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 × 10–2 kg m–1. What is (a) the speed of a transverse wave on the string, and (b) the tension in the string? | Learn NCERT solution | Education portal Class 11 Physics | Study online Unit-15 Waves



Q.14:- 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 × 10–2 kg m–1. What is (a) the speed of a transverse wave on the string, and (b) the tension in the string?

 

 

Answer:-

(a) Mass of the wire, m = 3.5 × 10–2 kg
Linear mass density, μ = m/l = 4.0 × 10-2 kg m-1
Frequency of vibration, v = 45 Hz∴ length of the wire, l = m/μ = 3.5 × 10–2 / 4.0 × 10-2 = 0.875 m
The wavelength of the stationary wave (λ) is related to the length of the wire by the relation:
λ = 2l/m
where,
n = Number of nodes in the wire
For fundamental node, n = 1:
λ = 2l
λ = 2 × 0.875 = 1.75 m
The speed of the transverse wave in the string is given as:
v = νλ= 45 × 1.75 = 78.75 m/s



(b) The tension produced in the string is given by the relation:
T = v2µ
= (78.75)2 × 4.0 × 10–2 = 248.06 N