Question

Statement I- Two longitudinal waves given by equations $y_1(x,t)=2\text{a}\sin (\omega t-kx)$ and $y_2(x,t)=\text{a}\sin (2\omega t-2kx)$ will have equal intensity.
Statement II- Intensity of waves of given frequency in same medium is proportional to square of amplitude only.

• A. Statement I is true, statement II true; statement II is the correct explanation of statement I
• B. Statement I is true, statement II is true; statement II is not correct explanation of statement I
• C. Statement I is ture, statement II is false
• D. Statement I is false, statement II is true

Answer 1

The correct option is B Statement I is true, statement II is true; statement II is not correct explanation of statement I

Statement I is true, Statement II is true; Statement II is not correct, explanation of Statement I
Explanation:
As Intensity , $I=\frac{1}{2}\rho {\omega }^2{A}^{2}v$
Here,
$\rho$ = density of medium,
$A$ = amplitude,
$\omega$ = angular frequency
$v$ = velocity of wave.
$\therefore$ Intensity depend upon amplitude, frequency as well as velocity of wave.
For given waves $I_2=\frac{1}{2}\rho (2\omega {)}^2{A}^{2}v$
$I_1=\frac{1}{2}\rho \left(\omega {)}^2\right(2A{)}^{2}v$
Also $I_1=I_2$