Class 11 Physics - Chapter Waves NCERT Solutions | A wire stretched between two rigid suppo
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
(a) the speed of a transverse wave on the string, and
(b) the tension in the string?
(a) Mass of the wire, m = 3.5 × 10-2 kg
Linear mass density, μ = m / l = 4.0 x 10-2 kg m-1
Frequency of vibration, V = 45 Hz
∴Length of the wire, l = m / μ = 3.5 × 10-2 / 4.0 x 10-2
The wavelength of the stationary wave (λ) is related to the length of the wire by the relation:
λ = 2l / n
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 = V λ = 45 × 1.75 = 78.75 m/s
(b) The tension produced in the string is given by the relation:
T = v2 µ
= (78.75)2 × 4.0 × 10-2 = 248.06 N
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