Question

Two waves in the same medium are represented by y-t curves in the figure shown. Find the ratio of their average intensities?

• A. $\frac{25}{16}$
• B. $\frac{23}{16}$
• C. $\frac{21}{16}$
• D. $\frac{27}{16}$

Answer 1

The correct option is A

$\frac{25}{16}$

Step 1: Given

Amplitude of first wave, $A_1=\text{5 unit}$

Amplitude of second wave, $A_2=\text{2 unit}$

Step 2: Calculating intensity

$I\propto A^2{f}^2$

Here, average intensity is $I$, amplitude is $A$, and frequency is $f$.

Average intensity Formula for First wave from above equation.

$I_1\propto A_1^2{f}_1^2$

Here, Intensity of first wave is $I_1$, frequency of first wave is $f_1$.

Average intensity formula for second wave from the above equation.

$I_2\propto A_2^2{f}_2^2$

Here, intensity of second wave is $I_2$, and frequency of second wave is $f_2$.

Step 3: Calculate ratio

From the figure given.

$f_1=\frac{f_2}{2}$

Divide $I_1$ to $I_2$.

$$\begin{gathered} \frac{I_1}{I_2}=\frac{A_1^2{f}_1^2}{A_2^2{f}_2^2} \\ =\frac{{\left(\text{5 unit}\right)}^2{\left({\displaystyle \raisebox{1ex}{$f_2$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right)}^2}{{\left(2\text{unit}\right)}^2{f}_2^2} \\ =\frac{25}{4\times 4} \\ =\frac{25}{16} \end{gathered}$$

Hence, the Option (A) is correct.