The equation of stationary wave on a string clamped at both ends and vibrating in third harmonic is $Y=0.5…
The equation of stationary wave on a string clamped at both ends and vibrating in third harmonic is $Y=0.5 \sin (0.314 x) \cos (600 \pi t)$ where $x$ and $y$ are in $\mathrm{cm}, t$ in second. The length of the vibrating string is
$20 \mathrm{~cm}$
$10 \mathrm{~cm}$
$40 \mathrm{~cm}$
$30 \mathrm{~cm}$
Solution
The standard equation of a standing wave is
$y=2 A \sin (k x) \cos (\omega t)$
On comparing with standard equation,
$\omega=600 \pi \mathrm{s}^{-1}$ and $k=\frac{\pi}{10}$
The wavelength of the wave can be obtained by using the wave number: $k=\frac{2 \pi}{\lambda}=\frac{\pi}{10}$
The wavelength is $\lambda=20 \mathrm{~cm}$
Frequency of the third harmonics is three times the fundamental.
Therefore, length of the string is: $L=3\left(\frac{\lambda}{2}\right)=3(10)=30 \mathrm{~cm}$