Question

A motion is described by $y=\frac{3}{a^2+(x+3t{)}^2}$ where y, x are in meter and t is in second.

• A. This represents equation of progressive wave propagating along -x direction with $3m{s}^{-1}$
• B. This represents equation of progressive wave propagating along +x direction with $3m{s}^{-1}$
• C. This does not represent a progressive wave equation.
• D. data is insufficient to arrive at any conclusion.

Answer 1

The correct option is A This represents equation of progressive wave propagating along -x direction with $3m{s}^{-1}$

A function f($\omega$t - kx) can represent a wave only if:

• Range of the function should be finite,

• The function is continuous (string can't be broken) and differentiable

As we can see the given function satisfies both conditions.

On comparison we see that 'k' = -1$m^{-1}$ and '$\omega$' = 3rad$s^{-1}$

Given that all constants are in SI.

velocity of wave (v) = $\frac{\omega }{v}$ = -3m$s^{-1}$