Calculating Coordinate of B in Sinusoidal Wave Equation

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SUMMARY

The coordinate of point B in the sinusoidal wave equation y = (15.0 cm)cos(0.157x-50.3t) can be calculated by understanding the phase difference. Given that point B is 60° out of phase with point A at the origin, the corresponding phase shift in radians is π/3. The wavenumber k is determined as 0.157, leading to the calculation of the wavelength λ as 2π/k, which equals approximately 40.0 cm. Therefore, the coordinate of point B is found to be 40.0 cm/6, resulting in a position of approximately 6.67 cm on the x-axis.

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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:

[tex]y = A cos(kx+\omega t)[/tex]

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

[tex]k=\frac{2\pi}{\lambda}[/tex]
[tex]\omega=\frac{2\pi}{T}[/tex]

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

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