Introduction:
When a tuning fork and an air column resonate together, they produce a phenomenon known as beats. Beats occur due to the interference of sound waves generated by the fork and the air column. The frequency of the beats can be calculated using the formula:
Frequency of beats (B) = |f1 - f2|

Given Information:
Frequency of tuning fork (f1) = 300 Hz
Temperature of air column (T1) = 27°C
Temperature of air column at 0°C (T2) = 0°C

Step 1: Finding the speed of sound in air at 27°C
The speed of sound in air depends on temperature. We can use the formula:
Speed of sound (v) = v0 * √(T/T0)

At 0°C, the speed of sound in air is v0 = 331.4 m/s.

Using the given temperature of 27°C, we can calculate the speed of sound in air at that temperature:
v1 = 331.4 * √(27/273) ≈ 346.4 m/s

Step 2: Finding the wavelength of the tuning fork
The wavelength of a sound wave produced by a tuning fork can be calculated using the formula:
Wavelength (λ1) = v1 / f1

Substituting the values:
λ1 = 346.4 / 300 ≈ 1.155 m

Step 3: Finding the speed of sound in air at 0°C
Using the given temperature of 0°C, we can calculate the speed of sound in air at that temperature:
v2 = 331.4 * √(0/273) ≈ 273.2 m/s

Step 4: Finding the wavelength of the tuning fork at 0°C
The wavelength of the sound wave produced by the tuning fork at 0°C can be calculated using the formula:
Wavelength (λ2) = v2 / f1

Substituting the values:
λ2 = 273.2 / 300 ≈ 0.911 m

Step 5: Finding the difference in wavelengths
The difference in wavelengths can be calculated as:
Δλ = |λ1 - λ2|

Substituting the values:
Δλ = |1.155 - 0.911| ≈ 0.244 m

Step 6: Finding the frequency of beats
The frequency of beats can be calculated using the formula:
Frequency of beats (B) = v2 / Δλ

Substituting the values:
B = 273.2 / 0.244 ≈ 1120.5 Hz

Conclusion:
Therefore, when a tuning fork of frequency 300 Hz resonates with an air column closed at one end at 27°C, the frequency of beats heard in the vibrations of the fork and the air column at 0°C is approximately 1120.5 Hz.

Anyone can answer this??m waiting for the answer