The equation of a wave traveling in a horizontal direction is expressed as y = 15 sin 2π5 (60t - x). What is its wavelength?
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Step-by-step solution
5 stepsIdentify the general form of a wave equation.
The general equation for a sinusoidal wave traveling in the positive x-direction is given by:
where is the amplitude, is the angular frequency, and is the wave number.
Rewrite the given equation in the standard form.
The given equation is .
First, distribute the term inside the parenthesis:Compare with the standard form to find the wave number .
By comparing with , we can identify:
Calculate the wavelength using the wave number .
The relationship between the wave number and the wavelength is:
Substitute the value of we found:
Solve for .
Divide both sides by :
The wavelength of the wave is 0.2 units.
The final answer is 0.2.
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