Determination of Velocity of Sound in Air Using Tuning Forks
Aim: To determine the velocity of sound in air at room temperature using tuning forks of known frequencies and an air column.
Apparatus:
1. Tuning forks (known frequencies: , unknown frequency ).
2. Resonance tube or pipe with adjustable air column.
3. Ruler or measuring tape.
Theory:
Resonance occurs when the natural frequency of vibration of the air column matches the frequency of the tuning fork.
The length of the air column () is related to the frequency () by the formula:
\(L = \frac{v}{4f}\)
Where:
= Length of the air column
= Velocity of sound in air
= Frequency of the tuning fork
The relationship between frequency and the reciprocal of length is linear.
Procedure:
1. Set up the apparatus: Place the tuning fork of known frequency over the resonance tube.
2. Adjust the length of the air column until resonance is observed (the loudest sound). Measure the corresponding length of the air column .
3. Repeat the experiment for all known frequencies , and measure the corresponding air column lengths .
4. For the unknown tuning fork , measure the air column length where resonance occurs.
Calculation:
1. Plot a graph of frequency on the y-axis and the reciprocal of air column length on the x-axis.
The relation between and is linear:
\(f = \frac{v}{4} \times \frac{1}{L}\)
2. Find the slope of the graph. The slope of the line gives .
3. Calculate the velocity of sound by multiplying the slope by 4:
\(v = 4 \times \text{slope}\)
Result:
The velocity of sound in air at room temperature is approximately .
Precautions:
1. Ensure the air column length is measured accurately.
2. The tuning fork should be struck at a constant force to ensure consistent frequency.
3. Perform the experiment in a quiet environment to clearly hear the resonance.
