JEE Advanced 2023 Paper 2 · Q10 · Sound Waves

Question

A string of length $1$ m and mass $2 	imes 10^{-5}$ kg is under tension $T$. When the string vibrates, two successive harmonics are found to occur at frequencies $750$ Hz and $1000$ Hz. The value of tension $T$ is ___ Newton.

SolveKar AI · Accepted Answer

For a fixed-fixed string, harmonic frequencies are $f_n = nv/(2L)$. Successive harmonics differ by $v/(2L) = 1000 - 750 = 250$ Hz. So $v = 500$ m/s. Linear mass density $\mu = m/L = 2	imes 10^{-5}$ kg/m. Tension $T = \mu v^2 = 2	imes 10^{-5} \cdot 500^2 = 2	imes 10^{-5}\cdot 2.5	imes 10^5 = 5$ N.

JEE Advanced 2023 Paper 2 · Q10 · Sound Waves

Solution