Numericals based on doppler effect — lesson. Science State Board, Class 10.

There will be no Doppler effect in the following situations, and the apparent frequency heard by the listener will be the same as the source frequency.

When both the source ((\S\)) and the listener ((\L\)) are at rest.
When ((\S\)) and ((\L\)) move in such a way that their distance from each other remains constant.
When the source ((\S\)) and the destination ((\L\)) are moving in opposite directions.
If the source is in the centre of the circle that the listener moves around in.

Numerical based on apparent change in frequency due to doppler effect:

Example 1:

A source producing a sound of frequency \(90\) \(Hz\) is approaching a stationary listener with a speed equal to (\(1/10\)) of the speed of sound. What will be the frequency heard by the listener?

Given:

Frequency(\n\)) \(=\) \(90\) \(Hz\)

Speed(\v\)) \(=\) (\(1/10\)) of the speed of sound

When the source is moving towards the stationary listener, the expression for apparent frequency is

\begin{array}{l} n^{'} = (\frac{V}{V - V_{S}}) n \\ Apply the known values, \\ n^{'} = (\frac{V}{V - (\frac{1}{10}) V}) \times 90 \\ n^{'} = (\frac{V}{V (1 - \frac{1}{10})}) \times 90 \\ n^{'} = (\frac{10}{9}) \times 90 \\ n^{'} = 10 \times 10 \\ n^{'} = 100 Hz \end{array}

Example 2:

A source producing a sound of frequency \(500\) \(Hz\) is moving towards a listener with a velocity of \(30\) \(m/s\). The speed of the sound is \(330\) \(m/s\). What will be the frequency heard by the listener?

Given:

Frequency of the sound (\(n\)) \(=\) \(500\) \(Hz\)

Velocity of the listener (

V_{L}

) \(=\) \(30\) \(m/s\)

Speed of the sound(\(V\)) \(=\) \(330\) \(m/s\)

When the source is moving towards the stationary listener, the expression for apparent frequency is

\begin{array}{l} n^{'} = (\frac{V}{V - V_{S}}) n \\ Apply the known values, \\ n^{'} = (\frac{330}{330 - 30}) \times 500 \\ n^{'} = (\frac{330}{300}) \times 500 \\ n^{'} = 110 \times 5 \\ n^{'} = 550 Hz \end{array}

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13. Numericals based on doppler effect

Theory: