Question

The length of a sonometer wire is $90cm$ and the stationary wave setup in the wire is represented by an equation $y=6\sin \left(\pi \frac{x}{30}\right)\cos \left(250\pi t\right)$ where $x,y$ are in cm and $t$ is in second. The distances of successive antinodes from one end of the wire are

• A. $22.5cm,67.5cm$
• B. $15cm,30cm,60cm$
• C. $15cm,45cm,75cm$
• D. $30cm,45cm,60cm$

Answer 1

The correct option is C $15cm,45cm,75cm$

$l=90cm$
$y=6\sin \left(\frac{\pi x}{30}\right)\cos \left(250\pi t\right)$
So, $k=\frac{\pi }{30}$ $k=\frac{2\pi }{\lambda }$
So, $\lambda =\frac{2\pi }{k}$
$\lambda =\frac{2\pi }{\frac{\pi }{30}}=60cm$
So, antinodes will be formed at
$=\frac{\lambda }{4},\frac{3\lambda }{4},\frac{5\lambda }{4}$
$=\frac{60}{4},3\times \frac{60}{4},5\times \frac{60}{4}$
$=15,45,75cm$