An electrically maintained tuning fork vibrates with constant frequency and constant amplitude. If the temperature of the surrounding air increases but pressure remains constant, the sound produced will have

Options

A. larger wavelength
B. larger frequency
C. larger velocity
D. larger time period

Answer

To solve the question, we need to analyze the effects of temperature on sound waves produced by a tuning fork that vibrates with constant frequency and amplitude. Here’s the step-by-step solution:

### Step 1: Understand the conditions
The tuning fork vibrates with a constant frequency and amplitude. This means that the frequency of the sound produced will not change regardless of external conditions.

**Hint:** Remember that the frequency of a sound source is determined by the source itself, not the medium through which it travels.

### Step 2: Analyze the effect of temperature on sound velocity
The velocity of sound in a gas is given by the formula:
\[ v = \sqrt{\gamma \cdot R \cdot T} \]
where:
- \( v \) = velocity of sound
- \( \gamma \) = adiabatic constant (depends on the gas)
- \( R \) = universal gas constant
- \( T \) = absolute temperature

As the temperature \( T \) increases, the velocity \( v \) of sound will also increase, provided that the pressure remains constant.

**Hint:** Increasing temperature increases the kinetic energy of the molecules in the air, which allows sound to travel faster.

### Step 3: Relate velocity, frequency, and wavelength
The relationship between the velocity \( v \), frequency \( f \), and wavelength \( \lambda \) of sound is given by:
\[ v = f \cdot \lambda \]

Since the frequency \( f \) is constant (as established in Step 1), if the velocity \( v \) increases due to the increase in temperature, the wavelength \( \lambda \) must also increase to maintain the equation.

**Hint:** If the speed of sound increases while frequency remains constant, wavelength must increase.

### Step 4: Determine the effects on time period
The time period \( T \) of a wave is the reciprocal of frequency:
\[ T = \frac{1}{f} \]

Since the frequency is constant, the time period will also remain constant.

**Hint:** The time period is directly related to frequency; if frequency does not change, neither does the time period.

### Conclusion
From the analysis:
- The sound produced will have a **larger wavelength** (Option 1 is correct).
- The sound produced will have a **larger velocity** (Option 3 is correct).
- The sound produced will **not** have a larger frequency (Option 2 is incorrect).
- The sound produced will **not** have a larger time period (Option 4 is incorrect).

### Final Answer
The correct options are:
- Larger wavelength (Option 1)
- Larger velocity (Option 3)