An air column in a pipe, which is closed at one end will be in resonance with a vibrating tuning fork of frequency 264 Hz for various lengths. Which one of the following lengths is not possible? (V = 330 m/s)

Beats are produced by waves $$\mathrm{y_1=a\sin2000\pi t}$$ and $$\mathrm{y_2=a\sin2008\pi t}$$. The number of beats heard per second is

The frequencies of three tuning forks $$\mathrm{A}, \mathrm{B}$$ and $$\mathrm{C}$$ are related as $$\mathrm{n}_{\mathrm{A}}>\mathrm{n}_{\mathrm{B}}>\mathrm{n}_{\mathrm{C}}$$. When the forks $$\mathrm{A}$$ and $$\mathrm{B}$$ are sounded together, the number of beats produced per second is '$$n_1$$'. When forks $$\mathrm{A}$$ and $$\mathrm{C}$$ are sounded together the number of beats produced per second is '$$n_2$$'. How may beats are produced per second when forks $$\mathrm{B}$$ and $$\mathrm{C}$$ are sounded together?

The equation of wave is given by $$\mathrm{y}=10 \sin \left(\frac{2 \pi \mathrm{t}}{30}+\alpha\right)$$. If the displacement is $$5 \mathrm{~cm}$$ at $$\mathrm{t}=0$$, then the total phase at $$\mathrm{t}=7.5 \mathrm{~s}$$ will be

$$\left[\sin 30^{\circ}=\cos 60^{\circ}=\frac{1}{2}, \cos 30^{\circ}=\sin 60^{\circ}=\frac{\sqrt{3}}{2}\right] $$