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 of a string given its fundamental frequency, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Fundamental Frequency**:
The fundamental frequency (first harmonic) is given as 220 cycles per second (cps), which is equivalent to 220 Hertz (Hz).
\[ f_0 = 220 \, \text{Hz} \]

2. **Understand the Harmonics**:
The frequency of the nth harmonic can be calculated using the formula:
\[ f_n = n \times f_0 \]
where \( f_n \) is the frequency of the nth harmonic, \( n \) is the harmonic number, and \( f_0 \) is the fundamental frequency.

3. **Calculate the Fifth Harmonic**:
To find the frequency of the fifth harmonic (\( f_5 \)), substitute \( n = 5 \) into the formula:
\[ f_5 = 5 \times f_0 \]
\[ f_5 = 5 \times 220 \, \text{Hz} \]

4. **Perform the Multiplication**:
Now calculate the value:
\[ f_5 = 1100 \, \text{Hz} \]

5. **State the Final Answer**:
Therefore, the frequency of the fifth harmonic is:
\[ f_5 = 1100 \, \text{Hz} \text{ or } 1100 \, \text{cps} \]

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

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