In the experiment of finding speed of sound by resonance tube, it is observed that for tunning fork of frequency `f= 480` Hz, length of air column cm, `I_(1) = 30 cm, I_(2) = 70 cm`, then `upsilon_(1)` is equal to

Options

A. `338 ms^(-1)`
B. `379 ms^(-1)`
C. `384 ms^(-1)`
D. `332 ms^(-1)`

Answer

To find the speed of sound in the resonance tube experiment, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Frequency of the tuning fork, \( f = 480 \, \text{Hz} \)
- Length of the air column for the first resonance, \( l_1 = 30 \, \text{cm} = 30 \times 10^{-2} \, \text{m} \)
- Length of the air column for the second resonance, \( l_2 = 70 \, \text{cm} = 70 \times 10^{-2} \, \text{m} \)

2. **Use the Formula for Speed of Sound:**
The formula to calculate the speed of sound in a resonance tube is given by:
\[ v = 2f(l_2 - l_1) \]

3. **Substitute the Values into the Formula:**
Substitute \( f \), \( l_1 \), and \( l_2 \) into the formula:
\[ v = 2 \times 480 \, \text{Hz} \times (70 \times 10^{-2} \, \text{m} - 30 \times 10^{-2} \, \text{m}) \]

4. **Calculate the Difference in Lengths:**
Calculate \( l_2 - l_1 \):
\[ l_2 - l_1 = (70 - 30) \times 10^{-2} \, \text{m} = 40 \times 10^{-2} \, \text{m} \]

5. **Substitute the Difference Back into the Formula:**
Now substitute this value back into the speed formula:
\[ v = 2 \times 480 \times (40 \times 10^{-2}) \]

6. **Calculate the Speed:**
Calculate the speed:
\[ v = 960 \times 40 \times 10^{-2} = 38400 \times 10^{-2} \, \text{m/s} = 384 \, \text{m/s} \]

7. **Final Answer:**
Therefore, the speed of sound \( v \) is:
\[ v = 384 \, \text{m/s} \]