Sketch the wave, showing both x < 0 and x > 0.

[aryan]

Homework Statement

[/B]A wave is represented by the wave function:
y = A cos(2πx/λ + π/3) for x < 0. For x > 0, the wavelength is λ/2. By applying continuity conditions at x = 0, find the amplitude (in terms of A) and phase of the wave in the region x > 0. Sketch the wave, showing both x < 0 and x > 0.

Homework Equations

[/B]y = A cos(2πx/λ + π/3) for x<0
and A cos(4πx/λ + φ) for x >0

The Attempt at a Solution

[/B]I guess using the equation above we can make this. How to apply continuity condition and solve this? I have a little idea over this. can anyone please guide me through the entire question. Thank You.

 

[RUber]

The continuity condition requires that y(0-) = y(0+) and y'(0-) = y'(0+). I think you need to have a different coefficient for the positive x, since the amplitude may be different.
$y(0-) = A cos(\pi/3), y(0+) = B cos(\phi)$
$y'(0-) = -\frac{2\pi}{\lambda} A sin(\pi/3), y'(0+) = -\frac{4\pi}{\lambda}B sin(\phi)$

 

[aryan]

Now from the above two equations i shall get the value of B and ϕ. Right?

 

[RUber]

Hopefully. Then I would recommend plotting the results to make sure they look consistent.