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← JEE Advanced 2023 · Paper 2
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JEE Advanced 2023 · Paper 2, Physics question 10

A string of length 1 m and mass 2×10−52\times10^{-5} kg is under tension TT. When the string vibrates, two successive harmonics are found to occur at frequencies 750 Hz and 1000 Hz. The value of tension TT is _____ Newton.

Answer and worked solution

Official answer: 5

Fundamental. Successive harmonics of a string differ by the fundamental, so f1=1000−750=250f_1=1000-750=250 Hz.

Tension. With μ=2×10−5\mu=2\times10^{-5} kg/m:
f1=12LTμ  ⟹  T2×10−5=500  ⟹  T=5 N.f_1=\frac1{2L}\sqrt{\frac T\mu}\implies\sqrt{\frac{T}{2\times10^{-5}}}=500\implies T=5\ \text{N}.

Topics:Standing waves in stringsSpeed of waves
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