Calculating Coordinate of B in Sinusoidal Wave Equation

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To find the coordinate of point B, which is 60° out of phase from point A at the origin, the phase difference must be converted into a fraction of the wavelength. Given the wave equation y = (15.0 cm)cos(0.157x-50.3t), the wavenumber k is 0.157, allowing the wavelength λ to be calculated as λ = 2π/k. A phase difference of 60° corresponds to 1/6 of a wavelength. Therefore, the coordinate of point B can be determined by calculating 1/6 of the wavelength and adding it to the origin, resulting in the specific coordinate for B.
dekoi
At a certain instant, a point A is at the origin and a point B is the first point on the x-axis that is 60° out of phase. What is the coordinate of B?

The equation of the wave is given as:
y = (15.0 cm)cos(0.157x-50.3t)
 
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dekoi said:
At a certain instant, a point A is at the origin and a point B is the first point on the x-axis that is 60° out of phase. What is the coordinate of B?

The equation of the wave is given as:
y = (15.0 cm)cos(0.157x-50.3t)

Hint:

y = A cos(kx+\omega t)

where A is the amplitude of the wave, k is the wavenumber, and \omega is the angular frequency. The latter two are given by

k=\frac{2\pi}{\lambda}
\omega=\frac{2\pi}{T}

where T and \lambda are the period and wavelength. What fraction of a wavelength is between the two points?
 
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