The displacement $$y$$ of a wave travelling in the $$x$$-direction is given by $$$y = {10^{ - 4}}\,\sin \left( {600t - 2x + {\pi \over 3}} \right)\,\,metres$$$
where $$x$$ is expressed in metres and $$t$$ in seconds. The speed of the wave - motion, in $$m{s^{ - 1}}$$, is

A tuning fork of known frequency $$256$$ $$Hz$$ makes $$5$$ beats per second with the vibrating string of a piano. The beat frequency decreases to $$2$$ beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

A tuning fork arrangement (pair) produces $$4$$ beats/sec with one fork of frequency $$288$$ $$cps.$$ A little wax is placed on the unknown fork and it then produces $$2$$ beats/sec. The frequency of the unknown fork is

Tube $$A$$ has bolt ends open while tube $$B$$ has one end closed, otherwise they are identical. The ratio of fundamental frequency of tube $$A$$ and $$B$$ is