Question

A stationary wave is represented by the equation, $y=3\cos \left(x/8\right)\sin \left(15t\right)$ where $x$ and $y$ are in $cm$ and $t$ is in $seconds$. The distance between the consecutive nodes is (in $cm$):

• A. $8$
• B. $12$
• C. $14$
• D. $16$

Answer 1

The correct option is B $12$

Distance between two consecutive nodes=$\frac{\lambda }{4}$

$\frac{\lambda }{4}=\frac{2\pi }{K}\times \frac{1}{4}$

From, $y=3\cos \left(\frac{x}{8}\right)\sin \left(15t\right)K=\frac{1}{8}\therefore \frac{\lambda }{4}=\frac{2\pi }{K}\times \frac{1}{4}=\frac{2\pi \times 8}{4}=4\pi$

Hence distance between the consecutive nodes is $4\pi$cm