Question

Equation of a stationary wave is given by $y=5\cos \left(\frac{\pi x}{25}\right)\sin \left(100\pi t\right)$. Here, $x$ is in $\text{centimeter}$ and $t$ in $\text{seconds}$. Node will not occur at distance

• A. $25\text{cm}$
• B. $62.5\text{cm}$
• C. $12.5\text{cm}$
• D. $37.5\text{cm}$

Answer 1

The correct option is A $25\text{cm}$

For the stationary wave represented by, $y=5\cos \left(\frac{\pi x}{25}\right)\sin \left(100\pi t\right)$
Considering a snapshot of string at some given instant of time.
Nodes will be formed where displacement of particle is zero.
It will happen when,
$\cos \left(\frac{\pi x}{25}\right)=0$
$\Rightarrow \frac{\pi x}{25}=\frac{\pi }{2},\frac{3\pi }{2},\frac{5\pi }{2},......$
$\Rightarrow x=12.5,37.5,62.5,....$.
$\therefore$ Node will not form at $x=25\text{cm}$