Two open pipes `A` and `B` are sounded together such that beats are heard between the first overtone of `A` and second overtone of `B`. If the fundamental frequency of `A` and `B` is `256 Hz` and `170 Hz` respectively , then the beat frequency heard is

Options

A. `4 Hz`
B. `3 Hz`
C. `2 Hz`
D. `1 Hz`

Explanation

To solve the problem, we need to find the beat frequency between the first overtone of pipe A and the second overtone of pipe B. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the terms
- The **fundamental frequency** of pipe A is given as \( f_A = 256 \, \text{Hz} \).
- The **fundamental frequency** of pipe B is given as \( f_B = 170 \, \text{Hz} \).

### Step 2: Calculate the frequencies of the overtones
- The **first overtone** of pipe A corresponds to the second harmonic, which is calculated as:
\[ f_{A, \text{first overtone}} = 2 \times f_A = 2 \times 256 \, \text{Hz} = 512 \, \text{Hz} \]

- The **second overtone** of pipe B corresponds to the third harmonic, which is calculated as:
\[ f_{B, \text{second overtone}} = 3 \times f_B = 3 \times 170 \, \text{Hz} = 510 \, \text{Hz} \]

### Step 3: Calculate the beat frequency
- The beat frequency is the absolute difference between the two frequencies:
\[ f_{\text{beat}} = |f_{A, \text{first overtone}} - f_{B, \text{second overtone}}| = |512 \, \text{Hz} - 510 \, \text{Hz}| = 2 \, \text{Hz} \]

### Conclusion
The beat frequency heard is \( 2 \, \text{Hz} \).

### Final Answer
The beat frequency is \( 2 \, \text{Hz} \).

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