Question:
A resonance tube completely filled with water has a small hole at the bottom. Length of the tube is 80 cm. A vibrating tuning fork of frequency 500 Hz is held near the open end of the tube. Water is slowly removed from the bottom. The maximum number of resonances heard will be (neglect end correction). Speed of sound in air is 340 m/s
A resonance tube completely filled with water has a small hole at the bottom. Length of the tube is 80 cm. A vibrating tuning fork of frequency 500 Hz is held near the open end of the tube. Water is slowly removed from the bottom. The maximum number of resonances heard will be (neglect end correction). Speed of sound in air is 340 m/s
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For resonance tubes, the number of resonances is dependent on the frequency and the length of the tube. Keep in mind that the speed of sound in air can vary with temperature.
Updated On: Jan 26, 2026
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The Correct Option is B
Solution and Explanation
Step 1: Resonance condition.
For resonance to occur, the length of the resonance tube must satisfy the condition where the tube supports standing waves. The formula for the frequency of resonance is: \[ f = \frac{v}{2L} \] Where: - \( f = 500 \, \text{Hz} \) - \( v = 340 \, \text{m/s} \) - \( L = 0.80 \, \text{m} \) Step 2: Calculating the number of resonances.
The total number of resonances can be found by: \[ N = \frac{v}{2fL} \] Substituting the known values: \[ N = \frac{340}{2 \times 500 \times 0.80} = 4 \] Thus, the correct answer is (B) 4.
For resonance to occur, the length of the resonance tube must satisfy the condition where the tube supports standing waves. The formula for the frequency of resonance is: \[ f = \frac{v}{2L} \] Where: - \( f = 500 \, \text{Hz} \) - \( v = 340 \, \text{m/s} \) - \( L = 0.80 \, \text{m} \) Step 2: Calculating the number of resonances.
The total number of resonances can be found by: \[ N = \frac{v}{2fL} \] Substituting the known values: \[ N = \frac{340}{2 \times 500 \times 0.80} = 4 \] Thus, the correct answer is (B) 4.
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