A whistle producing sound waves of frequencies $$9500$$ $$Hz$$ and above is approaching a stationary person with speed $$v$$ $$m{s^{ - 1}}.$$ The velocity of sound in air is $$300\,m{s^{ - 1}}.$$ If the person can hear frequencies upto a maximum of $$10,000$$ $$HZ,$$ the maximum value of $$v$$ upto which he can hear whistle is

A string is stretched between fixed points separated by $$75.0$$ $$cm.$$ It is observed to have resonant frequencies of $$420$$ $$Hz$$ and $$315$$ $$Hz$$. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is

When two tuning forks (fork $$1$$ and fork $$2$$) are sounded simultaneously, $$4$$ beats per second are heated. Now, some tape is attached on the prong of the fork $$2.$$ When the tuning forks are sounded again, $$6$$ beats per second are heard. If the frequency of fork $$1$$ is $$200$$ $$Hz$$, then what was the original frequency of fork $$2$$ ?

An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency ?