The frequency of vibration of a string depends of on, (i) tension in t

1.	The frequency of vibration of a string depends of on, (i) tension in the string (ii) mass per unit length of string, (iii) vibrating length of the string. Establish dimensionally the relation for frequency.
Answer» n ∝ I^a T^b m^c , [I] = M⁰L¹T⁰ [T] = M¹ L¹ T^–2 (force) [M] = M¹L^–1 T⁰ [M⁰L⁰T^–1] = [M⁰ L¹ T⁰]^a [M¹ L¹ T^–2]^b [M¹ L^–1 T⁰]^c b + c = 0 a + b – c = 0 - 2b = -1 => b = 1/2 c = - 1/2 a = 1 n ∝ 1/l √T/m.

The frequency of vibration of a string depends of on, (i) tension in the string (ii) mass per unit length of string, (iii) vibrating length of the string. Establish dimensionally the relation for frequency.

Answer»

n ∝ I^a T^b m^c , [I] = M⁰L¹T⁰

[T] = M¹ L¹ T^–2 (force)

[M] = M¹L^–1 T⁰

[M⁰L⁰T^–1] = [M⁰ L¹ T⁰]^a [M¹ L¹ T^–2]^b [M¹ L^–1 T⁰]^c

b + c = 0

a + b – c = 0

- 2b = -1 => b = 1/2

c = - 1/2 a = 1

n ∝ 1/l √T/m.