Q. 14

# A wire stre

(a) Given,

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, f = 45 Hz

So, Length of the wire, l = m/μ

l = (3.5 × 102 kg)/(4.0 × 10-2 kg m-1)

l = 0.875 m

The wavelength of the stationary wave (λ) and the length of the wire are related as

λ = 2l/m

where, n = Number of nodes in the wire

For fundamental node, n = 1

λ = 2l

λ = 2 × 0.875 m

λ = 1.75 m

The speed of the transverse wave in the string is given as

V = fλ= 45 m s-1 × 1.75 m

V = 78.75 m s-1

(b) The tension produced in the string is given as

T = v2μ = (78.75 m s-1)2 × 4.0 × 10–2 kg m-1

T = 248.06 N

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