horizontal wire

Use equation, v^2 = T/p
where v is the speed of wave on the string, T is the string tension, and p is the linear density (mass per unit length) of the string.
hence, 492^2 = 97/p
p = 97/492^2 kg/m = 4.007 x 10^-4 kg/m

Average power carried by the wave along the string
= (1/2)pv(wA)^2
where w is the angular frequency of the wave, and A is the amplitude
Therefore, 0.37 = (1/2).(4.007x10^-4).(492).[(2.pi.65)A]^2
solve for A gives A = 4.74 x 10^-3 m