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Question : 14
Total: 27
A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5×10–2‌kg and its linear mass density is 4.0×10–2‌kg‌m–1. What is (a) the speed of a transverse wave on the string, and (b) the tension in the string?
Solution:  
Here, υ=45 Hz, M=3.5×10–2 kg ;
mass/length =µ=4.0×10–2‌kg‌m–1
∴l=
M
µ
=
3.5×10−2
4.0×10−2
=
7
8
m
As wire vibrates in its fundamental mode
λ
2
=l=
7
8

∴λ=
7
4
m=1.75m
The speed of the transverse wave v=υλ =45×1.75=78.75ms−1
(b) As, v=√
T
µ

T=v2×µ =(78.75)2×4.0×10−2 =248.06N
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