ).
(a) At t = 0, is a plot of y versus x in the shape of a positive sine function or a negative sine function? What are (b) ym, (c) k, (d) , (e) , (f) the sign in front of , and (g) the wave speed (speed of the wave along the string) and (h) What is the transverse velocity of the particle at x = 0 when t = 3.00 s?
A sinusoidal transverse wave of wavelength 22.0 cm travels along a string in the positive direction of an x axis. The displacement y of the string particle at x = 0 is given in the figure as a function of time t. The scale of the vertical axis is set by ys = 2 cm. The wave equation is to be in the form of
y = ym sin(kx - t + ).
(a) At t = 0, is a plot of y versus x in the shape of a positive sine function or a negative sine function? What are (b) ym, (c) k, (d) , (e) , (f) the sign in front of , and (g) the wave speed (speed of the wave along the string) and (h) What is the transverse velocity of the particle at x = 0 when t = 3.00 s?
y (cm) ys 14 YsExplanation / Answer
The wave equation is in the form of
y(x,t) = ym*sin(kx - w*t + phi)
Here,ym is the maximum amplitude of the sinusoidal wave,k is the wave number,w is the angular velocity and is the phase of the wave.
(a) At t = 0,the plot of y versus x is in the shape of a negative sine function.
(b) Here,ym is the maximum amplitude of the sinusoidal wave and is equal to ym = 2 cm
(c) Here,k is the wave number of the wave and is given by
k = (2*pi/lambda)
k = (2 * 3.14/22.0)
= (6.28/22.0) = 0.285 rad/cm
(d) Here,w is the angular frequency of the wave and is given by
w = 2*pi*f = (2*Pi/T)
Here,T = 14 s
w = [(2 * 3.14)/(14)]
w = 0.448 rad/s
(e) Here,phi is the phase of the wave and is equal to the time taken by the wave to complete one crust,that is,to covera distance of pi radians.Therefore,the phase of the wave is pi radians.
(f) The sign in front of w is negative.This is because the wave travels equal distances in equal in tervals of time.
(g) The speed of the wave is
v = (lambda/t)
Here,lambda = 22 cm and t = 14s
v = (22/14) = 1.571 cm/s
(h) We know from the relation
v^2 - u^2 = 2*a*S
Here,v = 1.57 cm/s,u = 0 and S = 22 cm
or a = (v^2/2*S) = [(1.57)^2/(2 *22)]
or a = 5.60 * 10^-2 cm/s^2
Therefore,the transverse velocity of the particle at x = 0 is
v = u + at
Here,u = 0,a = 5.60 * 10^-2 cm/s^2 and t =3.0 s
or v = 0 + 5.60 * 10^-2 * 3.0
= 0.168 cm/s
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.