A string 728 cm long with a mass of 255 g is under tension o

A string 72.8 cm long with a mass of 2.55 g is under tension of 322N. Find the lowest frequency (fundamental frequency) at which the string will vibrate. Find the next two higher frequecies at which it will vibrate.

Solution

Speed of a wave on string, v = sqroot(T/mu)
T = Tension in string = 322N
mu = mass/length = 0.00255kg / 0.728 m = 0.00350 kg / m
so, v = sqroot(322/0.00350) = 303.19 m/s

now, for fundamental frequency, f1
v = l * f1 / 2
f1 = 832.95 Hz

similiarly, v = l * f2
f2 = 416.46 Hz

similiarly, v = 3 * l * f3 / 2
f3 = 277.64 Hz