vibration cycles in the third harmonic

Question

a 144 cm long rope undergoes exactly 64 complete vibrational cycles in 17.6 seconds when vibrating in the third harmonic ( in 3 equal length sections). determine the speed of the waves in the rope.

Answer 1

When vibrating in the 3rd harmonic mode, there are 3/2 wavelengths along the length of the rope.

 

(3/2)λ = L ⇒ 

 

λ = (2/3)L

 

L = 144 cm

 

T = (17.6 s)/64 = 0.275 s

 

v = λ/T = (2/3)L/T = (2/3)(144 cm)/(0.275 s) ≅ 349.1 cm/s