Question

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

1. the speed of a transverse wave on the string and

2. the tension in the string?

Answer 1

mass of wire M = 3.5 × 10^-2kg

Linear density µ = mass / length

= M/l = 4.0 × 10^-2kg

∴ Length of wire l = \(\frac{M}{μ}\)=\(\frac{3.5×10^{−2}} {4 \times 10^{-2}}\)m = 0.875m

In the fundamental mode,

λ =2l = 2 × 0.875m = 1.75m

1. Speed of transverse waves u = v λ

= 45 × 1.75ms^-1 = 78.75ms^-1

2. u= \(\sqrt{\frac{T}{μ}}\) or T = µu² = 4 × 10^-2(78.75)²N

= 278.06N.