Question:

A tuning fork with a frequency of 440 Hz is struck and held above a cylindrical tube filled with water. As the water level inside the tube is gradually lowered, the sound heard from the tuning fork becomes louder.

a) Explain why the sound becomes louder as the water level is lowered.

b) Calculate the speed of sound in the air inside the tube, given that the temperature is 25°C and the speed of sound in air at this temperature is approximately 346 m/s.

c) If the water level is then raised to a point where it completely covers the opening of the tube, explain what would be observed regarding the sound produced by the tuning fork.

Answer:

a) The phenomenon of sound becoming louder as the water level is lowered is due to the change in resonance inside the tube. When the water level is high, the air column inside the tube is longer and the natural frequency of the air column is lower. As the water level is lowered, the length of the air column decreases, causing the natural frequency of the air column to increase. When the natural frequency of the air column matches the frequency of the tuning fork, a condition of resonance occurs, resulting in a loud sound. Therefore, lowering the water level changes the length of the air column, allowing resonance to take place and making the sound louder.

b) To calculate the speed of sound in the air inside the tube, we can use the formula:

v = f * λ

where v is the speed of sound, f is the frequency of the tuning fork, and λ is the wavelength of the sound in the air column.

To find the wavelength of the sound, we can use the formula:

λ = 2 * L

where L is the length of the air column inside the tube.

Given f = 440 Hz, and assuming the length of the air column inside the tube is L, we can find the speed of sound using the equation:

v = f * λ = f * (2 * L) = 440 Hz * (2 * L)

Substituting the given speed of sound in air at 25°C (346 m/s) for v, we get:

346 m/s = 440 Hz * (2 * L)

Simplifying the equation:

2 * L = 346 m/s / (440 Hz)

2 * L ≈ 0.786 m

L ≈ 0.393 m

Therefore, the length of the air column inside the tube is approximately 0.393 m.

c) When the water level is raised to a point where it completely covers the opening of the tube, the sound produced by the tuning fork would become much softer or even completely inaudible. This is because when the water completely covers the opening of the tube, the air column inside the tube is no longer present. Without the air column, there are no longer any resonant conditions for the sound waves from the tuning fork to amplify. As a result, the sound produced by the tuning fork is significantly reduced or silenced altogether.