Step-by-step explanation:
The velocity of the wave is:
v = (9.0π rad/s) / (0.1π / cm)
v = 90 cm/s
v = 0.9 m/s
Velocity of a standing wave on a stretched string is:
v = √(T / (m/L))
0.9 m/s = √(0.081 N / (M / 2.0 m))
0.81 m²/s² = 0.081 N / (M / 2.0 m)
M / 2.0 m = 0.1 kg/m
M = 0.2 kg