A cylindrical tube open at both the ends hs a fundamental frequency of 390 hz and air. If 1/4 th of the tube is immersed vertically in water the fundamental frequency of air column is

Options

A. 260 Hz
B. 130 Hz
C. 390 Hz
D. 520 Hz

Answer

A

Explanation

A cylindrical tube upon at both the ends, its fundamental frequency is
`u=v/(lamda)=v/(2L)=390 Hz` …………………………I
where v is the velocity of sound in air.

If a (1/4)^(th) of cylindrical tube is immersed in a water, it will become a closed pipe of length three -fourth that of an open pipe as shown in figure. (ii).
Therefore, its fundamental frequency is
`v'=v/(lamda')=v/(3L)`
`v'=v/(3L)=2/3v/(2L)=2/3 xx 390 Hz` (using (i))
`=360 Hz`