What will be the effect of temperature on speed of sound ?

Options

A. The speed of sound decreases with the increases of temperature of the medium.
B. The speed of sound decreases with the decrease of temperature of the medium.
C. The speed of sound increases with the decrease of temperature of the medium.
D. The speed of sound increases with the increase of temperature of the medium.

Explanation

To understand the effect of temperature on the speed of sound, we can break down the explanation into several steps:

### Step 1: Understanding Speed of Sound
The speed of sound is the rate at which sound waves travel through a medium. It is influenced by various factors, including temperature.

### Step 2: Relationship Between Temperature and Speed of Sound
The speed of sound in a medium is directly related to the temperature of that medium. As the temperature increases, the speed of sound also increases. Conversely, if the temperature decreases, the speed of sound decreases.

### Step 3: Explanation of the Relationship
This relationship can be explained by considering the kinetic theory of gases. As temperature increases, the molecules in the medium move faster. This increased molecular motion allows sound waves to propagate more quickly through the medium.

### Step 4: Mathematical Representation
The speed of sound (v) can be expressed mathematically as:
\[ v = \sqrt{\frac{\gamma RT}{M}} \]
Where:
- \( \gamma \) (gamma) is the ratio of specific heats (Cp/Cv),
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature in Kelvin,
- \( M \) is the molar mass of the gas.

From this equation, we can see that as the temperature (T) increases, the speed of sound (v) also increases, since it is under a square root.

### Step 5: Conclusion
In summary, the effect of temperature on the speed of sound is that an increase in temperature results in an increase in the speed of sound, while a decrease in temperature results in a decrease in the speed of sound.

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