Question

Calculate the ratio of intensity of wavetrain A to wavetrain B.

• A. $4$
• B. $1$
• C. $3$
• D. $0.5$

Answer 1

The correct option is B $1$

Intensity of a wave is, given by
$I=2{\pi }^2{f}^2{A}^2\rho V$
where, $f\to$ frequency of wave, $\rho \to$ density of medium
For a given medium, the velocity of wave is constant.
$\Rightarrow I\propto A^2{f}^2..........\left(i\right)$


From the wave train shown in figure,
Amplitude, $A_A=2$ and time period, $T_A=2$
Similarly for second wave train,
$A_B=1$ and $T_B=1$
$\Rightarrow$ From Eq. (i),
$\frac{I_A}{I_B}=\frac{A_A^2{f}_A^2}{A_B^2{f}_B^2}$
$\Rightarrow \frac{I_A}{I_B}={\left(\frac{A_A}{A_B}\right)}^2\times {\left(\frac{T_B}{T_A}\right)}^2$
$\therefore \frac{I_A}{I_B}=4\times {\left(\frac{1}{2}\right)}^2=1$