Ratio of amplitude for two wave is 5:11 .Find the ratio of intensity?

Answer

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

### Step 1: Understand the Relationship Between Amplitude and Intensity
We know that 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
From the problem, we have the ratio of the amplitudes of the two waves:
\[ \frac{A_1}{A_2} = \frac{5}{11} \]

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

### Step 4: Substitute the Given Ratio of Amplitudes
Now, we substitute the given ratio of amplitudes into the equation:
\[ \frac{I_1}{I_2} = \left(\frac{5}{11}\right)^2 \]

### Step 5: Calculate the Square of the Ratio
Calculating the square of the ratio:
\[ \frac{I_1}{I_2} = \frac{5^2}{11^2} = \frac{25}{121} \]

### Step 6: Final Result
Thus, the ratio of the intensities of the two waves is:
\[ \frac{I_1}{I_2} = \frac{25}{121} \]

### Summary
The ratio of intensity \( I_1 : I_2 \) is \( 25 : 121 \).

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