In a resonance tube, using a tuning fork of frequency 325 Hz, two successive resonance lengths are observed at 25.4 m and 77.4 cm respectively. The velocity of sound is air is

Options

A. `338 ms^(-1)`
B. `328 ms^(-1)`
C. `330 ms^(-1)`
D. `320 ms^(-1)`

Explanation

To find the velocity of sound in air using the resonance tube method, we can follow these steps:

### Step 1: Understand the Given Information
We are given:
- Frequency of the tuning fork (f) = 325 Hz
- Two successive resonance lengths (L1 and L2):
- L1 = 25.4 cm
- L2 = 77.4 cm

### Step 2: Convert the Lengths to Meters
Since we need to work in standard SI units, we convert the lengths from centimeters to meters:
- L1 = 25.4 cm = 25.4 / 100 = 0.254 m
- L2 = 77.4 cm = 77.4 / 100 = 0.774 m

### Step 3: Calculate the Difference in Lengths
Now, we find the difference between the two resonance lengths:
- \( L2 - L1 = 0.774 m - 0.254 m = 0.520 m \)

### Step 4: Use the Formula for Velocity of Sound
The formula for the velocity of sound in air using the resonance tube is given by:
\[ V = 2f(L2 - L1) \]
Substituting the values we have:
- \( V = 2 \times 325 \, \text{Hz} \times 0.520 \, \text{m} \)

### Step 5: Perform the Calculation
Calculating the above expression:
- \( V = 2 \times 325 \times 0.520 \)
- \( V = 650 \times 0.520 \)
- \( V = 338 \, \text{m/s} \)

### Final Answer
The velocity of sound in air is approximately **338 m/s**.