5 beats / econd are heard when a tuning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either 0.95 m or 1 m. The frequency of the fork will be :

A tuning fork vibrates with frequency $$256$$ $$Hz$$ and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe ? (Speed of sound in air is $$340\,m{s^{ - 1}}$$)

In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r₁ and r₂ . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be 5×10⁻⁴ s, the difference in radii, $$\left| {} \right.$$r₁ $$-$$ r₂ $$\left| {} \right.$$ is best given by :

A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by

y(x, t) = 0.5 sin $$\left( {{{5\pi } \over 4}x} \right)\,$$ cos(200 $$\pi $$t).

What is the speed of the travelling wave moving in the positive x direction ?

(x and t are in meter and second, respectively.)