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 find 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 1: Identify the pattern in the frequencies
The given frequencies are:
- 1st frequency: 50 Hz
- 2nd frequency: 75 Hz
- 3rd frequency: 100 Hz
- 4th frequency: 125 Hz

The difference between consecutive frequencies is:
- 75 Hz - 50 Hz = 25 Hz
- 100 Hz - 75 Hz = 25 Hz
- 125 Hz - 100 Hz = 25 Hz

This indicates that the frequencies are increasing by a constant value of 25 Hz.

### Step 2: Determine the fundamental frequency
Since the frequencies are in arithmetic progression, we can identify the fundamental frequency (F0) as the first term of this sequence. The fundamental frequency is:
- F0 = 50 Hz

### Step 3: Determine the type of organ pipe
The problem does not specify whether the organ pipe is open or closed. However, since the frequencies are in arithmetic progression, we can assume that the organ pipe is an open pipe.

For an open organ pipe, the frequencies are given by:
- Fn = n * F0

### Step 4: Calculate the frequency of the 10th overtone
The overtone frequencies for an open organ pipe can be calculated using the formula:
- Frequency of nth overtone = (n + 1) * F0

To find the 10th overtone, we set n = 10:
- Frequency of 10th overtone = (10 + 1) * F0
- Frequency of 10th overtone = 11 * 50 Hz
- Frequency of 10th overtone = 550 Hz

### Step 5: Conclusion
Thus, the frequency of the 10th overtone is **550 Hz**.

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