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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)