Estimation of frequency of a wave forming a standing wave represented by `y = A sin kx cos t` can be done if the speed and wavelength are known using `speed = "Frequency" xx "wavelength"` . Speed of motion depends on the medium properties namely tension in string and mass per unit length of string . A string may vibrate with different frequencies . The corresponding wavelength should be related to the length of the string by a whole number for a string fixed at both ends . Answer the following questions:
Speed of a wave in a string forming a stationary wave does not depend on

Options

A. Tension
B. Mass of wire for a given length
C. Length of the wire for a given mass
D. Harmonics of string

Explanation

To solve the question regarding the speed of a wave in a string forming a stationary wave and what it does not depend on, we will follow these steps:

### Step 1: Understand the Wave Speed Formula
The speed of a wave on a string is given by the formula:
\[ v = \sqrt{\frac{T}{\mu}} \]
where:
- \( v \) is the speed of the wave,
- \( T \) is the tension in the string,
- \( \mu \) is the mass per unit length of the string.

### Step 2: Identify the Factors Affecting Wave Speed
From the formula, we can see that the speed of the wave depends on:
- The tension \( T \) in the string,
- The mass per unit length \( \mu \) of the string.

### Step 3: Analyze the Given Options
Now, we need to determine what the speed does not depend on. The options provided are:
1. Tension in the string
2. Mass of the wire for a given length
3. Length of the wire
4. Harmonics of the string

### Step 4: Evaluate Each Option
1. **Tension in the string**: The speed is directly dependent on tension, so this option is incorrect.
2. **Mass of the wire for a given length**: The speed is dependent on mass per unit length, so this option is also incorrect.
3. **Length of the wire**: The length of the wire affects the fundamental frequency and harmonics but does not directly affect the speed of the wave, so this option is incorrect.
4. **Harmonics of the string**: The speed of the wave does not depend on the harmonic mode (1st harmonic, 2nd harmonic, etc.). The speed remains constant regardless of the harmonic being produced, so this option is correct.

### Conclusion
The speed of a wave in a string forming a stationary wave does not depend on the harmonics of the string. Therefore, the correct answer is option 4.