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Standard XII

Physics

Frequency

A train S1, m...

Question

A train $S_{1}$ , moving with a uniform velocity of $108 km / h$ , approaches another train $S_{2}$ standing on a platform. An observer $O$ moves with a uniform velocity of $36 km/h$ towards $S_{2}$ as shown in figure. Both the trains are blowing whistles of same frequency $120 Hz$ . When O is $600 m$ away from $S_{2}$ and distance between $S_{1}$ and $S_{2}$ is $800 m$ , the number of beats heard by $O$ is.
[Speed of the sound $= 330 m / s$ ]

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Solution

Frequency observed by $O$ from $S_{1}$
$f_{1} = 120 [\frac{330 + 10 cos 53^{\circ}}{330 - 30 cos 37^{\circ}}]$ Hz
as sourse and observer both are moving

Frequency observed by $O$ from $S_{2}$
$f_{2} = 120 [\frac{330 + 10}{330}] Hz$
Here, observer is moving but source is at rest.

Beat frequency $Δ f = f_{1} - f_{2} = 120 \times [\frac{336}{306} - \frac{34}{33}] = 8.13 Hz$
In multiple of $100$
$= 8.13 \times 100 = 813 Hz$

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