If the fundamental frequency of string is 220 cps , the frequency of fifth harmonic will be

Options

A. 44 cps
B. 55 cps
C. 1100 cps
D. 440 cps

Answer

To find the frequency of the fifth harmonic when the fundamental frequency is given, we can follow these steps:

### Step 1: Understand the Fundamental Frequency
The fundamental frequency (first harmonic) is given as 220 cps (cycles per second), which is equivalent to 220 Hz.

### Step 2: Use the Formula for Harmonics
The frequency of the nth harmonic is given by the formula:
\[ f_n = n \times f_1 \]
where:
- \( f_n \) is the frequency of the nth harmonic,
- \( n \) is the harmonic number,
- \( f_1 \) is the fundamental frequency.

### Step 3: Substitute Values
For the fifth harmonic (n = 5):
\[ f_5 = 5 \times f_1 \]
Substituting the value of the fundamental frequency:
\[ f_5 = 5 \times 220 \, \text{Hz} \]

### Step 4: Calculate the Frequency
Now, perform the multiplication:
\[ f_5 = 5 \times 220 = 1100 \, \text{Hz} \]

### Step 5: Conclusion
Thus, the frequency of the fifth harmonic is 1100 cps or 1100 Hz.

### Final Answer
The frequency of the fifth harmonic is **1100 cps**.

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