When a source of sound passes us, whether it be a car horn or a train whistle, the pitch we hear goes from high to low. Explain why. Use any relation to support your explanation.

Answer

To explain why the pitch of sound changes from high to low as a sound source passes by, we can analyze the situation using the Doppler effect. Here’s a step-by-step breakdown of the explanation:

### Step 1: Understanding Pitch and Frequency
- **Explanation**: Pitch is the perceived frequency of a sound. Higher frequencies correspond to higher pitches, while lower frequencies correspond to lower pitches.
- **Relation**: The frequency of sound can be denoted as \( f \), and it is related to the speed of sound \( v \) and the speed of the source \( v_s \).

### Step 2: Sound Source Approaching the Observer
- **Explanation**: When a sound source (like a car or train) approaches an observer, the sound waves in front of the source get compressed. This compression leads to an increase in frequency.
- **Relation**: The frequency heard by the observer when the source is approaching is given by:
\[ f' = \frac{v}{v - v_s} f_0 \]
where \( f' \) is the observed frequency, \( v \) is the speed of sound, \( v_s \) is the speed of the source, and \( f_0 \) is the actual frequency of the sound.

### Step 3: Sound Source Moving Away from the Observer
- **Explanation**: Once the sound source passes the observer and starts moving away, the sound waves behind the source get stretched. This stretching leads to a decrease in frequency.
- **Relation**: The frequency heard by the observer when the source is moving away is given by:
\[ f' = \frac{v}{v + v_s} f_0 \]
In this case, \( v + v_s \) indicates that the effective speed of the sound waves relative to the observer increases, leading to a lower observed frequency.

### Step 4: Conclusion
- **Explanation**: As the sound source approaches, the pitch is perceived as high due to the increased frequency. As it moves away, the pitch drops to a lower frequency. This phenomenon is a direct result of the Doppler effect.
- **Final Relation**: Thus, the change in pitch from high to low can be explained through the changing relative velocities of the sound waves as the source moves towards and then away from the observer.