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 x 10⁻² kg and its linear mass density is 4.0 x 10⁻² kg m⁻¹. What is the tension in the string?

Answer 1

given,
mass of wire, m = 3.5 × 10^-2 kg
linear mass density , u = 4 × 10^-2 kg
so, length of wire , l = m/u = 3.5/4 = 0.875m
frequency of fundamental mode , f = 45Hz

for wire stretched between two rigid supports,
fundamental mode is given by,
l = λ/2 => λ = 2l = 2 × 0.875 = 1.75 m

now, use formula, v = λf , to find speed of wave
so, v = 1.75 × 45 = 78.75 m/s

now, use formula , $T=v^2u$
= (78.75)² × 4 × 10^-2
= 248.06N