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# CBSE Class 11-science Answered

frequency of vibration (n) of a stretched string depends on its length (l) , tension (t) and linear mass density taking proportionality constant k=½ find a relation between them
Asked by ss4172380 | 14 Nov, 2023, 08:05: AM
Let Frequency n la , where l is length of string and a is number .
Let Frequency n Tb , where T is tension force and b is number .
Let Frequency n mc , where m is linear mass density and c is number .

Hence we can write Frequency n as

n = k × l a × T b × m c .................... (1)

where k = 1/2 is proportionality constant .

Let M , L , T be the dimension symbol for mass, length and time respectively

Dimension of frequency = T-1

Dimension of length = M

Dimension of tension force = M L T-1/2

Dimension of linear mass density = mass / length = M L-1

Hence , if we apply dimensions to eqn.(1) , we get

By equating the respective exponents on both sides, we get

a + b - c = 0

b + c = 0

-2b = -1

By solving above equations , we get , a = -1 , b = 1/2 , c = -1/2

Hence , we rewrite eqn.(1) as

Answered by Thiyagarajan K | 14 Nov, 2023, 09:18: AM

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