Arope with a mass density of 1 kg/m has one end tied to a vertical support. you hold the other end so that the rope is horizontal and has a tension of 4 n. if you move the end of the rope back and forth, you produce a transverse wave in the rope with a wave speed of 2 m/s. if you double the amount of tension you exert on the rope, what is the wave speed?

Explanation:

Velocity of wave in stretched string is given by the formula

here we know that

T = 4 N

also we know that linear mass density is given as

so we have

now the tension in the string is double

so the velocity is given as

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .