(a) A tuning fork produces `4` beats per second with another tuning fork of frequency `256 Hz`. The first one is now loaded with a little wax and the beat frequency is found to increase to `6` per second. What was the original frequency of the tuning fork ?
(b) A plano wire `A` vibrates at a fundamental frequncy of `600 Hz`. A second identical wire `B` produces `6` betas per second with it, when of the tension in `A` is slightly increased. Find the ratio of the tension in `A` to the tension to `B`.
( c) A tunnig fork if frequency `256 Hz` produces `4` beats per second with a wire of length `25 cm` vibrating in its fundamental mode. The beat frequency decreases when the length is slightly shortened. What could be the minimum length by whech the wire be shortened so that it produces no beats with the tuning fork?

Explanation

(a) Let the frequency of tuning fork is `x`.
The value of `x` may be `256 +- 4 = 260 Hz or 250 Hz`. Now this fork is loaded with wax, its frequency decreases but beat frequency increases. This is possible when frequency of tuning fork is `252 Hz`.
(b) `f prop sqrt(T)`
`(606)/(600) = sqrt((T_(A))/(T_(B))) rArr (T_(A))/(T_(B))`
`= (1 + (6)/(600))^(2)`
`= (1 + 0.01)^(2) - 1.02`
(c)

When length is make smaller, frequency of string increases `f prop 1//l`.
But beat frequency decreases i.e. frequency of string is `256 - 4 = 252 Hz`.
For no beat frequency, frequency of string should be `256 Hz`.
`(f_(1))/(f_(2)) = (l_(2))/(l_(1))`
`(252)/(256) = (l_(2)) / (25) rArr l_(2) = 24.6 cm`
Decrease in length `= 25 - 24.6 = 0.4 cm`