Question

The differential equation, corresponding to sinusoidal waves, represented by

y = a sin(ωt – kx)

has the form \(\frac{\partial ^2y}{\partial x^2}=\frac{1}{v^2}\frac{\partial ^2 y}{\partial t^2}(v=\frac{ω}{k})\)

The general functional equation, for a periodic wave

y = af (ωt - kx)

(1) can represent a sinusoidal wave but its differential equation form would be different from above

(2) cannot represent a sinusoidal wave but its differential equation form would be same as above

(3) cannot represent a sinusoidal wave; its differential equation form would also be different from above

(4) can represent a sinusoidal wave; its differential equation form would also be the same as above

Answer 1

(4) can represent a sinusoidal wave; its differential equation form would also be the same as above

The general functional form, for a periodic wave, can represent a sinusoidal (SH) wave if

af (ωt - kx)

corresponds to a sin(ωt - kx) or a cos(ωt - kx)

Its differential form is same as above. This is because