Radio waves and gamma waves are both transverse in nature and electromagnetic in character and have the same speed in vacuum. In what respects are they different?

Options

A. Frequency
B. Wavelength
C. Both (a) and (b)
D. None of these

Explanation

To address the question regarding the differences between radio waves and gamma waves, we can break down the solution into clear steps:

### Step-by-Step Solution:

1. **Understanding the Nature of Waves**:
- Both radio waves and gamma rays are types of electromagnetic waves. They are transverse in nature, meaning that the oscillations of the electric and magnetic fields are perpendicular to the direction of wave propagation.

2. **Speed of Waves**:
- Both radio waves and gamma rays travel at the same speed in a vacuum, which is approximately \(3 \times 10^8\) m/s. This is a fundamental property of all electromagnetic waves in a vacuum.

3. **Frequency Comparison**:
- The frequency of a wave is defined as the number of oscillations (or cycles) that occur in a unit time. Gamma rays have a much higher frequency compared to radio waves. This can be expressed mathematically as:
\[ f_{\text{gamma}} > f_{\text{radio}} \]

4. **Wavelength Comparison**:
- Wavelength is the distance between successive peaks of a wave. There is an inverse relationship between frequency and wavelength, described by the equation:
\[ c = f \lambda \]
where \(c\) is the speed of light, \(f\) is frequency, and \(\lambda\) is wavelength. Since gamma rays have a higher frequency, they correspondingly have a shorter wavelength compared to radio waves:
\[ \lambda_{\text{gamma}} < \lambda_{\text{radio}} \]

5. **Conclusion**:
- In summary, the primary differences between radio waves and gamma rays are:
- **Frequency**: Gamma rays have a higher frequency than radio waves.
- **Wavelength**: Radio waves have a longer wavelength than gamma rays.

### Final Answer:
In respect to frequency and wavelength, radio waves and gamma rays differ significantly. Gamma rays have a higher frequency and shorter wavelength compared to radio waves.