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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.
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Solution
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 :
\[\frac{\lambda}{2} = I\]
\[ \Rightarrow \lambda = 2I\]
We know that :
v = fλ
\[\Rightarrow \lambda = \frac{v}{f}\]
\[ \Rightarrow l = \frac{v}{2 \times f}\]
On substituting the respective values in the above equation, we get :
\[ I = \frac{340}{2 \times 20}\]
\[ \Rightarrow l = \frac{34}{4} = 8 . 5 \text { m }\]
Length of the organ pipe is 8.5 m.
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