Question 55: Waves

Question

The displacement equations of two interfering waves are given by
$y_{1}=10 \sin \left(\omega t+\frac{\pi}{3}\right) \mathrm{cm}, y_{2}=5[\sin \omega t+\sqrt{3} \cos \omega t] \mathrm{cm}$ respectively.
The amplitude of the resultant wave is _______ $\mathrm{cm}$.

Accepted Answer

Given, $y_{1}=10 \sin \left(\omega t+\frac{\pi}{3}ight) \mathrm{cm}$ and
$y_{2}=5(\sin \omega t+\sqrt{3} \cos \omega t)$
$$
=10 \sin \left(\omega t+\frac{\pi}{3}ight)
$$
Thus the phase difference between the waves is 0 .
$$
	ext { so } A=A_{1}+A_{2}=20 \mathrm{~cm}
$$

Waves

The displacement equations of two interfering waves are given by y_{1}=10 \sin \left(\omega t+\frac{\pi}{3}\right) \mathrm{cm}, y_{2}=5[\sin \omega t+\sqrt{3} \cos \omega t] \mathrm{cm} respectively. The amplitude of the resultant wave is _______ \mathrm{cm}.

Integer / Numeric Answer Type