A sinusoidal wave of wavelength 2.17 m and amplitude 0.100 m travels on a string
ID: 1381464 • Letter: A
Question
A sinusoidal wave of wavelength 2.17 m and amplitude 0.100 m travels on a string with a speed of 1.10 m/s to the right. At t = 0, the left end of the string is at the origin.
(a) Find the frequency for this wave.
Hz
(b) Find the angular frequency for this wave.
rad/s
(c) Find the the angular wave number for this wave.
rad/m
(d) Find the wave function for this wave in SI units. (Do not enter units in your expression. Use the following as necessary:x,t.)
y =
(e) Determine the equation of motion in SI units for the left end of the string. (Do not enter units in your expression. Use the following as necessary:x,t.)
y =
(f) Determine the equation of motion in SI units for the point on the string at x = 1.45 m to the right of the left end. (Do not enter units in your expression. Use the following as necessary:x,t.)
y =
(g) What is the maximum speed of any element of the string?
m/s
Explanation / Answer
Given:-
Wavelength (w) = 2.17 m, Amplitude(A) = 0.100 m, speed (v) = 1.10 m/s
a) Frequency for this wave is
=> v = f*w
=> f = [1.10 m/s ] / 2.17 m
=> f = 0.50 Hz
b) Angular frequency (omega) = 2*pi*f
=> omega = 2*3.14*0.50
=> omega = 3.14 rad/sec
c) The angular wave number for this wave is (k) = (2*pi)/w
=> k = (2*3.14) / 2.17
=> k = 2.89 rad/m
d)