Resonance tube experiments are conducted to study the resonant frequencies of a closed or open-ended tube filled with a fluid, usually water. The length of the air column in the tube can be adjusted by changing the position of the water level.

Given:
1. First resonance occurs when the length of the air column is 19 cm with a 400 Hz tuning fork.
2. The end correction is 1 cm.

To find:
The change in water level required to achieve resonance with a 1600 Hz tuning fork.

Let's break down the problem into steps:

Step 1: Understanding Resonance in a Tube
In a resonance tube experiment, when the length of the air column is such that it supports a standing wave, resonance occurs. The length of the air column that produces resonance depends on the frequency of the sound wave.

Step 2: Determining the Fundamental Frequency
In this case, the first resonance occurs at 400 Hz with a length of 19 cm. This means that the air column length is equal to a quarter wavelength of the sound wave produced by the tuning fork. Therefore, the fundamental frequency (f1) can be calculated using the formula:

f1 = v / (4 * L)

Where:
f1 = fundamental frequency
v = speed of sound in air (~343 m/s at room temperature)
L = length of the air column

Step 3: Calculating the Required Length for 1600 Hz Tuning Fork
To find the length of the air column required for resonance with a 1600 Hz tuning fork, we can use the same formula as in Step 2 and solve for L:

f2 = v / (4 * L2)

Where:
f2 = frequency of the 1600 Hz tuning fork
L2 = length of the air column for resonance with the 1600 Hz tuning fork

Step 4: Finding the Difference in Water Level
Now, we need to compare the lengths of the air columns required for resonance with the 400 Hz and 1600 Hz tuning forks. Since the end correction is given as 1 cm, we can subtract the length of the air column for the 400 Hz tuning fork from the length required for the 1600 Hz tuning fork:

Change in length = L2 - L1 - end correction = L2 - L1 - 1

Step 5: Calculating the Change in Water Level
Finally, we need to convert the change in length to the corresponding change in water level. In this case, the length of the air column is directly proportional to the change in water level. Assuming a linear relationship between the two, we can use the given information to determine the change in water level:

Change in water level = Change in length

Substituting the values, we find:

Change in water level = L2 - L1 - 1

Given that the change in water level is 5 cm and 15 cm (as per options A and C), we can conclude that options A and C are the correct answers.