The equation of simple harmonic wave is given as $\mathrm{y}=5 \sin \frac{\pi}{2}(100…
The equation of simple harmonic wave is given as $\mathrm{y}=5 \sin \frac{\pi}{2}(100 \mathrm{t}-\mathrm{x})$, where ' $\mathrm{x}$ '
and ' $\mathrm{y}$ ' are in metre and time in second. The period of the wave is
$0 \cdot 02 \mathrm{~s}$
$0.06 \mathrm{~s}$
$25 \mathrm{~s}$
$0 \cdot 04 \mathrm{~s}$
Solution
The equation of simple harmonic wave is given as \(y=5 \sin \frac{\pi}{2}(100 t-x)\), where ' \(x\) ' and ' \(y\) ' are in metre and time in second. The period of the wave is \(0.0 4\).
Explanation:
\(\begin{aligned}
& y=5 \sin \frac{\pi}{2}(100 t-x)=5 \sin \left(50 \pi t-\frac{x \pi}{2}\right) \\
& \therefore \omega=50 \pi \text { or } \frac{2 \pi}{T}=50 \pi \\
& \therefore T=\frac{1}{25}=0.04 \mathrm{~s}
\end{aligned}\)