Here the pipe dipped in water is similar to pipe with one closed end and one open end. Now consider an instant when the length of water column above the water surface is "L" and the water column resonates with the tuning fork. At this instant if we should equate both the frequencies.

Problem:
A glass tube 1.52 meters long and open at both ends is immersed vertically in a water tank completely. A tuning fork of 600 hertz is vibrated and kept at the upper end of the tube and the tube is gradually raised out of the water. The total number of resonances heard before the tube comes out of the water is 6. Find the solution with an explanation.

Solution:

To understand the number of resonances heard, we need to consider the fundamental frequency and the harmonics produced by the tuning fork.

1. Fundamental Frequency:
The fundamental frequency is the lowest frequency produced by the tuning fork. In this case, the fundamental frequency is 600 hertz.

2. Harmonics:
Harmonics are the multiples of the fundamental frequency. In this case, the harmonics produced by the tuning fork would be 1200 Hz, 1800 Hz, 2400 Hz, and so on.

3. Resonance in a Tube:
When a tube is immersed in water, the length of the tube determines the resonant frequencies. The resonant frequencies for a tube open at both ends are given by the formula:

f = (n * v) / (2 * L)

Where:
- f is the frequency of resonance.
- n is the harmonic number.
- v is the speed of sound in air (approximately 343 m/s).
- L is the length of the tube.

4. Number of Resonances:
As the tube is gradually raised out of the water, the length of the air column inside the tube decreases. When the length of the air column matches the length required for resonance, a resonance is heard.

Since the tube is 1.52 meters long and open at both ends, the resonant frequencies can be calculated using the formula mentioned above. We need to find the number of resonances heard before the tube comes out of the water.

5. Calculation:
Let's calculate the length of the air column required for each resonance:

For the fundamental frequency (n = 1):
f = (1 * 343) / (2 * 1.52)
f = 112.99 Hz

For the first harmonic (n = 2):
f = (2 * 343) / (2 * 1.52)
f = 225.99 Hz

For the second harmonic (n = 3):
f = (3 * 343) / (2 * 1.52)
f = 338.99 Hz

Similarly, we can calculate the resonant frequencies for the other harmonics.

By comparing the calculated resonant frequencies with the frequencies produced by the tuning fork, we can determine the number of resonances heard. In this case, there are 6 resonances heard before the tube comes out of the water.

Conclusion:
In summary, the glass tube will produce resonant frequencies when the length of the air column matches the required length for resonance. By calculating the resonant frequencies based on the length of the tube and comparing them with the frequencies produced by the tuning fork, we can determine the number of resonances heard. In this case, there are 6 resonances heard before the tube comes out of the water.