Statement - 1: Two longitudinal waves given by equations: y1 (x, t) = 2a sin (ω t - kx) and y2 (x, t) = a sin (2ω t - 2kx) will have equal intensity. Statement - 2: Intensity of waves of given frequency in same medium is proportional to square of amplitude only.

Question

Statement - 1: Two longitudinal waves given by equations: y1 (x, t) = 2a sin (ω t - kx) and y2 (x, t) = a sin (2ω 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 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.

Tardigrade Admin · Accepted Answer

Since, I propto A2 ω2 I1 propto (2a)2 ω2 I2 propto a2 (2ω)2 I1 = I2 Intensity depends on frequency also.

Q. Statement - 1 :
Two longitudinal waves given by equations : $y_{1} (x, t) = 2 a$ sin ( $ω t - k x$ ) and $y_{2} (x, t)$ = a sin ( $2 ω t - 2 k x$ ) will have equal intensity.
Statement - 2 :
Intensity of waves of given frequency in same medium is proportional to square of amplitude only.

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

Statement-1 is true, statement-2 is true, statement-2 is the correct explanation of statment-1

Statement-1 is true, statement-2 is true, statement-2 is not the correct explanation of statement-1

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

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

Q. Statement - 1 : Two longitudinal waves given by equations : y1​(x,t)=2a sin (ωt−kx) and y2​(x,t) = a sin (2ωt−2kx) will have equal intensity. Statement - 2 : Intensity of waves of given frequency in same medium is proportional to square of amplitude only.