(A) : The lectromagnetic waves of shorter wavelengths can travel longer distances wavelengths.
(R) : Shorter the wavelength, the large is the speed of propagation of the wave.

Options

A. Both 'A' and 'R' are true and 'R' is the correct explanation of 'A'.
B. Both 'A' and 'R' are true and 'R' is not the correct explanation of 'A'.
C. A' is true abd 'R' false
D. A' is false and 'R' is false

Answer

To analyze the statements given in the question, we will evaluate both the assertion (A) and the reasoning (R) step by step.

### Step 1: Understanding the Assertion (A)
The assertion states: "The electromagnetic waves of shorter wavelengths can travel longer distances than those of longer wavelengths."

- **Explanation**: Electromagnetic waves with shorter wavelengths (like gamma rays and X-rays) generally have higher frequencies and can penetrate through various media more effectively than longer wavelengths (like radio waves). This is due to their ability to diffract less around obstacles and their lower susceptibility to atmospheric absorption.

### Step 2: Understanding the Reasoning (R)
The reasoning states: "Shorter the wavelength, the larger is the speed of propagation of the wave."

- **Explanation**: The speed of electromagnetic waves in a vacuum is constant and is approximately \(3 \times 10^8\) m/s, regardless of their wavelength. The relationship between speed (v), frequency (f), and wavelength (λ) is given by the equation: \(v = f \cdot \lambda\). This means that if the wavelength decreases, the frequency must increase to keep the speed constant. Therefore, the statement that shorter wavelengths travel faster is incorrect.

### Step 3: Conclusion
- The assertion (A) is **True**: Shorter wavelengths can indeed travel longer distances under certain conditions.
- The reasoning (R) is **False**: The speed of electromagnetic waves does not depend on their wavelength; it remains constant in a vacuum.

### Final Answer
- Assertion (A) is true, and Reasoning (R) is false.