A traveling sinusoidal wave is propagating in the +x direction on a string. You

Question

A traveling sinusoidal wave is propagating in the +x direction on a string. You make the following observations about the wave:

-The maximum transverse displacement of the string from its equilibrium position is 5 cm.

-At a fixed instant in time, the distance between two points where the string has zero displacement from its equilibrium position is 40 cm.

-At a fixed position along the string, you observe that the string has zero displacement from tis equilibrium position, and then it starts to be displaced. After 0.1 sec. elapses, you again observe that the string has zero displacement from its equilibrium position (at that position along the string).

Write doen the mathematical equation that describes this traveling wave. Your equation should have numerial values in it that you can deduce from the information given above.

Explanation / Answer

general equation for a wave moving in +x direction is given by

Y(x,t) = A sin (kx-wt)

where A is Amplitude of the wave

K is wave no. = 2pi/L

where L is wavelength

x is direction of the wave

W is angular frequency = 2pif

t is time

so

here now A = max displacemnt = 5 cm

Y(x,t) = 5 cm sin ( pi/20 x - 0.2 pi t)

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