Question

Two sound waves are represented by $y_1=\frac{1}{2}\sin \omega t+\frac{\sqrt{3}}{2}\cos \omega t$
and $y_2=\frac{\sqrt{3}}{2}\sin \omega t+\frac{1}{2}\cos \omega t$ .
The initial phase difference between the two waves is

• A. ${30}^o$
• B. ${60}^o$
• C. ${45}^o$
• D. $0^o$

Answer 1

Answer: (A)

${30}^o$

$y_1=\cos {60}^{o}sin\omega t+\sin {60}^{o}cos\omega t$
$y_1=\sin (\omega t+60)$
$y_2=\cos {30}^o\sin \omega t+\sin {30}^o\cos \omega t$
$y_2=\sin (\omega t+30)$
$\varphi ={\varphi }_1-{\varphi }_2$
$=60-{30}^o$
$={30}^o$