What is resonance? By drawing the diagram of a resonance tube, calculate the formula for velocity of sound in air.

Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration at its natural frequency. When the frequency of the external force matches the natural frequency of the object, resonance amplifies the vibrations and can lead to increased amplitude or energy transfer.

A resonance tube is a cylindrical tube with one end open and the other end closed. The tube is partially filled with a liquid, typically water, and a tuning fork is used to generate sound waves. By adjusting the water level, it is possible to find the resonance condition where a standing wave is established in the tube.

To calculate the formula for the velocity of sound in air using a resonance tube, we can use the relationship between the length of the tube and the wavelength of the sound wave. In a closed-end resonance tube, the first resonance occurs when the length of the tube is one-fourth of the wavelength (λ/4). Mathematically, we can express this as:

L = λ/4,

where L is the length of the tube and λ is the wavelength of the sound wave.

The velocity of sound (v) can be calculated using the formula:

v = f × λ,

where f is the frequency of the sound wave and λ is the wavelength.

Since the frequency of the tuning fork is known, we can rearrange the formula to solve for the velocity of sound:

v = 4fL.

Therefore, the formula for the velocity of sound in air using a resonance tube is v = 4fL, where v is the velocity of sound, f is the frequency of the sound wave, and L is the length of the tube.