Question

3. a) In an experiment with sound waves in a tube, one group of students found resonant frequencies at 540 Hz, 720 Hz, and 900 Hz. What is likely the fundamental frequency of this series? List at least one other resonant frequency they should be able to find.

b) Another group of students is also experimenting with sound waves in the same length tube and finds resonance at 270 Hz, 450 Hz, and 630 Hz. One student in the group says that the fundamental frequency is 180 Hz but another argues that it is only 90 Hz. Who is right? explain how you know

c) What is the difference between these two groups experimental setup? That is why are the frequencies they are finding not the same given that they are using tubes that are the same length?

Answer 1

a) highest common factor of 540, 720, 900 is 180

Therefore fundamental frequency = f₀ = 180 Hz

540 = 3f₀

720 = 4f₀

900 = 5f₀

Next frequency will be

6f₀ = 1080 Hz

They will find frequencies that are multiple of 180.

Since all harmonics are present , therefore it is an open tube at both ends.

b) highest common factor of 270, 450, 630 is 90.

Therefore fundamental frequency = f₀ = 90 Hz

270 = 3f₀

450 = 5f₀

630 = 7f₀

Therefore next frequency will be

9f₀ = 810 Hz

They will find frequencies that are odd multiple of f₀

Since only odd harmonics (multiples of f₀) is present therefore it is a tube closed at one end.

c) in first case, tube is open at both ends.

In second case tube is closed at one end.