A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the x-direction in 0.3
. The crest P is at
at
and maximum displacement of the wave is 2 cm. Which equation correctly represents this wave?
Text Solution
Verified by ExpertsA
To find the equation of the sinusoidal wave, we need to determine several properties of the wave:
Wave Velocity (v):
Given that the wave travels a distance of 1.2 cm in 0.3 seconds, the velocity
can be computed as:

Wave Number (k):
The wave number kis calculated using the wavelength
:

Angular Frequency (
):
Angular frequency
is related to the wave number and velocity by the equation
, thus:

Wave Equation:
The general form for a sinusoidal wave traveling in the positive x -direction is:

Given the maximum displacement (amplitude A) of the wave is 2 cm, the equation becomes:

This equation accurately describes the sinusoidal wave given the provided parameters.
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