Question

The vibrations of a string of length $60cm$ fixed at both ends are represented by the equation $y=4$ $\sin \left(\frac{\pi x}{15}\right)\cos \left(96\pi t\right)$ where $x$ and $y$ are in centimeters and ${}^{\prime }{t}^{\prime }$ is in seconds. The maximum displacement of a point at $x=5cm$ is

• A. $2\sqrt{3}cm$
• B. $2cm$
• C. $4\sqrt{3}cm$
• D. None of the above

Answer 1

The correct option is A $2\sqrt{3}cm$

$y=4\sin \left(\frac{\pi x}{15}\right)\cos \left(96\pi t\right)$

The maximum displacement will be when $\cos \left(96\pi t\right)=1$

$⟹y_{max}=4\sin \left(\frac{\pi x}{15}\right)$

$y_{max}$ at x=5cm

$=4\sin \left(\frac{\pi \times 5}{15}\right)$

$=4\times \sin \left(\frac{\pi }{3}\right)$

$=4\times \frac{\sqrt{3}}{2}=2\sqrt{3}cm$