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Find the Greatest Length of an Organ Pipe Open at Both Ends that Will Have Its Fundamental Frequency in the Normal Hearing Range - Physics

Sum

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 = 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.

Concept: Speed of Wave Motion
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APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 16 Sound Waves
Q 44 | Page 355
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