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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

Respuesta :

Explanation:

The beat frequency is given by :

[tex]\omega_{beat}=|\omega_1-\omega_2|[/tex]..........(1)

[tex]\omega=\dfrac{2\pi}{T}[/tex]

Where

T is the time period

Equation (1) becomes :

[tex]\dfrac{2\pi}{T_{beat}}=\dfrac{2\pi}{T_1}-\dfrac{2\pi}{T_2}[/tex]

[tex]\dfrac{1}{T_{beat}}=\dfrac{1}{T_1}-\dfrac{1}{T_2}[/tex]

[tex]\dfrac{1}{T_{beat}}=\dfrac{T_2-T_1}{T_1T_2}[/tex]

[tex]T_{beat}=\dfrac{T_1T_2}{T_2-T_1}[/tex]

So, the correct option is (a) "[tex]T_{beat}=\dfrac{T_1T_2}{T_2-T_1}[/tex]". Hence, this is the required solution.

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