If in an experiment for determination of velocity of sound by resonance tube method using a tuning fork of `512 Hz`, first resonance was observed at `30.7 cm` and second was obtained at `63.2 cm`, then maximum possible error in velocity of sound is (consider actual speed of sound in air is `332m//s`)

Options

A. 204 cm/sec
B. 110 cm/sec
C. 58 cm/sec
D. 80 cm/sec

Explanation

To solve the problem of determining the maximum possible error in the velocity of sound using the resonance tube method, we will follow these steps:

### Step 1: Understand the relationship between wavelength, frequency, and length
In the resonance tube method, the wavelength (λ) of the sound can be determined using the lengths of the resonances observed. The formula for the wavelength is given by:
\[ \lambda = 2(L_2 - L_1) \]
where \(L_1\) is the length of the first resonance and \(L_2\) is the length of the second resonance.

### Step 2: Substitute the given values
From the problem, we have:
- \(L_1 = 30.7 \, \text{cm}\)
- \(L_2 = 63.2 \, \text{cm}\)

Now we can calculate the wavelength:
\[ \lambda = 2(63.2 \, \text{cm} - 30.7 \, \text{cm}) = 2(32.5 \, \text{cm}) = 65.0 \, \text{cm} \]

### Step 3: Convert the wavelength to meters
To work in standard SI units, we convert the wavelength from centimeters to meters:
\[ \lambda = 65.0 \, \text{cm} = 0.65 \, \text{m} \]

### Step 4: Use the relationship between speed, wavelength, and frequency
The speed of sound (V) can be calculated using the formula:
\[ V = f \cdot \lambda \]
where \(f\) is the frequency of the tuning fork. Given that \(f = 512 \, \text{Hz}\), we can substitute the values:
\[ V = 512 \, \text{Hz} \cdot 0.65 \, \text{m} = 332.8 \, \text{m/s} \]

### Step 5: Determine the actual speed of sound
The actual speed of sound in air is given as:
\[ V_0 = 332 \, \text{m/s} \]

### Step 6: Calculate the error in the velocity of sound
The error in the velocity of sound can be calculated as:
\[ \text{Error} = V - V_0 = 332.8 \, \text{m/s} - 332 \, \text{m/s} = 0.8 \, \text{m/s} \]

### Conclusion
Thus, the maximum possible error in the velocity of sound determined by the experiment is:
\[ \text{Maximum Possible Error} = 0.8 \, \text{m/s} \]