The speed of sound in air at NTP is 332 m/s. If air pressure becomes four times the normal then the speed of sound waves will :

Options

A. Double
B. Quadruple
C. Remain the same
D. become `(1)/(4)` of the original value

Explanation

To determine the effect of increased air pressure on the speed of sound, we can follow these steps:

### Step 1: Understand the relationship between speed of sound and pressure
The speed of sound in a gas is given by the formula:
\[ V = \sqrt{\frac{\gamma \cdot R \cdot T}{M}} \]
where:
- \( V \) is the speed of sound,
- \( \gamma \) is the adiabatic index (ratio of specific heats),
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature,
- \( M \) is the molar mass of the gas.

### Step 2: Analyze the variables
In this formula, we can observe that the speed of sound depends on the temperature \( T \) and the properties of the gas (represented by \( \gamma \) and \( M \)). Importantly, pressure does not appear directly in this formula.

### Step 3: Consider the effect of increased pressure
When the pressure of the air increases, while keeping the temperature constant, the density of the air also increases. However, the speed of sound in an ideal gas is not directly affected by pressure at constant temperature. This is because the increase in pressure is accompanied by an increase in density, which cancels out the effect on the speed of sound.

### Step 4: Conclusion
Since the speed of sound is not affected by the increase in pressure (as long as the temperature remains constant), we conclude that the speed of sound remains the same.

Thus, the speed of sound in air at NTP remains 332 m/s even if the air pressure becomes four times the normal.

### Final Answer:
The speed of sound waves will remain 332 m/s.

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