Question

Vibrations of rope tied by two rigid ends shown by equation $y=cos2\pi tsin2\pi x$, then minimum length of the rope will be

• A. $1m$
• B. $\frac{1}{2}m$
• C. $5m$
• D. $2\pi m$

Answer 1

Answer: (B)

$\frac{1}{2}m$

The wave-vector $k$ of a standing wave is related to the wavelength as $\lambda =\frac{2\pi }{k}$.

Now from the equation of wave $k=2\pi m^{-1}$, which means $\lambda =1m$.

The length of the rope is related to the wavelength of a standing wave as: $L=n\frac{\lambda }{2}$.

The minimum length will be for the fundamental mode where $n=1$.

Minimum length, $L_{min}=\frac{1}{2}m$ .