Given: \(m=0.04 kg , l=0.80 cm\),
\(f=4.0 Hz\),
speed of a transverse wave in string is given by
\(v=\sqrt{\frac{T}{\mu}}---(1)\)
also, \(f=\frac{1}{2 /} \sqrt{\frac{T}{\mu}}\)
\(f=\frac{1}{2 l} \sqrt{\frac{T}{\mu}}\)ross multiply
\(2 f l=\sqrt{\frac{T}{\mu}}--(2)\)
substitute for \(V\) in (1) i.e
$$
V=2 f=2 \times 40 \times 0.8=64 m / s
$$
Or
alternatively, if the string vibrates in fundamental mode, we have $$
l=\frac{\lambda}{2}=0.8, \lambda=2 \times 0.8=1.6 m
$$
but \(v=f \lambda\)
$$
v=40 \times 1.6=64 m / s
$$