Of the following properties of a wave, the one that is independent of the others is it

Options

A. Wave number
B. Wave length
C. Frequency
D. Amplitude

Answer

To solve the question regarding which property of a wave is independent of the others, we can analyze each property step by step:

### Step 1: Identify the Properties of Waves
The properties of waves mentioned in the question are:
1. Wave number (denoted as \( \tilde{\nu} \))
2. Wavelength (denoted as \( \lambda \))
3. Frequency (denoted as \( \nu \))
4. Amplitude

### Step 2: Analyze the Relationships
- **Wave Number**: The wave number \( \tilde{\nu} \) is defined as the inverse of the wavelength:
\[ \tilde{\nu} = \frac{1}{\lambda} \]
This shows that wave number is directly related to wavelength.

- **Wavelength**: Wavelength \( \lambda \) is the distance between successive crests of a wave. It is directly related to wave number and frequency.

- **Frequency**: Frequency \( \nu \) is related to wavelength by the equation:
\[ \nu = \frac{c}{\lambda} \]
where \( c \) is the speed of light. Frequency can also be expressed in terms of wave number:
\[ \nu = c \cdot \tilde{\nu} \]
This indicates that frequency is related to both wavelength and wave number.

- **Amplitude**: Amplitude is the maximum extent of a wave's oscillation from its rest position. It is a measure of the wave's energy but does not depend on wavelength, frequency, or wave number.

### Step 3: Conclusion
From the analysis, we can see that wave number, wavelength, and frequency are all interrelated. However, amplitude stands alone and does not depend on the other properties.

Thus, the property of a wave that is independent of the others is **amplitude**.

### Final Answer
The correct answer is **Amplitude** (Option 4).

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