A wire having tension 225 N produces six beats per second when it vibrates with some tuning fork. When the tension changes to 256 N , it vibrates with the same fork with the number of beats remaining unchanged. The frequency of the fork will be

Step-by-step solution

For wire vibrating under tension, the fundamental frequency is given by f 1 = 1 2 L T μ   , Where T is tension and μ linear mass density of string It is given that, when it is sounded with a tuning fork of frequency x , 6 beats per second were heard ∴   x - f = 6 f 1 = 1 2 L 225 μ f 2 = 1 2 L 256 μ undefined ∴   x + 6 = 16 15 ( x - 6 ) ∴   15 x + 90 = 16 x - 96 ∴   x = 186   H z