When both the listener and source are moving towards each other, then which of the following is true regarding frequency and wavelength of wave observed by the observer?

Options

A. More frequency, less wavelength
B. More frequency, more wavelength
C. Less frequency, less wavelength
D. More frequency, constant wavelength

Answer

To solve the problem regarding the frequency and wavelength of waves observed by a listener when both the source and the listener are moving towards each other, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Scenario**:
- We have a sound source and a listener (observer).
- Both the sound source and the observer are moving towards each other.

2. **Doppler Effect**:
- The situation described involves the Doppler Effect, which is the change in frequency (and wavelength) of a wave in relation to an observer moving relative to the wave source.
- When both the source and the observer are moving towards each other, the observed frequency increases.

3. **Effect on Frequency**:
- As the source moves towards the observer, the sound waves are compressed. This compression results in an increase in the frequency observed by the listener.
- Mathematically, the frequency observed (\( f' \)) can be expressed as:
\[ f' = f \left( \frac{v + v_o}{v - v_s} \right) \]
where:
- \( f \) = original frequency of the source
- \( v \) = speed of sound in the medium
- \( v_o \) = speed of the observer towards the source
- \( v_s \) = speed of the source towards the observer

4. **Effect on Wavelength**:
- The wavelength (\( \lambda' \)) of the wave is inversely related to the frequency. Since frequency increases, the wavelength must decrease.
- The relationship between wavelength and frequency is given by:
\[ v = f \lambda \]
Rearranging gives:
\[ \lambda = \frac{v}{f} \]
- As frequency increases, the wavelength decreases, confirming that the waves are compressed.

5. **Conclusion**:
- Therefore, when both the listener and the source are moving towards each other, the frequency observed by the listener increases, and the wavelength decreases.

### Final Answer:
- The correct conclusion is that the frequency increases and the wavelength decreases.