15.14 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. What is:

(a) the speed of a transverse wave on the string, and
(b) the tension in the string?

It is given in the question that:
Mass of the wire, m = 3.5 × 10-2 kg
Linear mass density, μ=ml=4.0×10-2kg m-1
Frequency of vibration, ν= 45 Hz  
 Length of the wire,   l=mμ=3.5×10-24.0×10-2=0.875 m
The wavelength of the stationary wave:  λ=2ln
where, n=number of nodes in the wire 
For fundamental node, n=1-
 λ=2lλ=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 
The tension produced in the string: 
T=v2μ=(78.75)2×4.0×10-2=248.06 N