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14.Waves and Sound
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Show that when a string fixed at its two ends vibrates in $1$ loop, $2$ loops, $3$ loops and $4$ loops, the frequencies are in the ratio $1 : 2 : 3 : 4$.
Option A
Option B
Option C
Option D
Solution
In case of stationary waves, frequency in the $n^{\text {th }}$ mode of vibration is, $f_{n}=\frac{n v}{2 \mathrm{~L}} \quad$ (Where $v=\sqrt{\frac{\mathrm{T}}{\mu}}=$ speed of
transverse wave in stretched string)
$\therefore f_{n} \propto n$
$\Rightarrow f_{1}: f_{2}: f_{3}: f_{4}=1: 2: 3: 4$
Standard 11
Physics
