The equation of a transverse progressive wave is y = 0 . 02 sin (x + 40 t) m . Find out the tension in a wire of linear density `10^(-4) kg * m^(-1)` , If the wave travels along it .

Answer

Comparing the given equation with the standard form ` y = sin (omega t + kx)` , we have k = 1 and ` omega = 40 ` . So, the wave velocity, ` v = (omega)/(k) = (40)/(1) = 40 m * s^(-1)` .
If T = tension and m = linear density of the wire,
` V = sqrt((T)/(m)) or, T = V^(2) m = (40)^(2) xx 10^(-4) = 0 . 16 N` .