Question

Calculate the fundamental frequencies and the first 3 overtones of a pipe of length 1.7 m
and closed at one end.

Answer 1

Answer on Question #40593, Physics, Acoustics

Question:

Calculate the fundamental frequencies and the first 3 overtones of a pipe of length $1.7\mathrm{m}$ and closed at one end.

Answer:

The fundamental frequency is defined as the lowest frequency of a periodic waveform. For a tube of length L with one end closed and the other end open the wavelength of the fundamental harmonic is 4L.

Therefore,

$$f _ {0} = \frac {v}{4 L} = \frac {3 4 0}{4 \cdot 1 . 7} \frac {1}{s} = 5 0 H z$$

where $v$ is speed of sound.

For overtones wavelength equals:

$$\lambda_ {n} = \frac {4 L}{1 + 2 n}$$

where $n$ is number of overtones, therefore:

$$f _ {n} = \frac {v}{4 L} (1 + 2 n) = f _ {0} (1 + 2 n)$$ $$f _ {1} = 5 0 (1 + 2) = 1 5 0 H z$$ $$f _ {2} = 5 0 (1 + 4) = 2 5 0 H z$$ $$f _ {3} = 5 0 (1 + 6) = 3 5 0 H z$$