Two strings X and Y of a sitar produce a beat frequency 4 Hz. Whe… - Vidyadip

MCQ

Two strings $X$ and $Y$ of a sitar produce a beat frequency $4 Hz$. When the tension of the string $Y$ is slightly increased the beat frequency is found to be $2 Hz.$ If the frequency of $X$ is $300 Hz,$ then the original frequency of $Y$ was .... $Hz$

✓
$296$
B
$298$
C
$302$
D
$304$

✓

Answer

Correct option: A.

$296$

a
(a) ${n_x} = 300Hz,$ ${n_y} = ?$

$x =$ beat frequency $= 4 Hz,$ which is decreasing $(4→2)$

after increasing the tension of the string $y. $

Also tension of wire $y$ increasing so ${n_y} \uparrow $ ($ \because n \propto \sqrt T$)

Hence ${n_x} - {n_y} \uparrow = x \downarrow $ $\rightarrow$ Correct

${n_y} \uparrow - {n_x} = x \downarrow $ $\rightarrow$ Wrong

==> ${n_y} = {n_x} - x = 300 - 4 = 296Hz$

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