Velocity of sound (v) depends on pressure (P) density

Physics Units, Dimensions and Measurement Dimensions MCQ (Single Correct)

and frequency of sound (f). Then derive the relation among v, P, d & f by dimensional method.

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Sol. v ∝ P a d b f c

[M 0 L 1 T –1 ] = [M 1 L –1 T –2 ] a [M 1 L –3 T 0 ] b [M 0 L 0 T –1 ] c M

0 L 1 T –1 = M a+b L –a–3b T –2a–c a + b = 0 ....(1)

a – 3b = 1 ....(2)

–2a – c = –1 ....(3)

a = , b = – , c = 0

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