1. Tardigrade
  2. Question
  3. Physics
  4. 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.

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Q. 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.

AIEEEAIEEE 2011Waves

Solution:

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.