A man is watching two trains, one leaving and the other coming with equal speed of $4\,m/s$. If they sound their whistles each of frequency $240\, Hz$, the number of beats per sec heard by man will be equal to (velocity of sound in air $= 320\, m/s$)
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$\mathrm{n}^{\prime}=\mathrm{n}\left[\frac{\mathrm{v}}{\mathrm{v}-v_{\mathrm{s}}}\right]$
$\mathrm{n}^{\prime \prime}=\mathrm{n}\left[\frac{\mathrm{v}}{\mathrm{v}+\mathrm{v}_{\mathrm{s}}}\right]$
$ \Delta \mathrm{n} =\mathrm{n}^{\prime}-\mathrm{n}^{\prime \prime} $
$=\mathrm{nv}\left[\frac{1}{v-v_{\mathrm{s}}}-\frac{1}{v+v_{\mathrm{s}}}\right]=\mathrm{nv}\left[\frac{2 \mathrm{v}_{\mathrm{s}}}{v^{2}-v_{\mathrm{s}^{2}}}\right] $
$=\frac{2 \mathrm{nv}_{\mathrm{s}}}{\mathrm{v}}=\frac{2 \times 240 \times 4}{320}=6 $
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