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A 40 cm long wire having a mass 3.2 gm and area of cross section 1 mm2 is stretched between the support 40.05 cm apart. In its fundamental mode, it vibrates with a frequency 1000/64 Hz. The young's modulus of the wire is 10x N/m2, then find x :


Solution

For fundamental frequency,
μ=3.2 gm40 cm=3.2×10340×102=3.2400=324000 kg/m
l=λ2λ=2l     ...(1)


f=vλ=12lTμ
100064=12×40×102T32/4000
[100064×2×40×102]2324000=T
1000064×324000=T     T=108 N
Now, y=10/8106.05×10240×102=107840(.05)=109 N/m2

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