Question

IIT JEE QUESTION PHYSICS

27. A closed organ pipe produces standing waves in third harmonic mode. If L is the length of the pipe and V is the speed of sound in air, express
the frequency v of this harmonic in terms of V and L.

Keeping the mode of standing wave same, would the frequency be
increased or decreased, if the length of the pipe is increased by half of
its original value ?​

Answer 1

Answer:

For a closed organ pipe resonating in third harmonic, we'll have 2 antinodes(AN) and 2 nodes(N). AN-N-AN-N (displacement picture). Distance between AN-N = λ/4

In the third harmonic mode 3λ/4 = L

---> λ = 4L/3

Third harmonic f = v/λ = 3v/4L

From the above relation we know that frequency in inversely proportional to the Length of the pipe

If L' ---> 3L/2

Then frequency f' = 3v/4L' = 3v/4(3L/2) = v/2L

The frequency decreased from 3v/4L to v/2L