Question

The displacement of a wave pulse is given by y= 10/4+(4t-x)^2 metre. The velocity of wave pulse is?

Answer 1

we know that, Formula of displacement of a wave pulse is given by y = P/{ Q+ ( vt - x² ) }

Here, Given y = 10/ { 4 + { 4t - x² } m

The given equation is directly in Standard units. so no need to change units.

If we compare, We get v = 4m/s

Therefore Velocity of the wave pulse is 4 m/s .

Hope helped!

Answer 2

Displacement of a wave pulse is given by , y = $\bold{\frac{10}{4+(4t-x)^2}}$
This wave equations is in the form of f(x,t) = P/{Q + (vt - x)²}, here P and Q is constant and v is velocity of wave , x is displacement of wave and f(x,t) shows displacement of particle in wave.
Now, compare both the given equation ,
What you get ,velocity of wave = 4 m/s

Well, you can solve it with help of (1/v²)d²y/dt² = d²y/dx² , but it's too lengthy so, just memorize form of wave for finding anything related to it .