The frequency of the sound emitted by an organ pipe will increase if the air in it is replaced by
`(a)` hot air `(b)` moist air `(c )` hydrogen

Options

A. `a` is true
B. `a,b` are true
C. `b,c` are true
D. `a,b,c` are true

Answer

To solve the question regarding the frequency of sound emitted by an organ pipe when the air is replaced by hot air, moist air, or hydrogen, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship Between Frequency and Velocity**:
The frequency of sound (f) is related to the velocity of sound (v) and the wavelength (λ) by the formula:
\[ f = \frac{v}{\lambda} \]
This means that if the velocity of sound increases, the frequency will also increase, assuming the wavelength remains constant.

2. **Identify How Velocity of Sound Changes**:
The velocity of sound in a medium is influenced by the density of that medium. Generally, the velocity of sound is given by:
\[ v = \sqrt{\frac{B}{\rho}} \]
where \(B\) is the bulk modulus of the medium and \(\rho\) is the density of the medium.

3. **Compare Densities of the Mediums**:
- **Hot Air**: When air is heated, its density decreases. However, the speed of sound increases due to increased kinetic energy of the air molecules.
- **Moist Air**: Moist air has a lower density compared to dry air because water vapor is less dense than nitrogen and oxygen. This also increases the speed of sound.
- **Hydrogen**: Hydrogen is much less dense than air. The speed of sound in hydrogen is significantly higher than in air.

4. **Conclusion on Frequency**:
Since all three mediums (hot air, moist air, and hydrogen) either have a lower density or higher energy states compared to normal air, the velocity of sound in these mediums will be greater than in normal air. Therefore, when the air in the organ pipe is replaced with any of these three options, the frequency of the sound emitted will increase.

5. **Final Answer**:
Thus, the frequency of the sound emitted by the organ pipe will increase if the air in it is replaced by:
- (a) hot air
- (b) moist air
- (c) hydrogen