The equation of a wave on a string of linear mass density $0.02\ \text{kg m}^{-1}$ is $Y = 0.01\sin\left[2\pi\left(\dfrac{t}{0.02} - \dfrac{x}{0.50}\right)\right]$ m. The tension in the string is

A wire of length '$L$', diameter '$d$', density of material '$\rho$' is under tension '$T$' has fundamental frequency of vibration '$n_A$'. Another wire of length '$2L$', diameter '$3d$', density of material '$2\rho$' is vibrated under tension '$2T$', the fundamental frequency of vibration becomes '$n_B$'. The ratio $n_B : n_A$ is

The 'Loudness' and 'Pitch' of sound respectively are the human perception to

A tuning fork of frequency '$n$' is held near the open end of a tube which is dipped in water and length of the tube is adjusted until resonance occurs. If the two shortest lengths that produce resonance are $l_1$ and $l_2$, the speed of sound in air is (neglect end correction)