A tuning fork having a frequency of 512 Hz is vibrated alongside a sonometer wire, producing 6 beats per second. If the tension in the wire is slightly increased, the beat frequency decreases. Determine the original frequency of vibration of the wire.

Step-by-step solution

Let the frequency of the tuning fork be f_ t = 512 Hz . The beat frequency is n = 6 Hz . The frequency of the sonometer wire f_ w is given by f_ w = f_ t n . f_ w = 512 + 6 = 518 Hz or f_ w = 512 - 6 = 506 Hz . The frequency of a sonometer wire is directly proportional to the square root of tension ( f T ). When the tension in the wire is slightly increased, its frequency f_ w increases. If the original frequency was 518 Hz , increasing the tension would increase the frequency, resulting in a new beat frequency gre