The equation for the vibration of a string fixed at both ends vibrating in its third harmonic is given by y=2 cm sin [(0.6 cm -1) x] cos [(500 π s-1) t]The length of the string is:

Question

The equation for the vibration of a string fixed at both ends vibrating in its third harmonic is given by y=2 cm sin [(0.6 cm -1) x] cos [(500 π s-1) t]The length of the string is: (A) 24.6 cm (B) 12.5 cm (C) 20.6 cm (D) 15.7 cm

Tardigrade Admin · Accepted Answer

Wave number K=(2 π/λ)=0.6 cm -1 ∴ (λ/2)=(π/0.6) cm ∴ l=(3 λ/2)=3((π/0.6)) cm =15.7 cm

Q. The equation for the vibration of a string fixed at both ends vibrating in its third harmonic is given by $y = 2 c m$ $sin [(0.6 c m^{- 1}) x] cos [(500 π s^{- 1}) t]$ The length of the string is:

24.6 cm

12.5 cm

20.6 cm

15.7 cm

Wave number $K = \frac{2 π}{λ} = 0.6 c m^{- 1}$
$∴ \frac{λ}{2} = \frac{π}{0.6} c m$
$∴ l = \frac{3 λ}{2} = 3 (\frac{π}{0.6}) c m$
$= 15.7 c m$

Q. The equation for the vibration of a string fixed at both ends vibrating in its third harmonic is given by y=2cm sin[(0.6cm−1)x]cos[(500πs−1)t]The length of the string is: