Two tuning forks X and Y have frequencies 280 | vedclass

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(D) Given, frequencies of tuning forks $X$ and $Y$ are:$n_X = 280 \,Hz$$n_Y = 284 \,Hz$Let the frequency of tuning fork $Z$ be $n_Z$ and the beat freq

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$278$

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(D) Given, frequencies of tuning forks $X$ and $Y$ are:$n_X = 280 \,Hz$$n_Y = 284 \,Hz$Let the frequency of tuning fork $Z$ be $n_Z$ and the beat frequency produced by $X$ and $Z$ be $b$.From the first condition, $b = |n_Z - 280|$.From the second condition, the beat frequency produced by $Y$ and $Z$ is $3b$, so $3b = |n_Z - 284|$.Case $1$: If $n_Z > 284$, then $n_Z - 280 = b$ and $n_Z - 284 = 3b$. Substituting $b$, we get $n_Z - 284 = 3(n_Z - 280) \Rightarrow n_Z - 284 = 3n_Z - 840 \Rightarrow 2n_Z = 556 \Rightarrow n_Z = 278 \,Hz$. This contradicts $n_Z > 284$.Case $2$: If $n_Z Thus, the frequency of $Z$ is $278 \,Hz$.

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