The dimension of frequency , force constant , wavelength
Answers
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].
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].