Which of the following is correct

Options

A. Doppler effect in sound and light is asymmetric
B. Doppler effect in sound and light is symmetric
C. Doppler effect in sound is asymmetric and in light it is symmetric
D. none

Answer

To solve the question regarding the Doppler effect in sound and light, we will analyze the characteristics of the Doppler effect in both mediums step by step.

### Step-by-Step Solution:

**Step 1: Understanding the Doppler Effect in Sound**
- The Doppler effect describes the change in frequency (or wavelength) of a wave in relation to an observer moving relative to the source of the wave.
- For sound, the formula for apparent frequency \( f \) when the source is at rest and the observer is moving towards the source is given by:
\[ f = f_0 \left( \frac{v}{v - v_o} \right) \]
where:
- \( f_0 \) is the original frequency,
- \( v \) is the velocity of sound,
- \( v_o \) is the velocity of the observer.

**Hint for Step 1:** Remember that the formula changes based on whether the source or observer is moving.

**Step 2: Analyzing the Case of the Source Moving Towards the Observer**
- If the source is moving towards a stationary observer, the formula becomes:
\[ f = f_0 \left( \frac{v + v_s}{v} \right) \]
where \( v_s \) is the velocity of the source.
- In both scenarios (observer moving towards the source and source moving towards the observer), the apparent frequency is different.

**Hint for Step 2:** Focus on how the movement of the source or observer affects the frequency perceived.

**Step 3: Conclusion for Sound**
- Since the apparent frequency changes depending on whether the observer or the source is moving, we conclude that the Doppler effect in sound is asymmetric.

**Hint for Step 3:** Asymmetry means that the results differ based on the direction of movement.

**Step 4: Understanding the Doppler Effect in Light**
- For light, the formula for apparent frequency when considering the relative motion of the source and observer is:
\[ f = f_0 \left( 1 + \frac{v}{c} \right) \]
or
\[ f = f_0 \left( 1 - \frac{v}{c} \right) \]
where \( c \) is the speed of light.
- In this case, the speed of light is constant for all observers regardless of their motion.

**Hint for Step 4:** The constancy of the speed of light is crucial in determining the symmetry of the Doppler effect for light.

**Step 5: Conclusion for Light**
- Since the apparent frequency remains the same whether the source is moving towards the observer or the observer is moving towards the source, the Doppler effect in light is symmetric.

**Hint for Step 5:** Symmetry means that the results are the same regardless of the direction of movement.

**Final Conclusion:**
- The correct statement is that the Doppler effect in sound is asymmetric while the Doppler effect in light is symmetric. Therefore, the correct option is:
- "Doppler effect in sound is asymmetric and in light is symmetric."