A tuning fork of 512 Hz is used to produce resonance in a resonance tube experiment . The level of water at first resonance is 30. 7 cm and at second resonance is 63 . 2 cm . The error in calculating velocity of sound is (speed of sound in air = 330 m/s)

Options

A. 204.1 cm/s
B. 110 cm/s
C. 58 cm/s
D. 280 cm /s

Answer

To solve the problem step by step, we will follow the given information and apply the relevant formulas.

### Step 1: Identify the given data
- Frequency of the tuning fork (f) = 512 Hz
- Level of water at first resonance (L1) = 30.7 cm
- Level of water at second resonance (L2) = 63.2 cm

### Step 2: Calculate the distance between the two resonance points
The distance between the first and second resonance points gives us the distance between two successive nodes (or antinodes).

\[ \text{Distance (d)} = L2 - L1 = 63.2 \, \text{cm} - 30.7 \, \text{cm} = 32.5 \, \text{cm} \]

### Step 3: Calculate the wavelength (λ)
The distance between two successive nodes (or antinodes) is equal to half the wavelength (λ/2). Therefore, we can find the wavelength as follows:

\[ \frac{\lambda}{2} = d \implies \lambda = 2d = 2 \times 32.5 \, \text{cm} = 65 \, \text{cm} \]

### Step 4: Convert the wavelength to meters
Since we need the speed of sound in meters per second, we convert the wavelength from centimeters to meters:

\[ \lambda = 65 \, \text{cm} = 0.65 \, \text{m} \]

### Step 5: Calculate the speed of sound (v)
The speed of sound can be calculated using the formula:

\[ v = f \times \lambda \]

Substituting the values we have:

\[ v = 512 \, \text{Hz} \times 0.65 \, \text{m} = 332.8 \, \text{m/s} \]

### Step 6: Calculate the error in the speed of sound
The error in the calculated speed of sound is the difference between the actual speed of sound in air and the calculated speed:

\[ \text{Error} = \text{Actual speed} - \text{Calculated speed} = 330 \, \text{m/s} - 332.8 \, \text{m/s} = -2.8 \, \text{m/s} \]

### Step 7: Convert the error to centimeters per second
To express the error in centimeters per second:

\[ \text{Error} = -2.8 \, \text{m/s} = -280 \, \text{cm/s} \]

### Final Result
The error in calculating the velocity of sound is **-280 cm/s**.

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