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

length of a string tied to two rigid supports is $$40$$ $$cm$$. Maximum length (wavelength in $$cm$$) of a stationary wave produced on it is

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