Question

Two strings A and B, made of same material, are stretched
by same tension. The radius of string A is double of radius
of B. A transverse wave travels on A with speed vA and on
B with speed vB. The ratio vA / vB is
(a) 1/2 (b) 2
(c) 1/4 (d) 4

Answer 1

Answer:

Velocity of a transverse wave in a stretched string v=  root of T / μ  

​  where T is the tension of the string and μ is mass per unit length of the string.

μ=πr ² ×ρ

where r is the radius or the string and ρ is the density of the material of the string.

∴v=  1 / r root (T/ πp )

​

Since T,ρ are constant

∴v∝  1/r

​  

 

v A/ vB = rB /rA = ( rB / 2rB) = 1/2

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