Question

The length of a sonometer wire is 0.75 m and density is 9 × 103 kg/m3. it can bear a stress of 8.1 × 108 n/m2 without exceeding the elastic limit. then the fundamental frequency that can be produced in the wire is

Answer 1

The fundamental frequency will be 200 Hz.

Explanation:

let A be the area of the wire,

we know that

Stress = Force/area

=> F = S x A = 8.1 x 10⁸ x A

Mass = density x volume

=> M = d x l x A

= 9 x 10³ x l x A

Hence mass per unit length = M/l

= 9 A x 10³

We know that speed of wave in the string,

S = √(Force/mass per unit length)

= √(8.1 x A x 10⁸/9xAx10³)

=√9x10⁴

= 300

Hence frequency ,

f = speed/2l

= 300/2x0.75

=300/1.5

=200Hz

Hence frequency of the wave will be 200 Hz