A string fixed at both ends is vibrating in its fundamental mode at a frequency of 25 Hz . The speed of the transverse waves on the string is 100 m s ⁻¹ . If the linear mass density of the string is 12 g m ⁻¹ , the total mass of the string is _______ g .

Step-by-step solution

The frequency of the fundamental mode is f = 25 Hz and the wave speed is v = 100 m s ⁻¹ . The wavelength of the transverse wave is: = v f = 100 25 = 4 m For a string fixed at both ends vibrating in its fundamental mode, the length l of the string is: l = 2 = 4 2 = 2 m Given the linear mass density = 12 g m ⁻¹ , the total mass m of the string is: m = l = 12 2 = 24 g Answer: 24