Question

Transverse waves of the same frequency are generated in two steel wires A and B. The diameter of A is twice that of B and the tension in A is half that in B. The ratio of the velocities of waves in A and B is ____________.

पर्याय

• 1 : 2

• `1 : sqrt2`

• `1 : 2 sqrt2`

• `3 : 2 sqrt2`

Answer 1

Transverse waves of the same frequency are generated in two steel wires A and B. The diameter of A is twice that of B and the tension in A is half that in B. The ratio of the velocities of waves in A and B is `1 : 2 sqrt2`.

Explanation:

`"v"_"A"/"v"_"B" = sqrt ("T"_"A"/"T"_"B" xx "m"_"B"/"m"_"A"`

`"Let m" = "M"/"L" = ("AL"rho)/"L" = "A"rho Rightarrow "m" prop "r"^2`

`therefore "v"_"A"/"v"_"B" = sqrt ("T"_"A"/"T"_"B" xx "r"_"B"^2/"r"_"A"^2`

`= sqrt ("T"_"B"/(2"T"_"B") xx ("r"_"B"/(2"r"_"B"))^2`

`= 1/sqrt 8`

`= 1/2 sqrt2`