A sonometer wire 36 cm long, vibrates with a fundamental frequency of

1.	A sonometer wire 36 cm long, vibrates with a fundamental frequency of 280 Hz, when it is under tension of 24.5 N. Calculate mass per unit length of wire.
Answer» Data : L = 36 cm = 0.36 m, n = 280 Hz, T = 24.5 N n = \(\frac 1{2L}\)\(\sqrt{\frac Tm}\) ∴ Linear density, m = \(\frac T{4L^2n^2}\) ∴ m = \(\frac{24.5}{4(0.36)^2(280)^2}\) = 6.0 × 10^-4 kg/m

A sonometer wire 36 cm long, vibrates with a fundamental frequency of 280 Hz, when it is under tension of 24.5 N. Calculate mass per unit length of wire.

Answer»

Data : L = 36 cm = 0.36 m, n = 280 Hz, T = 24.5 N

n = \(\frac 1{2L}\)\(\sqrt{\frac Tm}\)

∴ Linear density, m = \(\frac T{4L^2n^2}\)

∴ m = \(\frac{24.5}{4(0.36)^2(280)^2}\)

= 6.0 × 10^-4 kg/m