The tension produced in a sonometer wire is 60 N and the length between two bridges is 40 cm. The length of wire is 1 m and the mass of the wire is 2g. The speed of transverse waves produced in the wire is

Options

A. 100 m/s
B. 173.2 m/s
C. 200 m/s
D. 150 m/s

Explanation

To find the speed of transverse waves produced in the sonometer wire, we can follow these steps:

### Step 1: Identify the given values
- Tension (T) = 60 N
- Length between two bridges (L) = 40 cm = 0.4 m
- Length of the wire = 1 m
- Mass of the wire = 2 g = 2 × 10^(-3) kg

### Step 2: Calculate the mass per unit length (μ)
The mass per unit length (μ) can be calculated using the formula:
\[ \mu = \frac{\text{mass}}{\text{length of wire}} = \frac{2 \times 10^{-3} \text{ kg}}{1 \text{ m}} = 2 \times 10^{-3} \text{ kg/m} \]

### Step 3: Calculate the frequency (f)
The frequency of the wave can be calculated using the formula:
\[ f = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \]
Substituting the values:
- \(L = 0.4 \text{ m}\)
- \(T = 60 \text{ N}\)
- \(\mu = 2 \times 10^{-3} \text{ kg/m}\)

\[ f = \frac{1}{2 \times 0.4} \sqrt{\frac{60}{2 \times 10^{-3}}} \]

Calculating the square root:
\[ \sqrt{\frac{60}{2 \times 10^{-3}}} = \sqrt{30000} \approx 173.2 \]

Now substituting this value back into the frequency formula:
\[ f = \frac{1}{0.8} \times 173.2 \approx 216.5 \text{ Hz} \]

### Step 4: Calculate the wavelength (λ)
The wavelength (λ) in a sonometer wire is given by:
\[ \lambda = 2L = 2 \times 0.4 = 0.8 \text{ m} \]

### Step 5: Calculate the speed of the wave (v)
The speed of the wave can be calculated using the formula:
\[ v = f \cdot \lambda \]
Substituting the values:
\[ v = 216.5 \text{ Hz} \times 0.8 \text{ m} \approx 173.2 \text{ m/s} \]

### Final Answer
The speed of the transverse waves produced in the wire is approximately **173.2 m/s**.

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