Ratio of amplitude for two wave is 1:2 .Find the ratio of intensity?

Answer

To solve the problem of finding the ratio of intensity given the ratio of amplitude, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship Between Intensity and Amplitude**:
- Intensity (I) is proportional to the square of the amplitude (A). This can be expressed mathematically as:
\[ I \propto A^2 \]

2. **Set Up the Given Ratio of Amplitudes**:
- The problem states that the ratio of the amplitudes of two waves is given as:
\[ \frac{A_1}{A_2} = \frac{1}{2} \]

3. **Express the Ratio of Intensities**:
- Since intensity is proportional to the square of the amplitude, we can express the ratio of intensities as:
\[ \frac{I_1}{I_2} = \left(\frac{A_1}{A_2}\right)^2 \]

4. **Substitute the Given Amplitude Ratio**:
- Now, substitute the given ratio of amplitudes into the equation:
\[ \frac{I_1}{I_2} = \left(\frac{1}{2}\right)^2 \]

5. **Calculate the Ratio of Intensities**:
- Calculate the square of the fraction:
\[ \frac{I_1}{I_2} = \frac{1^2}{2^2} = \frac{1}{4} \]

6. **Express the Final Ratio**:
- Therefore, the ratio of intensities can be expressed as:
\[ I_1 : I_2 = 1 : 4 \]

### Final Answer:
The ratio of intensity \( I_1 : I_2 \) is \( 1 : 4 \).

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