A steel wire with mass per unit length `7.0times10^(-3)kgm^(-1)` is under tension of `70N`.The speed of transverse waves in the wire will be

Options

A. `10 m//s`
B. ` 100 m//s`
C. `200pi m//s`
D. `50 m//s

Answer

To find the speed of transverse waves in a steel 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.

### Step 1: Identify the given values
- Mass per unit length \( \mu = 7.0 \times 10^{-3} \, \text{kg/m} \)
- Tension \( T = 70 \, \text{N} \)

### Step 2: Substitute the values into the formula
Now we can substitute the values into the formula for the speed of the wave:

\[ v = \sqrt{\frac{70 \, \text{N}}{7.0 \times 10^{-3} \, \text{kg/m}}} \]

### Step 3: Simplify the expression
Calculate the fraction inside the square root:

\[ \frac{70}{7.0 \times 10^{-3}} = \frac{70}{7.0} \times \frac{1}{10^{-3}} = 10 \times 10^{3} = 10^{4} \]

### Step 4: Calculate the speed
Now we take the square root:

\[ v = \sqrt{10^{4}} = 10^{2} = 100 \, \text{m/s} \]

### Final Answer
Thus, the speed of transverse waves in the wire is:

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