Question

A wave pulse is described by y(x, t) = ae^-(bx - ct)^(2), where a,b,and c are positive constants. What is speed of this wave?

Answer 1

Speed=c/b

As speed of wave =

coefficient of t/coefficient of x

So here coefficient of t=c

Coefficient of x= b

So speed:c/b

Answer 2

Given :

Equation of wave pulse :

$y(x,t)= ae^{-(bx-ct)^{2} }$

TO Find :

Speed of this wave = ?

Solution :

∴The given equation is comparable to :

$y(x,t) = ae^{-(kx -wt)^{2} }$

So comparing the given equation to the above equation we get :

k =b  and ω=c

Where k is wave number and ω is angular frequency.

∴The speed v of a wave is :

$v=\frac{w}{k}\\v =\frac{c}{b}$

So the speed of the given wave is $v=\frac{c}{b}$ .