Question

A group of students were tasked with collecting information about standing waves. This table is a series of their data, showing the length of an air column and a resonant frequency present when the column is struck.

Length (m)	Resonant Frequency (Hz)
1	83.25
2	41.5
3	27.5
4	21

(a)

From their data, determine whether the air column was open on each end or closed on one end.

A.open on each end

B.closed on one end    

(b)

Predict the resonant frequency (in Hz) of the column at a length of 3.5 meters.

Answer 1

Hey there!

The formula for the sound frequency for which are produced in a tube open at both ends can be given with the formula

Here the velocity of sound will be a fixed constant. While applying the values above you will notice that the values satisfy the above condition as well. The values are found to be just inversely proportional to the L values given.

In that sense, to find the frequency for L=3.5m, we could just give the divide the frequency for L=1 by 3.5 , hence that is

84.5 / 3.5 = 24.14 Hz

I hope the solution helps... Feel free to comment and discuss further... Cheers :)