Answer :

(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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