Question

Two strings A and B of same material are stretched by same tension. The radius of the string A is double the radius of string B. Transverse wave travels on string A with speed 'V_A' and on string B with speed 'V_B'. The ratio `"V"_"A"/"V"_"B"` is ______.

Options

• `1/4`

• `1/2`

• 2

• 4

Answer 1

Two strings A and B of same material are stretched by same tension. The radius of the string A is double the radius of string B. Transverse wave travels on string A with speed 'V_A' and on string B with speed 'V_B'. The ratio  `"V"_"A"/"V"_"B"` is `1/2`.

Explanation:

Velocity of transverse wave on string, `"V" alpha 1/"r"`

∴ `"V" _"A" alpha  1/"r"_"A"`    ...(i)

 `"V" _"B" alpha  1/"r"_"B"` ....(ii)

Divide equation (i) by eqLiation (ii)

∴ `"V" _"A"/ "V" _"B" = "r"_"B"/"r"_"A" = "r"_"B"/(2"r"_"B")` ...`(∵"r"_"A"= 2"r"_"B")`

∴ `"V" _"A"/ "V" _"B" =1/2`