If consecutive freuquencies emitted from an organ pipe are 50 Hz, 75Hz, 100 Hz, 125 Hz, then the frequency of the `10^(th)` overtone is

Options

A. 200 Hz
B. 250 Hz
C. 275 Hz
D. 300 Hz

Answer

To solve the problem of finding the frequency of the 10th overtone emitted from an organ pipe with given consecutive frequencies of 50 Hz, 75 Hz, 100 Hz, and 125 Hz, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Frequencies**: The consecutive frequencies given are 50 Hz, 75 Hz, 100 Hz, and 125 Hz.

2. **Determine the Difference Between Frequencies**: Calculate the difference between consecutive frequencies:
- 75 Hz - 50 Hz = 25 Hz
- 100 Hz - 75 Hz = 25 Hz
- 125 Hz - 100 Hz = 25 Hz
This shows that the difference is consistent at 25 Hz.

3. **Identify the Fundamental Frequency**: Since the difference between the frequencies is constant, we can infer that the fundamental frequency (f₁) is 50 Hz. The frequencies can be expressed as:
- 1st harmonic (fundamental frequency) = 50 Hz
- 2nd harmonic = 50 Hz + 25 Hz = 75 Hz
- 3rd harmonic = 50 Hz + 2(25 Hz) = 100 Hz
- 4th harmonic = 50 Hz + 3(25 Hz) = 125 Hz

4. **Determine the Type of Organ Pipe**: Since the frequencies follow a pattern of consecutive harmonics, this indicates that the organ pipe is open at both ends. For an open organ pipe, the nth overtone corresponds to the (n+1)th harmonic.

5. **Calculate the 10th Overtone**: The 10th overtone corresponds to the 11th harmonic. Therefore, we need to calculate:
- 11th harmonic = 11 * fundamental frequency
- 11th harmonic = 11 * 50 Hz = 550 Hz

6. **Final Answer**: The frequency of the 10th overtone is 550 Hz.

### Summary:
The frequency of the 10th overtone is **550 Hz**.

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