Question

Statement-1:
Two longitudinal waves given by equations; $y_1$(x,t) = 2a $\sin (\omega t-kx)$ and $y_2(x,t)$ = a $\sin (2\omega t-2kx)$ will have equal intensity.

Statement-2:

Intensity of waves of given frequency in same medium is proportional to square of amplitude only.

• A. Statement-1 is true, statement -2 is true; statement-2 is not correct explanation of statement -1.
• B. Statement-1 is false, statement -2 is true.
• C. Statement-1 is true, statement -2 is false.
• D. Statement -1 is true, statement-2 true; statement-2 is the correct explanation of statement-1.

Answer 1

Answer: (C)

Statement-1 is true, statement -2 is false.

$\text{Solution}:$

$y_1(x,t)=2asin(wt-kx)$

$y_2(x,t)=asin(2wt-2kx)$

$I=2{\pi }^2{n}^2{a}^2\rho v$

$⟹\frac{I_1}{I_2}=(\frac{2a}{a}\times \frac{n}{2n}{)}^2=\frac{1}{1}$

Intensity depends on frequency and amplitude

$\text{Hence C is the correct option}$