The Equation for the vibration of a string fixed at both ends vibrating in its third harmonic is given by y=2sin(0.6x)cos(500t) ( x, y are in cm 't' is in sec). The length of the string is.

Third harmonic = Three loops ∴  Length of wire = 3 (length of each loop)l=3(λ2)=32λ y=2sin(0.6x)cos(500πt) y=2Asin(kx)cos(ωt) On comparing2πλ=0.6   (∵k=2πλ) ⇒λ=2π0.6=10π3 ∴  Length of the stringl=32λ =32(10π3) ∴ l=15.7 cm