Question

Find the greatest length of an organ pipe open at both ends that will have its fundamental frequency in the normal hearing range (20 − 20,000 Hz). Speed of sound in air = 340 m s⁻¹.

Answer 1

Given:
Speed of sound in air v = 340 ms⁻¹
We are considering a minimum fundamental frequency of f = 20 Hz,
since, for maximum wavelength, the frequency is a minimum.
Length of organ pipe l = ?
We have:
$$\begin{gathered} \frac{\mathrm{\lambda }}{2}=I \\ \Rightarrow \mathrm{\lambda }=2I \end{gathered}$$

We know that:
v = fλ
$$\begin{gathered} \Rightarrow \lambda =\frac{v}{f} \\ \Rightarrow l=\frac{v}{2\times f} \end{gathered}$$

On substituting the respective values in the above equation, we get:

$$\begin{gathered} I=\frac{340}{2\times 20} \\ \Rightarrow l=\frac{34}{4}=8.5\mathrm{m} \end{gathered}$$
Length of the organ pipe is 8.5 m.