Question

The vibrations of a string of length $60\, cm$ fixed at both the ends are represented by the equation $y=2 sin \left(\frac{4\pi x}{15}\right) cos \left(96\pi t\right)$ where $x$ and $y$ are in cm. The maximum number of loops that can be formed in it is

• A. $6$
• B. $16$
• C. $5$
• D. $15$

Answer 1

Answer: (B)

$16$

Answer 2

Given, $y=2 \sin \left(\frac{4 \pi x}{15}\right) \cos\, (96 \pi t)$ and $l=60\, cm$ We know that $f=\frac{P}{2l} \times v$ where, P= number of loops $\frac{96 \pi}{2 \pi}=\frac{P}{2 \times 60} \times \frac{\omega}{K}$ $\frac{96 \pi}{2 \pi}=\frac{P}{2 \times 60} \times \frac{96 \pi}{\frac{4 \pi}{15}}$ $\Rightarrow \,P=16$