Two traveling sinusoidal waves are described by the wave functions where x, y1 and y2 are in meters and t is seconds.
y1 = (5.45 m) sin[(4.30x - 1260t)]
y2 = (5.45 m) sin[(4.30x - 1260t - 0.25)]
a) What is the amplitude of the resultant wave?
b) What is the frequency of the resultant wave?
You can use the trig identity sin u + sin v = 2 sin(½(u+v)) cos(½(u−v)) with u=4.30x - 1260t and v=4.30x - 1260t - 0.25. You should find that the resultant wave is given by 2*(5.45m)* sin(4.3x-1260t-.125) *cos(.125). That means:
a) The amplitude is 2*(5.45m)*cos(.125) =10.81m
b)The frequency is the same as it was for y1 and y2: the angular frequency w =1260 rad/s or f = w/(2*Pi) = (1260 rad/s)/(2*Pi rad) = 200.5 Hz.
Hope that helps!
a) = 2(5.45)cos(0.125) = 10.815
b) = (1260 x Pi) / (2 x Pi) => = 1260/2 = 630