Question

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

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

Answer 1

Answer: (A)

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

Answer 2

Since, $I \propto A^{2} \omega^{2}$ $I_{1} \propto \left(2a\right)^{2} \omega^{2}$ $I_{2} \propto a^{2} \left(2\omega\right)^{2}$ $I_{1} = I_{2}$ Intensity depends on frequency also.