When a fork of frequency 512 Hz in sounded, the difference in level of water in tube between two successive positions of resonance is found to be 0.33 m. What is the velocity of sound in air ?

Answer

To find the velocity of sound in air given the frequency of the fork and the difference in water levels in the tube, we can follow these steps:

### Step 1: Understand the relationship between the resonance positions and wavelength
The difference in the level of water in the tube between two successive positions of resonance (L2 - L1) is equal to half the wavelength (λ/2) of the sound wave produced by the tuning fork.

### Step 2: Set up the equation for the wavelength
From the relationship established in Step 1, we can write:
\[ L2 - L1 = \frac{\lambda}{2} \]
Given that \( L2 - L1 = 0.33 \, \text{m} \), we can substitute this into the equation:
\[ 0.33 = \frac{\lambda}{2} \]

### Step 3: Solve for the wavelength (λ)
To find λ, we can multiply both sides of the equation by 2:
\[ \lambda = 2 \times 0.33 = 0.66 \, \text{m} \]

### Step 4: Use the wave equation to find the velocity of sound
The velocity of sound (V) can be calculated using the formula:
\[ V = f \cdot \lambda \]
where \( f \) is the frequency of the tuning fork. We are given that \( f = 512 \, \text{Hz} \).

### Step 5: Substitute the values into the equation
Now we can substitute the values of \( f \) and \( λ \) into the equation:
\[ V = 512 \, \text{Hz} \times 0.66 \, \text{m} \]

### Step 6: Calculate the velocity of sound
Now, perform the multiplication:
\[ V = 512 \times 0.66 = 337.92 \, \text{m/s} \]

### Conclusion
The velocity of sound in air is approximately \( 337.92 \, \text{m/s} \).