Wave pulse can travel along a tense string like a violin spring. Aseries of experiments showed that the wave velocity V of a pulse depends on the following quantities, the tension T of the string, the

Question

Wave pulse can travel along a tense string like a violin spring. Aseries of experiments showed that the wave velocity V of a pulse depends on the following quantities, the tension T of the string, the cross-section area A of the string and then as per unit volume ρ of the string. Obtain an expression for V in terms of the T , A and ρ using dimensional analysis.

TestHub · Accepted Answer

Let V = kT a A b ρ c , k = dimensional constant Writing dimension on both we side [ LT − 1 ] ​ = [ MLT − 2 ] a [ L 2 ] b [ ML − 3 ] c = [ M a + c L a + 2 b − 3 c T − 2 a ] ​ Comparing power on both sides we have a + c = 0 , a + 2 b − 3 c = 1 , − 2 a = − 1 ∴ a = 2 1 ​ , c = − 2 1 ​ ⇒ b = − 2 1 ​ ∴ V = k A ρ T ​ ​ ​

Physics - Unit & Dimension Question with Solution | TestHub

Options:

Doubts & Discussion