Question

I did a glass bottle lab where I have to fill the right amounts of water to play certain notes. To find frequency, I used f = n (v/4L) where 340 is the constant velocity.

My lengths are 17.3 cm, 15.5 cm, and 20.3 cm.

I know n is nodes, but I don’t know what numbers to use for it. Please help. Also, this is a open closed system, so n was said to deal with odd numbers.

Thanks in advance.

Answer 1

Since, the distance between any node and an antinode is always

In a open closed system or one end closed system, the closed end has a node while the open end has an antinode.

The following diagram could help in understanding the harmonics in one end closed system.

For fundamental frequency of one end closed system, one could say that the length of pipe should be:

where,  

(for first harmonic)

Now, for first harmonic, the length becomes:

using above relations, the first harmonic becomes:

For second harmonic, the length will be:

thus, the second harmonic will be:

Thus, the general condition for harmonics in one end closed system is:         (n = 1,3,5.....) odd no(s)

Now, in the question, the given data are: v=340 m/s, L₁=0.173 m, L₂=0.155 m and L₃=0.203 m

• for L₁=0.173 m, the harmonics are:

, and

similarly other harmonics could be found.

• for L₂=0.155 m, the harmonics are:

and

similarly for other harmonics.

for L₂=0.203 m, the harmonics are:

and

similarly for other harmonics.

One can see that with decreasing the length of the pipe, the harmonic frequency increases.