To determine which of the following statements is incorrect, we will analyze each option step by step.
### Step 1: Analyze Option 1
**Statement:** "Frequency of waves does not change with change in medium."
- **Explanation:** The frequency of a wave is determined by the source of the wave. When a wave travels from one medium to another, the frequency remains constant. This is because the frequency is a property of the source and does not depend on the medium through which the wave is traveling. Therefore, this statement is **correct**.
### Step 2: Analyze Option 2
**Statement:** "Velocity of transverse wave in stretched string is independent of length of string. It is clamped horizontally."
- **Explanation:** The speed of a transverse wave in a stretched string is given by the formula \( v = \sqrt{\frac{T}{\mu}} \), where \( T \) is the tension in the string and \( \mu \) is the mass per unit length. In a horizontally clamped string, the tension remains constant regardless of the length of the string. Therefore, the speed of the wave does not depend on the length of the string. This statement is also **correct**.
### Step 3: Analyze Option 3
**Statement:** "For a rope suspended vertically, the velocity of the transverse pulse produced at the lower end increases as it moves up."
- **Explanation:** In a vertically suspended rope, the tension increases as you move up the rope because more of the rope's weight is supported. Since the speed of the wave is dependent on the tension, which increases as you go up, the speed of the wave will indeed increase as it moves upward. Thus, this statement is **correct**.
### Step 4: Analyze Option 4
**Statement:** "Velocity of sound decreases with increase in humidity in air."
- **Explanation:** The speed of sound in air is given by the formula \( v = \sqrt{\frac{\gamma P}{\rho}} \), where \( \gamma \) is the adiabatic index, \( P \) is the pressure, and \( \rho \) is the density of the air. When humidity increases, water vapor (H2O) replaces some of the heavier air molecules (like O2 and N2), which decreases the overall density of the air. Since the speed of sound is inversely proportional to the square root of the density, as the density decreases, the speed of sound actually increases. Therefore, this statement is **incorrect**.
### Conclusion
The incorrect statement is **Option 4**: "Velocity of sound decreases with increase in humidity in air."
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