Question

Which is(are) the factor(s) on which the frequency of sound emitted due to vibration in an air column depends?

• A. Length of air column
• B. Diameter of air column
• C. Both A and B
• D. None of these

Answer 1

Answer: (C)

Both A and B

In a closed air column, the frequency of mth mode of vibration is given by:

$f_m=\frac{v(2m-1)}{4l}$ m=1,2,3......,

In a open air column, the frequency of mth mode of vibration is given by:

$f_m=\frac{vm}{2l}$ m=1,2,3......

We can see that frequency depends upon the length of air column $l$ .

Rayleigh stated that in an air column the antinodes are not formed exactly at the open end, but slightly outside. The distance of the antinode from the antinode is called end correction (e), therefore the length of the air column will change due to end correction hence frequency, this end correction depends upon the radius, r (or diameter) of air column and is equal to $0.6r$.

Therefore frequency of vibration depends upon on both length and diameter of air column .