A point performs simple harmonic oscillation of period T and the equation of motion is given by x = a sin($$\omega $$t + $$\pi $$/6). After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity?

A transverse wave propagating along x-axis is represented by y(x, t) = 8.0 sin (0.5 $$\pi $$x $$-$$ 4$$\pi $$t $$-$$ $$\pi $$/4) where x is in metres and t is in seconds. The speed of the wave is

Two vibrating tuning forks produce waves given by y₁ = 4 sin 500$$\pi $$t and y₂ = 2 sin506 $$\pi $$t. Number of beats produced per minute is

Two sound waves with wavelengths 5.0 m and 5.5. m respectively, each propagate in a gas with velocity 330 m/s. We expect the following number of beats per second.