Two vibrating tuning forks produce waves given by ${y_1} = 4\sin 500\pi t$ and ${y_2} = 2\sin 506\pi t$. The number of beats produced per minute is

  • A
    $360$
  • B
    $180$
  • C
    $3$
  • D
    $60$

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$A$ source of frequency $\nu$ gives $6 \text{ beats/second}$ when sounded with a source of frequency $200 \text{ Hz}$. The second harmonic of frequency $2\nu$ of the source gives $8 \text{ beats/second}$ when sounded with a source of frequency $420 \text{ Hz}$. The value of $\nu$ is (in $text{ Hz}$)

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