Question

A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5 × 10^-2 kg and its linear mass density is 4.0 × 10^-2kgm^-1. What is 

1. The speed of a transverse wave on the string, 

2. The tension in the string?

Answer 1

Given : f = 45 Hz mass of wire

= m =3.5×10^-2 kg

linear mass density

= µ = mass per unit length

= 4 × 10^-2 kg m^-1

∴ length of the wire

l = 0.875 m

1. We vibrate in fundamental mode

⇒ λ = 2l

∴ λ = 2 × 0.875 = 1.75 m

∴ Speed of wave

= v =fλ = 45 × 1.75

= 78.75 ms^-1

2. We know that

T = µV²

∴ Tension, T = 4×10^-2 × 78.75^-2 = 248.06 N