A tuning fork with a frequency of 440 Hz is connected to a long string having a linear mass density of 0.01 kg m ⁻¹ and maintained under a tension of 49 N . The tuning fork generates transverse waves with an amplitude of 0.50 mm along the string. Determine the maximum speed and acceleration of a particle on the string.

Step-by-step solution

Given: Frequency of the tuning fork, f = 440 Hz Amplitude of the transverse wave, A = 0.50 mm = 0.50 10⁻³ m The angular frequency of the wave is: = 2 f = 2 440 = 880 rad s ⁻¹ The maximum speed of a particle on the string is given by: v_ max = A v_ max = (0.50 10⁻³ m ) (880 rad s ⁻¹) = 0.44 m s ⁻¹ v_ max 1.38 m s ⁻¹ 1.4 m s ⁻¹ The maximum acceleration of a particle on the string is given by: a_ max = A ^2 a_ max = v_ max = 0.44 880 3824 m s ⁻² a_ max 3.8 km s ⁻² The values of tension and linear mass density are not