Question

Fundamental frequencies problem. The beat frequency is ωbeat = |ω1−ω2|. In the experiment, you measure periods. Re-express the beat period in terms of the fundamental periods T1 and T2/, Which of the following expressions is correct?

A.Tbeat = T1 T2 / (T2 − T1) B.Tbeat = T1 T2 / 2 π T2 − T1 C.Tbeat = 2 π T2 − T1 / T1 T2 D.Tbeat = T2 − T1 / T1 T2

Answer 1

Step-by-step explanation:

The beat frequency is given by :

`\omega_(beat)=|\omega_1-\omega_2|`..........(1)

`\omega=(2\pi)/(T)`

Where

T is the time period

Equation (1) becomes :

`(2\pi)/(T_(beat))=(2\pi)/(T_1)-(2\pi)/(T_2)`

`(1)/(T_(beat))=(1)/(T_1)-(1)/(T_2)`

`(1)/(T_(beat))=(T_2-T_1)/(T_1T_2)`

`T_(beat)=(T_1T_2)/(T_2-T_1)`

So, the correct option is (a) "
`T_(beat)=(T_1T_2)/(T_2-T_1)`". Hence, this is the required solution.