`S_(1)` : A standing wave pattern if formed in a string. The power transfer through a point (other than node and antinode) is zero always
`S_(2)`: if the equation of transverse wave is `y= sin 2pi[t/0.04-x/40]`, where distance is in cm. time in second, then the wavelength will be 40 cm.
`S_(3)`: if the length of the vibrating string is kept constant, then frequency of the string will be directly proportional to `sqrt(T)`

Options

A. FTT
B. TTF
C. TFT
D. FFF

Explanation

To analyze the statements and determine their truth values, let's break down each statement step by step.

### Statement 1:
"A standing wave pattern is formed in a string. The power transfer through a point (other than node and antinode) is zero always."

1. **Understanding Standing Waves**: In a standing wave, nodes are points of zero amplitude, and antinodes are points of maximum amplitude.
2. **Power Transfer**: Power transfer in a wave is related to the product of force and velocity. Mathematically, \( P = F \cdot v \cdot \cos(\theta) \), where \( \theta \) is the angle between the force and velocity vectors.
3. **At Nodes and Antinodes**: At nodes, the amplitude is zero, hence power is zero. At antinodes, the amplitude is maximum, and power is maximum.
4. **Other Points**: At points other than nodes and antinodes, the wave still has amplitude, and thus both force and velocity are not zero. Therefore, power is not zero.
5. **Conclusion**: The statement is **false** because power is not zero at points other than nodes and antinodes.

### Statement 2:
"If the equation of transverse wave is \( y = \sin(2\pi[t/0.04 - x/40]) \), where distance is in cm and time in seconds, then the wavelength will be 40 cm."

1. **Wave Equation Format**: The general form of a wave equation is \( y = A \sin(\omega t - kx) \).
2. **Identifying Parameters**: From the given equation, we can identify:
- \( \omega = \frac{2\pi}{0.04} \) (angular frequency)
- \( k = \frac{2\pi}{40} \) (wave number)
3. **Finding Wavelength**: The wavelength \( \lambda \) is related to the wave number \( k \) by the formula \( k = \frac{2\pi}{\lambda} \). Therefore, rearranging gives \( \lambda = \frac{2\pi}{k} = 40 \) cm.
4. **Conclusion**: The statement is **true** because the wavelength calculated is indeed 40 cm.

### Statement 3:
"If the length of the vibrating string is kept constant, then the frequency of the string will be directly proportional to \( \sqrt{T} \)."

1. **Frequency of a String**: The frequency \( f \) of a vibrating string is given by the formula \( f = \frac{V}{2L} \), where \( V \) is the wave speed and \( L \) is the length of the string.
2. **Wave Speed**: The wave speed \( V \) can be expressed as \( V = \sqrt{\frac{T}{\mu}} \), where \( T \) is the tension and \( \mu \) is the linear mass density.
3. **Substituting for Frequency**: Substituting \( V \) into the frequency equation gives \( f = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \).
4. **Keeping Length Constant**: If the length \( L \) is constant, then \( f \) is directly proportional to \( \sqrt{T} \).
5. **Conclusion**: The statement is **true** because the frequency is indeed directly proportional to \( \sqrt{T} \) when length is constant.

### Final Evaluation:
- **Statement 1**: False
- **Statement 2**: True
- **Statement 3**: True