If `(I_("max"))/(I_("min"))=(36)/(25)` then find ratio of maximum to minimum amplitude:-

Options

A. `11:1`
B. `121:1`
C. `6:5`
D. `81:1`

Answer

To solve the problem, we need to find the ratio of maximum amplitude to minimum amplitude given the ratio of maximum intensity to minimum intensity.

### Step-by-Step Solution:

1. **Understanding the relationship between intensity and amplitude:**
The intensity (I) of a wave is proportional to the square of its amplitude (A). This can be expressed mathematically as:
\[ I \propto A^2 \]
Therefore, we can write:
\[ I_{\text{max}} \propto A_{\text{max}}^2 \quad \text{and} \quad I_{\text{min}} \propto A_{\text{min}}^2 \]

2. **Setting up the ratio of intensities:**
Given the ratio of maximum intensity to minimum intensity:
\[ \frac{I_{\text{max}}}{I_{\text{min}}} = \frac{36}{25} \]

3. **Expressing the ratio of amplitudes:**
Since intensity is proportional to the square of the amplitude, we can write:
\[ \frac{I_{\text{max}}}{I_{\text{min}}} = \frac{A_{\text{max}}^2}{A_{\text{min}}^2} \]
Therefore, we can substitute the given ratio:
\[ \frac{A_{\text{max}}^2}{A_{\text{min}}^2} = \frac{36}{25} \]

4. **Taking the square root to find the ratio of amplitudes:**
To find the ratio of the amplitudes, we take the square root of both sides:
\[ \frac{A_{\text{max}}}{A_{\text{min}}} = \sqrt{\frac{36}{25}} = \frac{\sqrt{36}}{\sqrt{25}} = \frac{6}{5} \]

5. **Final Result:**
Thus, the ratio of maximum amplitude to minimum amplitude is:
\[ A_{\text{max}} : A_{\text{min}} = 6 : 5 \]