Physics, asked by npadwaith44, 3 months ago

The dimension of frequency , force constant , wavelength

Answers

Answered by hukamsingh8448
1

Answer:

The dimensional formula of Frequency is given by,

[M0 L0 T-1]

Where,

M = Mass

L = Length

T = Time

Derivation

Frequency (v) = number of vibrations × sec-1 . . . . . (1)

The dimensional formula of time = [M0 L0 T1] . . . . (2)

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

Frequency = number of vibrations × sec-1

Or, v = [M0 L0 T1]

Therefore, frequency is dimensionally represented as [M0 L0 T1].

Answered by renuthakur3333
3

Answer:

1. Frequency:- The dimensional formula of Frequency is given by,

[M0 L0 T-1]

Where,

M = Mass

L = Length

T = Time

Derivation

Frequency (v) = number of vibrations × sec-1 . . . . . (1)

The dimensional formula of time = [M0 L0 T1] . . . . (2)

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

Frequency = number of vibrations × sec-1

Or, v = [M0 L0 T1]

Therefore, frequency is dimensionally represented as [M0 L0 T1].

2. force constant:- The dimensional formula of energy density is given by,

[M1 L0 T-2]

Where,

M = Mass

L = Length

T = Time

Derivation

Force Constant= Force × [Displacement]-1 . . . (1)

Since, Force = m × a

Therefore, the dimensions of force = [M1 L1 T-2] . . . (2)

And, the dimensional formula of displacement = [M0 L1 T0] . . . . (3)

On substituting equation (2) and (3) in equation (1) we get,

Force Constant= Force × [Displacement]-1

= [M1 L1 T-2] × [M0 L1 T0]-1 = [M1 L0 T-2].

Therefore, the energy density is dimensionally represented as [M1 L0 T-2].

3. wavelength:- The dimensional formula of wavelength is given by,

[M0 L1 T0]

Where,

M = Mass

L = Length

T = Time

Derivation

Wavelength = Distance between identical points in the adjacent cycles of a waveform

Since, the dimensional formula of distance = [M0 L1 T0]

Therefore, the wavelength is dimensionally represented as [M0 L1 T0].

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