Which of the following actions will increase the frequency of the note played on a guitar string?

decreasing the tension in the string

increasing the mass of the string

Dimensional Formula of Intensity

The dimensional formula of Intensity is given by,

[M¹ L⁰ T^-3]

Where,

Intensity (I) = Power × [Area]^-1 . . . . . (1)

The dimensional formula of area = [M⁰ L² T⁰] . . . . (2)

Since, Power = Work × [Time]^-1 . . . . (3)

And, Work = Force × Displacement = M × a × Displacement

⇒ Work = [M] × [M⁰ L¹ T^-2] × [L]

Therefore, the dimensional formula of work = [M¹ L² T^-2] . . . . (4)

On substituting equation (4) in equation (3) we get,

Power = [M¹ L² T^-2] × [M⁰ L⁰ T¹]^-1

Therefore, the dimensional formula of power = [M¹ L² T^-3] . . . . (5)

On substituting equation (2) and (5) in equation (1) we get,

Intensity (I) = Power × [Area]^-1

Or, I = [M¹ L² T^-3] × [M⁰ L² T⁰]^-1 = [M¹ L⁰ T^-3]

Therefore, the time period is dimensionally represented as [M¹ L⁰ T^-3].