One end of a string is attached to a rigid wall on a tabletop. The string is run over a frictionless pulley and the other end of the string is attached to a stationary hanging mass. The distance between the wall and the pulley is 0.405 meters, When the mass on the hook is 25.4 kg, the horizontal portion of the string oscillates with a fundamental frequency of 261.6 Hz (the same frequency as the middle C note on a piano). Calculate the linear mass density of the string.

The linear mass  density is of the string  

Explanation:

    From the question we are told that

            The distance between wall and pulley is

            The mass on the hook is

            The frequency of oscillation is  

    Generally, the frequency of oscillation is mathematically  represented as

Where T is the tension mathematically represented as

                T = mg

Substituting values

    is the mass linear density

Making   the subject of the formula above

Substituting values

0.005550 Kg/m

Explanation:

The picture attached below shows the full explanation