A tuning fork is vibrate with constant frequency and amplitude. If the air is heated without changing pressure the following quantities will increase.

Options

A. Wavelength
B. Frequency
C. Velocity
D. Time period

Explanation

To solve the problem, we need to analyze what happens to the properties of sound waves when the air is heated while keeping the pressure constant. Here’s a step-by-step solution:

### Step 1: Understand the relationship between temperature, velocity, and wavelength
The speed of sound in a medium is given by the formula:
\[ V = \sqrt{\frac{\gamma RT}{m}} \]
Where:
- \( V \) is the speed of sound,
- \( \gamma \) is the adiabatic index (ratio of specific heats),
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature,
- \( m \) is the molar mass of the gas.

### Step 2: Analyze the effect of heating on temperature
When the air is heated, the temperature \( T \) increases. Since \( V \) is directly proportional to the square root of the temperature, an increase in temperature will lead to an increase in the speed of sound \( V \).

### Step 3: Relate speed, frequency, and wavelength
The speed of sound is also related to frequency \( f \) and wavelength \( \lambda \) by the equation:
\[ V = f \cdot \lambda \]
Since the frequency \( f \) of the tuning fork is constant (as given in the problem), any increase in \( V \) must be accompanied by an increase in \( \lambda \) (wavelength).

### Step 4: Identify which quantities increase
From the above analysis:
- As the temperature increases, the speed of sound \( V \) increases.
- Since the frequency \( f \) is constant, the wavelength \( \lambda \) must also increase to maintain the relationship \( V = f \cdot \lambda \).

### Step 5: Determine the quantities that remain constant
The frequency \( f \) is constant, and since the frequency is constant, the time period \( T \) (which is the inverse of frequency) also remains constant:
\[ T = \frac{1}{f} \]

### Conclusion
Thus, when the air is heated without changing pressure:
- The speed of sound \( V \) increases.
- The wavelength \( \lambda \) increases.
- The frequency \( f \) remains constant.
- The time period \( T \) remains constant.

### Final Answer
The quantities that will increase are:
1. Wavelength (\( \lambda \))
2. Speed of sound (\( V \))