To determine the maximum height at which resonance occurs in a cylindrical tube when a tuning fork of frequency 340 Hz is used, we need to understand the concept of resonance in relation to sound waves and the properties of the tube. ### Step-by-Step Explanation 1. **Understanding Resonance**: - Resonance occurs when the frequency of the tuning fork matches the natural frequency of the air column in the tube. This leads to a significant increase in amplitude of the sound waves, which we perceive as a loud sound. 2. **Speed of Sound**: - The speed of sound in air is given as \( v = 340 \, \text{m/s} \). 3. **Calculating Wavelength**: - The relationship between speed, frequency, and wavelength is given by the formula: \[ v = f \lambda \] where \( v \) is the speed of sound, \( f \) is the frequency, and \( \lambda \) is the wavelength. - Rearranging this formula to find the wavelength: \[ \lambda = \frac{v}{f} = \frac{340 \, \text{m/s}}{340 \, \text{Hz}} = 1 \, \text{m} \] 4. **Understanding the Tube**: - The cylindrical tube is open at one end (the top) and closed at the other end (the bottom where the water is). This configuration supports standing waves. - For a tube closed at one end, the fundamental frequency (first harmonic) has a quarter of a wavelength fitting into the length of the tube. The relationship can be expressed as: \[ L = \frac{\lambda}{4} \] where \( L \) is the length of the air column above the water. 5. **Finding the Height of the Air Column**: - Since we calculated the wavelength \( \lambda = 1 \, \text{m} \), we can find the length of the air column at resonance: \[ L = \frac{1 \, \text{m}}{4} = 0.25 \, \text{m} \] - This means that when the air column is 0.25 m, resonance occurs. 6. **Calculating Maximum Height of Water**: - The total height of the tube is 1.2 m. The height of the air column at resonance is 0.25 m, so the height of the water in the tube when resonance occurs is: \[ \text{Height of water} = \text{Total height of tube} - \text{Height of air column} = 1.2 \, \text{m} - 0.25 \, \text{m} = 0.95 \, \text{m} \] ### Conclusion The maximum height at which resonance occurs when water is poured into the tube is **0.95 m**. ### Why Other Options Are Incorrect: - **Option B (0.60 m)**: This height does not correspond to any harmonic of the closed tube. It is not a quarter wavelength or any other significant fraction of the wavelength. - **Option C (0.50 m)**: Similar to option B, this height does not match the conditions for resonance in a closed tube. - **Option D (0.45 m)**: This is also incorrect as it does not correspond to the calculated height of the air column at resonance. ### Revision Summary: - Resonance occurs when the frequency of the tuning fork matches the natural frequency of the air column. - The speed of sound in air is 340 m/s, leading to a wavelength of 1 m for a frequency of 340 Hz. - For a closed tube, the length of the air column at resonance is \( \frac{\lambda}{4} \). - The maximum height of water for resonance in this case is 0.95 m.