Question

The equation of a simple harmonic wave is given by $y=5\sin \frac{\mathrm{\pi }}{2}(100t-x)$ where $x$ and $y$ are in $metre$ and time is in $second$. The period of the wave in $second$ will be?

Answer 1

Step 1: Given:

Simple harmonic wave equation $y=5\sin \frac{\mathrm{\pi }}{2}(100t-x)$

Step 2: Formula used:

Standard wave equation; $y=A\sin (\omega t-kx)$, ($A$is the amplitude of the wave, $k$ is the wave number, $\omega$ is the angular frequency)

$\omega =\frac{2\pi }{T}$ ($\omega$ is the angular frequency of the wave, $T$ is the time period of the wave)

Step 3: Find the period of the wave:

Comparing the given equation and the standard wave equation, we get

$$\begin{gathered} \omega =50\pi \\ \Rightarrow \frac{2\pi }{T}=50\pi \\ \Rightarrow T=0.04second \end{gathered}$$

Thus, The period of the wave will be $0.04second$.