Question

Two wave are represented by equation$y_1=a\sin \omega tand{y}_2=a\cos \omega t$.the first wave:

• A. leads the second by $\pi$
• B. lags the second by $\pi$
• C. leads the second by $\frac{\pi }{2}$
• D. lags the second by $\frac{\pi }{2}$

Answer 1

The correct option is D lags the second by $\frac{\pi }{2}$

$$\begin{array}{c}Here,\\ \cos A=\sin \left(a+\frac{\pi }{2}\right)\\ \Rightarrow y_2=a\cos \omega t=a\sin (\omega t+\frac{\pi }{2})\\ \Rightarrow y_1=a\sin \omega t\\ thus,\\ y_{1}lags{y}_{2}by\frac{\pi }{2}\\ or,lagsthesecondby\frac{\pi }{2}\\ andthecorrectoptionisD.\end{array}$$