For an organ pipe, four of the six harmonics of frequency less than 1000 Hz are 300, 600, 750 and 900 Hz. The two missing harmonics are

Options

A. 75 Hz, 150 Hz
B. 150 Hz, 450 Hz
C. 400 Hz, 800 Hz
D. 250 Hz, 400 Hz

Answer

To find the two missing harmonics of the organ pipe with the given frequencies of 300 Hz, 600 Hz, 750 Hz, and 900 Hz, we can follow these steps:

### Step 1: Identify the Given Frequencies
The given frequencies are:
- 300 Hz
- 600 Hz
- 750 Hz
- 900 Hz

### Step 2: Analyze the Frequencies
We need to find a pattern or a common difference in these frequencies. The harmonics of an organ pipe can be represented as multiples of a fundamental frequency.

### Step 3: Calculate the Differences
Let's calculate the differences between the given frequencies:
- 600 Hz - 300 Hz = 300 Hz
- 750 Hz - 600 Hz = 150 Hz
- 900 Hz - 750 Hz = 150 Hz

The differences are not consistent, indicating that the harmonics are not in a simple arithmetic progression.

### Step 4: Check for Missing Frequencies
To find the missing harmonics, we can look for frequencies that would fit into a pattern. We can try to find a common frequency increment.

### Step 5: Guess Possible Frequencies
We can try to find the missing harmonics by checking for frequencies that would fit in between the existing ones. A reasonable guess would be to check lower frequencies.

### Step 6: Test Frequencies
Let's test 150 Hz and 450 Hz:
- If we include 150 Hz, we get: 150 Hz, 300 Hz, 450 Hz, 600 Hz, 750 Hz, 900 Hz.
- The differences are:
- 300 - 150 = 150 Hz
- 450 - 300 = 150 Hz
- 600 - 450 = 150 Hz
- 750 - 600 = 150 Hz
- 900 - 750 = 150 Hz

This shows that the frequencies are now in an arithmetic progression with a common difference of 150 Hz.

### Step 7: Conclusion
The two missing harmonics are:
- 150 Hz
- 450 Hz