Q.

A long uniform steel wire has a diameter of 2.0 mm. what should be the tension in the wire, so that the speed of the transverse wave on it equals the speed of sound at STP (320 m/s) the density of steel is  7800 kg/m3.

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a

120 N

b

130 N

c

2508 N

d

25.1N

answer is C.

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Detailed Solution

Volume of wire V=πr2l=πd2l/4 Mass of wire=(M)=Volume×density=πd2lρ4 Linear Mass Density μ=Ml=πd2ρ4 Wave Speed v=Tμ Tension in wire T=μv2=πd2ρv24⇒T= 3.142×(2×10−3)2×7800×(320)24Substituting  v, ρ, d we have T=2508 N
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