Ratio of amplitude for two wave is 7:10 .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
Intensity (I) of a wave is directly proportional to the square of its amplitude (A). This can be expressed mathematically as:
\[ I \propto A^2 \]
This means that if we have two waves with amplitudes \( A_1 \) and \( A_2 \), the ratio of their intensities can be written as:
\[ \frac{I_1}{I_2} = \left(\frac{A_1}{A_2}\right)^2 \]

### Step 2: Write down the given data
We are given the ratio of the amplitudes of the two waves:
\[ \frac{A_1}{A_2} = \frac{7}{10} \]

### Step 3: Substitute the ratio of amplitudes into the intensity ratio formula
Using the relationship we established in Step 1, we can substitute the given ratio of amplitudes into the formula for intensity:
\[ \frac{I_1}{I_2} = \left(\frac{A_1}{A_2}\right)^2 = \left(\frac{7}{10}\right)^2 \]

### Step 4: Calculate the square of the amplitude ratio
Now we calculate the square of the ratio:
\[ \left(\frac{7}{10}\right)^2 = \frac{7^2}{10^2} = \frac{49}{100} \]

### Step 5: Write the final answer
Thus, the ratio of the intensities \( I_1 \) to \( I_2 \) is:
\[ \frac{I_1}{I_2} = \frac{49}{100} \]

### Conclusion
The ratio of intensity for the two waves is \( 49:100 \).

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