Question 350: Waves

Question

Two simple harmonic progressive waves have displacements $\rightarrow \mathrm{y}_1=\mathrm{a}_1 \sin \left(\frac{2 \pi \mathrm{x}}{\lambda}-\omega \mathrm{t}\right)$ and $\mathrm{y}_2=\mathrm{a}_2 \cos \left(\frac{2 \pi \mathrm{x}}{\lambda}-\omega \mathrm{t}+\phi\right)$
What is the phase difference between two waves?

Accepted Answer

$$\begin{aligned}
y_1 & =a_1 \sin \left(\frac{2 \pi x}{\lambda}-\omega tight) \quad	ext{.... (i)}\
y_2 & =a_2 \cos \left(\frac{2 \pi x}{\lambda}-\omega t+\phiight) \
& =a_2 \sin \left(\frac{2 \pi x}{\lambda}-\omega t+\phi+\frac{\pi}{2}ight)\quad	ext{.... (ii)}
\end{aligned}$$
From (ii) and (i)
$	herefore \quad$ Phase difference $=\phi+\frac{\pi}{2}$

Answer

$\left(\phi+\frac{\pi}{2}\right)$

Answer

$\phi$

Answer

$\left(\phi-\frac{\pi}{2}\right)$

Answer

$(\phi+\pi)$

Waves

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