Question

Two waves are represented by the equations
$y_1=asin(\omega t+kx+0.57)m$ and
$y_2=acos(\omega t+kx)m$,
Where $x$ is in meters and $t$ is in seconds. The phase difference between them is then

• A. $1.0$ radian
• B. $1.25$ radian
• C. $1.57$ radian
• D. $0.57$ radian

Answer 1

The correct option is A $1.0$ radian

$y_1=asin(\omega t+kx+0.57)$
$\therefore Phase,{\varphi }_1=(\omega t+kx+\frac{\pi }{2})$
$y_2=acos(\omega t+kx)=asin(\omega t+kx+\frac{\pi }{2})$
$\therefore Phase,{\varphi }_2=\omega t+kx+\frac{\pi }{2}$
Phase different, $△\varphi ={\varphi }_2-{\varphi }_1$
$=(\omega t+kx+\frac{\pi }{2})-(\omega t+kx+0.57)$
$=\frac{\pi }{2}-0.57=1.57-0.57=1$ radian