1. Given data

• Linear mass density: $\mu = 9.8\,\text{g/m} = 9.8 \times 10^{-3}\,\text{kg/m}$
• Tension: $T = 10\,\text{kg-wt} = 10g\,\text{N} = 98\,\text{N}$
• Length of wire between supports: $L = 1\,\text{m}$

2. Wave speed on the stretched wire

The transverse wave speed is $v = \sqrt{\frac{T}{\mu}}$

Substitute the values: $v = \sqrt{\frac{98}{9.8\times 10^{-3}}}$

$v = \sqrt{10000} = 100\,\text{m/s}$

3. Natural frequencies of the wire

For a string fixed at both ends, $f_m = \frac{m v}{2L}, \qquad m=1,2,3,\dots$

So the fundamental frequency is $f_1 = \frac{100}{2\times 1} = 50\,\text{Hz}$

4. Effect of alternating current in magnetic field

The wire passes through the magnetic field at its middle point. The magnetic force on the wire is proportional to the current: $F \propto I$

Since the current is alternating with frequency $n$, the driving force also has frequency $n$.

Resonance occurs when the driving frequency equals a natural frequency of the wire. Since the wire is driven at its middle point, the strongest resonance is with the fundamental mode, whose antinode is at the center.

Hence, $n = 50\,\text{Hz}$

5. Check options

• A: $50\,\text{Hz}$ ✅
• B: $100\,\text{Hz}$ ❌
• C: $200\,\text{Hz}$ ❌
• D: $25\,\text{Hz}$ ❌

Therefore, the correct answer is A.