Question

The vibrations of a string fixed at both ends are described by the equation $y=\left(5.00mm\right)$ $\sin \left[\right(1.57c{m}^{-1}\left)x\right]\sin \left[\right(314s^{-1}\left)t\right]$. If the length of a string is $10.0cm$, locate the nodes. How many loops are formed in the vibration?

• A. a)$2n$b)$5$
• B. a)$3n$b)$5$
• C. a)$3n$b)$6$
• D. a)$n$b)$6$

Answer 1

The correct option is A a)$2n$

b)$5$

The nodes occur where the amplitude is zero, i.e,,

$\sin \left(1.57c{m}^{-1}\right)x=0$

$\left(\frac{\pi }{2}c{m}^{-1}\right)x=n\pi$,

where n is integer

Thus, $x=2n$ cm

The nodes, occur at $x=0cm$, $2cm$, $4cm$, $8cm$, $10cm$, antinodes occur in between them i.e., at $x=1cm$, $3cm$, $5cm$, $7cm$ and $9cm$. Hence it is clear that string vibrated in five loops.