Question

The pitch of an organ pipe vibrating in a certain mode for a given temperature is highest when the pipe is filled with

• A. Nitrogen
• B. Hydrogen
• C. Oxygen
• D. Fluorine

Answer 1

The correct option is B Hydrogen

We know that, Subjective quality of frequency is known as pitch.

So, we can say that,

$\text{Pitch}\propto \text{Frequency}...........\left(1\right)$

and

velocity of sound is given by $v=f\lambda$

For a given organ pipe vibrating in a certain mode, $\lambda =\text{constant}$.

$\Rightarrow f\propto v................\left(2\right)$

Also, from laplace's correction we know that , $v=\sqrt{\frac{\gamma RT}{M}}$

For the given diatomic gas at the given temperature,

$v\propto \sqrt{\frac{1}{M}}..............\left(3\right)$

From $\left(1\right)$, $\left(2\right)$ and $\left(3\right)$,

$\therefore$ Pitch $\propto$ $\sqrt{\frac{1}{M}}$

Here, hydrogen has the minimum molecular mass, thus, maximum pitch.

Hence, option (b) is the correct answer.

Note:- Pitch is directly related to frequency. Higher frequency waves will lead to higher pitch of the sound being heard.