Length and Mass of the Wire:
Given:
Length of the wire, L = 0.5 m
Mass of the wire, m = 0.98 * 10^(-3) kg

Stretching Force:
The wire is stretched by a weight of 2 kg. We know that weight = mass * acceleration due to gravity.
Therefore, the stretching force, F = 2 kg * 9.8 m/s^2 = 19.6 N

Velocity of Transverse Wave:
The velocity of a transverse wave along a wire can be calculated using the formula:
v = √(F/μ)

Where,
v is the velocity of the transverse wave,
F is the stretching force, and
μ is the linear density of the wire.

Linear Density of the Wire:
The linear density, μ, of the wire can be calculated using the formula:
μ = m/L

Where,
m is the mass of the wire, and
L is the length of the wire.

Calculating the Linear Density:
μ = (0.98 * 10^(-3) kg) / (0.5 m) = 1.96 * 10^(-3) kg/m

Calculating the Velocity of Transverse Wave:
v = √(19.6 N / (1.96 * 10^(-3) kg/m))

Simplifying the equation:
v = √(10^4 m^2/s^2)

Taking the square root:
v = 100 m/s

Therefore, the velocity of the transverse wave along the wire is 100 m/s.

Fundamental Frequency:
The fundamental frequency of a wave is the lowest frequency at which the wave can oscillate. In the case of a wire, the fundamental frequency is given by:
f = (v/2L)

Where,
f is the fundamental frequency,
v is the velocity of the wave, and
L is the length of the wire.

Calculating the Fundamental Frequency:
f = (100 m/s) / (2 * 0.5 m)

Simplifying the equation:
f = 100 Hz

Therefore, the fundamental frequency of the wave is 100 Hz.

In conclusion, the velocity of the transverse wave along the wire is 100 m/s, and the fundamental frequency of the wave is 100 Hz.