The diagram below shows the fundamental standing wave pattern in an air column that is closed at one end and open at the other.
- On the same diagram, draw the shape of the first overtone (which corresponds to the third harmonic) standing wave pattern. (2 marks)
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- State the frequencies of the fundamental and the first overtone (third harmonic) resonance modes for this air column. (2 mark)
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a.
b. The fundamental frequency is 425 Hz.
The frequency of the first overtone is 1275 Hz.
Show Worked Solution
a.
b. For the fundamental frequency \((f_1)\), \(\dfrac{\lambda_1}{4} = 0.2\ \text{m}\ \Rightarrow\ \lambda_1 = 0.8\ \text{m}\)
\(f_1 = \dfrac{v}{\lambda_1} = \dfrac{340}{0.8} = 425\ \text{Hz}\).
For the frequency of the first overtone \((f_2)\):
\(f_2 = 3 \times f_1 = 3 \times 425 = 1275\ \text{Hz}\).
