Question 36: Waves

Question

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

Accepted Answer

$I=1 \mathrm{~m}, m=2 	imes 10^{-5} \mathrm{~kg},$
T : Tension in the string.
$\because$ Successive frequencies are being given
$	herefore$ It is the case of both ends fixed.
Now,
$$
\begin{aligned}
& f_{n+1}-f_n=1000-750 \\
\Rightarrow & \frac{(n+1)}{2 l} \sqrt{\frac{T}{\mu}}-\frac{n}{2 l} \sqrt{\frac{T}{\mu}}=250 \\
\Rightarrow & \frac{1}{2 l} \sqrt{\frac{T}{\mu}}=250
\end{aligned}
$$
$\begin{aligned} & \Rightarrow \sqrt{\frac{T}{2 	imes 10^{-5}}}=250 	imes 2 	imes 1 \\ & \Rightarrow \frac{T}{2 	imes 10^{-5}}=25 	imes 10^{-4} \\ & \Rightarrow T=50 	imes 10^{-1} \\ & T=5 \mathrm{~N}\end{aligned}$

Waves

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

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