Calculate the speed of a transverse wave in a wire of `1.0 mm^(2)` cross-section under a tension of `0.98 N`. Density of the material of wire is `9.8 xx 10^(3) kg//m^(3)`

Explanation

To calculate the speed of a transverse wave in a wire, we can use the formula:

\[ v = \sqrt{\frac{T}{\mu}} \]

where:
- \( v \) is the speed of the wave,
- \( T \) is the tension in the wire,
- \( \mu \) is the mass per unit length of the wire.

The mass per unit length \( \mu \) can be calculated using the formula:

\[ \mu = \rho \cdot A \]

where:
- \( \rho \) is the density of the material of the wire,
- \( A \) is the cross-sectional area of the wire.

### Step 1: Identify the given values
- Tension \( T = 0.98 \, \text{N} \)
- Density \( \rho = 9.8 \times 10^3 \, \text{kg/m}^3 \)
- Cross-sectional area \( A = 1.0 \, \text{mm}^2 = 1.0 \times 10^{-6} \, \text{m}^2 \)

### Step 2: Calculate the mass per unit length \( \mu \)
Using the formula \( \mu = \rho \cdot A \):

\[ \mu = (9.8 \times 10^3 \, \text{kg/m}^3) \cdot (1.0 \times 10^{-6} \, \text{m}^2) \]

Calculating \( \mu \):

\[ \mu = 9.8 \times 10^{-3} \, \text{kg/m} \]

### Step 3: Substitute \( T \) and \( \mu \) into the wave speed formula
Now we can substitute \( T \) and \( \mu \) into the wave speed formula:

\[ v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{0.98 \, \text{N}}{9.8 \times 10^{-3} \, \text{kg/m}}} \]

### Step 4: Calculate the speed \( v \)
Calculating the value inside the square root:

\[ v = \sqrt{\frac{0.98}{9.8 \times 10^{-3}}} \]

Calculating the division:

\[ \frac{0.98}{9.8 \times 10^{-3}} = 100 \]

Now taking the square root:

\[ v = \sqrt{100} = 10 \, \text{m/s} \]

### Final Answer
The speed of the transverse wave in the wire is:

\[ \boxed{10 \, \text{m/s}} \]