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Question: A 10 m long steel wire has mass 5 g. If the wire is under a tension of 80 N, the speed of transverse...

A 10 m long steel wire has mass 5 g. If the wire is under a tension of 80 N, the speed of transverse waves on the wire is

A

100 m s–1

B

200 m s–1

C

400 m s–1

D

500 m s–1

Answer

400 m s–1

Explanation

Solution

Here, Length, L=10m

Mass, M=5g=5×10−3kgM = 5g = 5 \times 10^{- 3}kg

Tension, T=80NT = 80N

Mass per unit length of the wire is

μ=ML=5×10−3kg10m=5×10−4kgm−1\mu = \frac{M}{L} = \frac{5 \times 10^{- 3}kg}{10m} = 5 \times 10^{- 4}kgm^{- 1}

Speed of the transverse wave on the wire is

v=Tμ=80N5×10−4kgm−1v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{80N}{5 \times 10^{- 4}kgm^{- 1}}}

=4×102ms−1=400ms−1= 4 \times 10^{2}ms^{- 1} = 400ms^{- 1}