6 beats are produced in 3 seconds by two tuning forks T and T'. T resounds with a closed air column 20 cm long and T' is resounding with an open column 42 cm long. Neglecting end correction, find the frequencies of two forks.

Explanation

To solve the problem, we need to find the frequencies of two tuning forks T and T', given the conditions of their resonance in closed and open air columns, respectively. Here's a step-by-step solution:

### Step 1: Determine the Beat Frequency
We know that 6 beats are produced in 3 seconds. The beat frequency (f_beat) can be calculated as:
\[ f_{\text{beat}} = \frac{\text{Number of beats}}{\text{Time taken}} = \frac{6}{3} = 2 \text{ Hz} \]

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