Velcity of sound in an open organ pipe of 330m/s. The frequency of wave is 1.1 kHz and the length of tube is 30cm. To which harmoninc does this frequency corresponds?
(A)2nd (B)3rd (C)4th (D)5th

Options

A. 2nd
B. 3rd
C. 4th
D. 5th

Answer

To determine which harmonic corresponds to the given frequency in an open organ pipe, we can follow these steps:

### Step 1: Identify the given values
- Velocity of sound (v) = 330 m/s
- Frequency of the wave (f) = 1.1 kHz = 1100 Hz
- Length of the tube (L) = 30 cm = 0.3 m

### Step 2: Calculate the fundamental frequency
The fundamental frequency (f₁) for an open organ pipe is given by the formula:
\[ f_1 = \frac{v}{2L} \]
Substituting the values:
\[ f_1 = \frac{330 \, \text{m/s}}{2 \times 0.3 \, \text{m}} \]
\[ f_1 = \frac{330}{0.6} \]
\[ f_1 = 550 \, \text{Hz} \]

### Step 3: Determine the harmonic number
The harmonic number (n) can be found using the formula:
\[ n = \frac{f}{f_1} \]
Substituting the values:
\[ n = \frac{1100 \, \text{Hz}}{550 \, \text{Hz}} \]
\[ n = 2 \]

### Conclusion
The frequency of 1.1 kHz corresponds to the 2nd harmonic.

### Final Answer
The answer is (A) 2nd harmonic.

---