Two transverse sinusoidal waves travel in opposite directions along a string. The speed of transverse waves…
Two transverse sinusoidal waves travel in opposite directions along a string. The speed of transverse waves in the string is $0.5 \text{ cm s}^{-1}$. Each has an amplitude of $3.0 \text{ cm}$ and wavelength of $6.0 \text{ cm}$. The equation for the resultant wave is
$y = 6 \sin \frac{\pi t}{6} \cos \frac{\pi x}{3}$
$y = 6 \sin \frac{\pi x}{3} \cos \frac{\pi t}{6}$
Both may be correct
Both are wrong
Solution
Standing wave will be formed by the superposition of two waves.
$k = \frac{2\pi}{\lambda} = \frac{2\pi}{6} = \frac{\pi}{3}\text{ cm}^{-1} \implies \omega = vk = 0.5 \times \frac{\pi}{3} = \frac{\pi}{6}\text{ s}^{-1}$
$A_{\text{max}} = 2A = 6\text{ cm}$