Wavelength of sound in air and speed calculation.

Resonance tube experiment to determine the wavelength of sound and calculate its speed, considering end correction and the influence of temperature.

Apparatus

Resonance tube apparatus
Two tuning forks of known frequency
Plumb line
Vernier calipers
Rubber pad
Thermometer
Set of squares
Pinch cork
Beaker

Observations

Vernier Constant of Caliper: 0.01 cm
Zero Correction of Caliper: ……… cm
Internal Diameter of Resonance Tube:
- (i) … cm
- (ii) … cm
- (iii) … cm
Mean Corrected Diameter (D): … cm
End Correction: 0.3 D = … cm
Room Temperature at Start: t₁ °C
Room Temperature at End: t₂ °C
Mean Room Temperature: t = (t₁ + t₂)/2 = … °C
Position of Open End of Tube (X): … cm

Calculation:

Velocity of sound in air at 0⁰C =V⁰ =V₁ -6It =……………..cm/sec.

Actual value of velocity of sound at 0⁰C =………cm / sec.

Difference =………..cm /sec.

=………………%

Procedure

Place the apparatus on a smooth, horizontal surface and check the level using a plumb line. Adjust the apparatus with foot screws if necessary.
Determine the vernier constant of the caliper and check its zero error.
Measure the internal diameter of the resonance tube at multiple points and calculate its mean diameter. Apply zero correction.
Note the initial water temperature (t₁ °C) with a thermometer. Record the position of the upper end of the resonance tube as X.
Raise the water reservoir to its highest level, then open the pinch cock.
Gently strike a tuning fork of known frequency (e.g., 512 Hz) on the rubber pad and hold it horizontally above the open end of the tube.
Gradually lower the water level until resonance occurs with a loud note. Record the resonance position using set squares.
Repeat the procedure when the water level is rising, and note this position. Take the mean value as Y.
Calculate t = Y – X. Record the final temperature (t₂ °C).
Repeat the experiment with the second tuning fork.
Finally, calculate the velocity of sound at 0°C using the observed data and corrections.

Calculations

Velocity of Sound at 0°C: V₀ = V₁ – 0.61t … cm/sec
Actual Velocity at 0°C: … cm/sec
Difference: … cm/sec = … %

Precautions

Strike the tuning fork gently on the rubber pad.
Keep the resonance tube vertical.
Ensure the prongs of the tuning fork do not touch the tube.
Hold the vibrating tuning fork horizontally above the open end.
Read the low meniscus of water using two set squares.

Viva-Voce

Q1. What is meant by resonance?
Ans: Resonance occurs when a small periodic force acts on a body whose natural period matches that of the force, causing large-amplitude vibrations.

Q2. What is end correction?
Ans: The antinode does not lie exactly at the open end but slightly above it. This shift, called end correction, is approximately 0.3 D, where D is the internal diameter of the tube.

Q3. What is the effect of temperature on the velocity of sound?
Ans: The velocity of sound increases by approximately 61 cm/sec for every 1°C rise in temperature.

Q4. Define node and antinode.
Ans:

Node: A point where the strain is maximum and the amplitude is zero.
Antinode: A point where the strain is minimum and the amplitude is maximum.