The speed of sound in air is independent from its

Options

A. Amplitude
B. frequency
C. Phase
D. All of these

Answer

To solve the question regarding the speed of sound in air and its independence from certain factors, we can follow these steps:

### Step 1: Understand the Formula for Speed of Sound
The speed of sound in a medium can be expressed using the formula:
\[ v = \sqrt{\frac{\gamma P}{\rho}} \]
or alternatively,
\[ v = \sqrt{\frac{\gamma RT}{M}} \]
where:
- \( v \) = speed of sound
- \( \gamma \) = adiabatic index (depends on the medium)
- \( P \) = pressure
- \( \rho \) = density of the medium
- \( R \) = universal gas constant
- \( T \) = absolute temperature
- \( M \) = molar mass of the gas

### Step 2: Identify Dependencies
From the formula, we can identify that the speed of sound depends on:
- Temperature (\( T \))
- Properties of the medium (such as \( \gamma \), \( \rho \), and \( M \))

### Step 3: Analyze the Given Options
The question asks about the independence of the speed of sound from:
1. Amplitude
2. Frequency
3. Phase

### Step 4: Evaluate Each Option
- **Amplitude**: The amplitude of a sound wave relates to its loudness but does not affect the speed of sound. Therefore, speed is independent of amplitude.
- **Frequency**: The frequency of a sound wave affects its pitch but does not influence the speed of sound. Thus, speed is independent of frequency.
- **Phase**: The phase of a wave refers to its position in time relative to a reference point and does not affect the speed of sound. Hence, speed is independent of phase.

### Step 5: Conclusion
Since the speed of sound in air is independent of amplitude, frequency, and phase, we conclude that it is independent of all three factors.

### Final Answer
The speed of sound in air is independent of:
- Amplitude
- Frequency
- Phase