A particle is performing S.H.M. about $x = 0$, with an amplitude $a$ and time period $T$. The speed of the particle at $x = \dfrac{a}{3}$ will be

Two sound waves each of wavelength $\lambda$ and same amplitude $A$ interfere at point $Q$. If the path difference is $\dfrac{\lambda}{4}$, the amplitude of the resultant wave at point $Q$ is $\left[\sin\dfrac{\pi}{2} = 1, \cos\dfrac{\pi}{2} = 0\right]$

Two monoatomic ideal gases '1' and '2' of molecular masses $m_1$ and $m_2$ respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas '1' to that in gas '2' is

Two waves are represented as
$y_1 = a_1\sin\left(\omega t - \dfrac{2\pi x}{\lambda}\right)$ and
$y_2 = a_2\cos\left(\omega t - \dfrac{2\pi x}{\lambda} + \dfrac{\pi}{6}\right)$
The path difference between two waves is