Is there a Doppler effect in the case of sound when the observer or the source moves at right angles to the line joining them? How then can we determine the Doppler effect when the motion has a component at right angles to this line?

Explanation

To determine if there is a Doppler effect in the case of sound when the observer or the source moves at right angles to the line joining them, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Doppler Effect**: The Doppler effect refers to the change in frequency (or wavelength) of a wave in relation to an observer who is moving relative to the wave source. It is important to note that only the component of motion along the line joining the source and the observer affects the frequency.

2. **Identify the Scenario**: In the case where the observer or the source moves at right angles to the line joining them, we need to analyze the components of their velocities. Let's denote:
- \( v_s \): velocity of the source
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