A plano creates sound by gently strinking a taut wire with a soft hammer when a key on the piano is pressed.All piano wires in a given piano are approximately the same length.However, each wire is tied down at two points.the bridge and the giraffe. The length of the wire between the bridge and the agraffe is called the speaking length.The speaking length is the part of the wire that resonates.The point of the wire struck by the hammer is displaced perpendicularly to the wire's length.A standing wave is generated by the hammer strike, where v is the velocity of travelling wave.T is the tension in the wire, and `mu` is the mass per unit length of the wire.
`v=sqrt(T/mu)`
Tuning a piano involves adjustment of the tension in the wires until just the right pitch is achieved.Correct pitch is achieved by listening to the beat frequency between the piano and a precalibrated tuning fork.
A piano note is compared to a tuning fork vibrating at 440 Hz.Three beats per second are listened by the piano tunner.When the tension in the string is increased slightly, the beat frequency increases.What was the initial frequency of the piano wire ?

Options

A. 434 Hz
B. 437 Hz
C. 443 Hz
D. 446 Hz

Explanation

`f prop sqrtT`
So `Deltaf` increases by increasing T.
i.e. `f_2=f_1+3=443 Hz]`