Question

please help solve 1

1. A one-dimensional wave equation may be written D, (x,t)-7 sin(6π_x + 2- ) where 7 is the amplitude and Do is the "height" of the light wave at a particular point in space at a partcular time. A) Write the equation of a wave Di(x,t) that will interfere destructively with Do(x.t). B) Write the equation of a wave D(x,t) that looks just like D(x,t), but is going the other direction.

Answer 1

a) the the wave interference is said to be destructive, if the wave out of phase with same frequency.

that is angle, pi/4 will be added to pi. so pi+ pi/4 = 5pi /4

$D_{1}(x,t)= 7 sin (6\Pi \frac{rad}{m}x + 2\frac{rad}{sec}t+\frac{5\Pi }{4})$

b) in the given wave equation, +2t shows that wave is going in left direction. -ve sign gives the right and opposite direction.

$D_{2}(x,t)= 7 sin (6\Pi \frac{rad}{m}x - 2\frac{rad}{sec}t+\frac{5\Pi }{4})$