Question

transverse waves with a speed of 50m/s are to be produced on a stretched string. A 5 m length of string with a total mass of 0.06 kg is used.
a. what is the required tension in the string?
b. calculate the wave speed in the string if the tension is 8 N.

Answer 1

Concepts and reason

The concepts used to solve this problem are transverse wave and linear mass density.

Initially, use the velocity, mass, and length of the string to find the tension of the wave in the stretched string.

Finally, use tension on the string, mass, and length of the string to find the velocity of the wave in the stretched string.

Fundamentals

The speed of a transverse wave in a stretched string is as follows:

Here, the speed of the standing wave is , tension on the string is , and linear mass density is .

The expression for linear mass density is as follows:

Here, the mass is and length of the string is .

(a)

The speed of a transverse wave in a stretched string is as follows:

Square on both the sides as follows:

Rearrange the expression to get .

…… (1)

The expression for linear mass density is as follows:

Substitute for in Equation (1).

Substitute for , for , and for .

(b)

The speed of a transverse wave in a stretched string is as follows:

The expression for linear mass density is as follows:

Substitute for in the expression for transverse velocity.

Substitute for , for , and for .

Ans: Part a

The tension needed in the string is .

Part b

The wave velocity of a string is .