Statement-1`:` Two longitudinal waves given by equation `y_(1)(x,t)=2asin(omegat-kx)`
and `y_(2)(x,t)=a sin (2 omegat-2kx)`
will have equal intensity.
Statement-2 `:` Intensity of waves of given frequency in same medium is proportional to square of amplitude only.

Options

A. Assertion is correct, reason is correct, reason is a correct explanation for assertion.
B. Assertion is correct, reason is correct, reason is not a correct explanation for assertion
C. Assertion is correct, reason is incorrect
D. Assertion is incorrect, reason is correct

Explanation

To solve the problem, we need to analyze the two statements provided and determine their validity based on the principles of wave physics.

### Step-by-Step Solution:

1. **Understanding the Waves**:
- The first wave is given by the equation:
\[ y_1(x,t) = 2a \sin(\omega t - kx) \]
- The second wave is given by the equation:
\[ y_2(x,t) = a \sin(2\omega t - 2kx) \]

2. **Identifying Amplitudes**:
- The amplitude of the first wave \( y_1 \) is \( 2a \).
- The amplitude of the second wave \( y_2 \) is \( a \).

3. **Calculating Intensities**:
- The intensity \( I \) of a wave is proportional to the square of its amplitude. Therefore:
\[ I_1 \propto (2a)^2 = 4a^2 \]
\[ I_2 \propto (a)^2 = a^2 \]

4. **Comparing Intensities**:
- For the two waves to have equal intensity, we need:
\[ 4a^2 = a^2 \]
- This equation is not true unless \( a = 0 \), which is not a practical case for wave intensity.

5. **Conclusion on Statement 1**:
- Since the calculated intensities are not equal, **Statement 1 is false**.

6. **Analyzing Statement 2**:
- Statement 2 claims that the intensity of waves of given frequency in the same medium is proportional to the square of the amplitude only. This is generally true for waves, but it does not account for other factors that can influence intensity (like frequency and medium properties).
- Therefore, **Statement 2 is also false**.

7. **Final Evaluation**:
- Since both statements are false, we conclude that neither statement supports the other.

### Final Answer:
- **Statement 1 is false and Statement 2 is false.**