A sonometer wire resonates in its fundamental mode at frequency f. The vibrating length is then doubled without changing the wire. By what factor must the tension be changed so that the fundamental frequency remains unchanged?
Options

Question

A sonometer wire resonates in its fundamental mode at frequency f. The vibrating length is then doubled without changing the wire. By what factor must the tension be changed so that the fundamental frequency remains unchanged?

Options

G1 Physics · Accepted Answer

For the same wire, f = [1/(2L)]√(T/μ). Thus, f ∝ √T/L. To keep f unchanged when L' = 2L, we require √T'/2L = √T/L. Therefore, √T' = 2√T. Squaring, T' = 4T. Correct option: B.