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: Understand the Harmonics of an Organ Pipe
An organ pipe can produce harmonics based on its fundamental frequency. The harmonics are typically in integer multiples of the fundamental frequency. For a closed organ pipe, the harmonics are odd multiples of the fundamental frequency.

### Step 2: List the Given Frequencies
The given frequencies are:
- 300 Hz
- 600 Hz
- 750 Hz
- 900 Hz

### Step 3: Identify the Pattern of Frequencies
To find the missing harmonics, we need to identify the frequency pattern. The frequencies should ideally be spaced evenly if they are harmonics of the same fundamental frequency.

### Step 4: Calculate the Differences Between Frequencies
Let's calculate the differences between the given frequencies:
- From 300 Hz to 600 Hz: 600 - 300 = 300 Hz
- From 600 Hz to 750 Hz: 750 - 600 = 150 Hz
- From 750 Hz to 900 Hz: 900 - 750 = 150 Hz

### Step 5: Determine the Missing Frequencies
The pattern of differences suggests that the missing frequencies should fit into the sequence. Since we have a gap before 300 Hz and after 900 Hz, we can find the missing harmonics by working backwards and forwards from the known frequencies.

1. The frequency before 300 Hz should be:
- 300 Hz - 150 Hz = 150 Hz
2. The frequency after 900 Hz should be:
- 900 Hz + 150 Hz = 1050 Hz (but this is greater than 1000 Hz, so we ignore this)

### Step 6: Check for Other Possible Frequencies
Since we need to find two missing frequencies and we already identified 150 Hz, we can check if there is another harmonic that fits within the 1000 Hz limit:
- The next harmonic after 150 Hz would be:
- 150 Hz + 150 Hz = 300 Hz (already known)
- 150 Hz + 300 Hz = 450 Hz (this is a new frequency)

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

### Summary of Missing Harmonics
The two missing harmonics of the organ pipe are **150 Hz and 450 Hz**.

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