Ratio of amplitude for two wave is 9:10 .Find the ratio of intensity?

Explanation

To solve the problem, we need to find the ratio of intensities of two waves given the ratio of their amplitudes. Here's a step-by-step solution:

### Step 1: Understand the relationship between amplitude and intensity
The intensity (I) of a wave is directly proportional to the square of its amplitude (A). This can be expressed mathematically as:
\[ I \propto A^2 \]

### Step 2: Write the given data
We are given the ratio of the amplitudes of two waves:
\[ \frac{A_1}{A_2} = \frac{9}{10} \]

### Step 3: Express the ratio of intensities
Using the relationship between intensity and amplitude, we can express the ratio of intensities (I1 and I2) as follows:
\[ \frac{I_1}{I_2} = \left(\frac{A_1}{A_2}\right)^2 \]

### Step 4: Substitute the values
Now we substitute the given ratio of amplitudes into the equation:
\[ \frac{I_1}{I_2} = \left(\frac{9}{10}\right)^2 \]

### Step 5: Calculate the square of the ratio
Calculating the square of the fraction:
\[ \frac{I_1}{I_2} = \frac{9^2}{10^2} = \frac{81}{100} \]

### Step 6: Conclusion
Thus, the ratio of the intensities of the two waves is:
\[ \frac{I_1}{I_2} = \frac{81}{100} \]

### Final Answer:
The ratio of intensity is 81:100.

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