The End Correction of Resonance Column

The end correction of a resonance column refers to the adjustment needed to account for the presence of the column ends. It is the distance by which the actual length of the column is greater than the length measured from the open end to the closed end.

Given Information:
- End correction = 1.0 cm
- Shortest length resonating with the tuning fork = 15.0 cm

Calculating the Actual Length of the Column:
To find the next resonating length, we need to consider the actual length of the column. We can calculate it by subtracting the end correction from the measured length.

Actual length of the column = Measured length - End correction

In this case, the measured length is 15.0 cm and the end correction is 1.0 cm. Therefore,

Actual length of the column = 15.0 cm - 1.0 cm = 14.0 cm

Calculating the Next Resonating Length:
The next resonating length can be found by adding half a wavelength to the actual length of the column. Since we know that the shortest length resonating with the tuning fork is 15.0 cm, we can calculate the wavelength using the formula:

Wavelength = 2 * Actual length of the column

Wavelength = 2 * 14.0 cm = 28.0 cm

Now, we can find the next resonating length by adding half a wavelength to the actual length:

Next resonating length = Actual length + (Wavelength / 2)

Next resonating length = 14.0 cm + (28.0 cm / 2) = 14.0 cm + 14.0 cm = 28.0 cm

Therefore, the next resonating length is 28.0 cm.

Explanation:
The end correction is a correction factor added to account for the presence of the column ends. It is necessary because the sound waves produced by the tuning fork reflect at the ends of the column, causing a phase change. By subtracting the end correction from the measured length, we obtain the actual length of the column.

To find the next resonating length, we add half a wavelength to the actual length. This is because when the column length is an integer multiple of half a wavelength, resonance occurs. In this case, the next resonating length is found to be 28.0 cm.

It is important to consider the end correction and calculate the actual length of the column accurately to determine the resonating lengths correctly.