A certain organ pipe resonates in its fundamental mode at a frequency of 500 Hz in air. What will be the fundamental frequency if the air is replaced by hydrogen at the same temperature? The density of air is `1.20kgm^-3` and that of hydrogen is `0.089 kgm^-3`.

Explanation

To determine the fundamental frequency of an organ pipe when the air is replaced by hydrogen, we can follow these steps:

### Step 1: Understand the relationship between frequency and speed of sound
The fundamental frequency (ν₀) of an organ pipe is related to the speed of sound (v) and the length of the pipe (L). For a closed organ pipe, the fundamental frequency is given by:
\[ \nu_0 = \frac{v}{4L} \]
For an open organ pipe, it is given by:
\[ \nu_0 = \frac{v}{2L} \]
In both cases, we can see that frequency is proportional to the speed of sound.
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