A string fixed at both ends is vibrating in its third harmonic. The equation for its vibration is given by y = (0.4 cm ) [(0.314 cm ⁻¹) x] [(600 s ⁻¹)t] . Determine the positions of the nodes.

Step-by-step solution

The equation of the standing wave is given by y = 0.4 (0.314 x) (600 t) . The amplitude of the wave at position x is A = 0.4 (0.314 x) . For nodes, the amplitude must be zero, which gives: (0.314 x) = 0 0.314 x = n , where n = 0, 1, 2, Using = 3.14 , we get: 0.314 x = n(3.14) x = 10n cm The positions of the nodes are x = 0, 10, 20, 30, cm . The wave number is k = 0.314 cm ⁻¹ , so the wavelength is = 2 k = 2 3.14 0.314 = 20 cm . Since the string is vibrating in its third harmonic, the length of the string is L = 3 (