Given the progressive wave equation y = 5 sin (2000 πt - 0.4x), calculate wave length

Answer Details

In the equation y = 5 sin (2000 πt - 0.4x), the term inside the sine function (2000 πt - 0.4x) represents the phase of the wave, which should be constant for a given wave. The wavelength (λ) is the distance between two consecutive points in the wave that are in phase with each other.
To find the wavelength, we need to isolate the term that represents the distance between two consecutive points in phase. In this case, that term is -0.4x, which is the coefficient of the x variable. We know that the wavelength is given by the formula λ = 2π/k, where k is the wave number, which is equal to the coefficient of the x variable.
So, we have k = -0.4. Plugging this value into the formula for wavelength gives λ = 2π/-0.4 ≈ 15.7 meters.
Therefore, the wavelength of the wave is 15.7 meters.