Answer:
[tex]\dfrac{v_A}{v_B}=1.47[/tex]
Explanation:
given,
diameter of string A = 0.5 mm
tension in string A = 440 N
diameter of string B = 1 mm
tension in string B = 820 N
wave speed =
[tex]v = \sqrt{\dfrac{T}{M}}[/tex]
M is the linear density that is mass per unit length =mass / length
mass = density x volume
[tex]M = \dfrac{\pi r^2d}{l}[/tex]
[tex]v = \sqrt{\dfrac{T}{\pi r^2d}}[/tex]
from the above equation
[tex]v \alpha\ \sqrt{\dfrac{T}{ r^2}}[/tex]
now,
[tex]\dfrac{v_A}{v_B}=\sqrt{\dfrac{T_A}{ T_B}\times \dfrac{r_B^2}{r_A^2}}[/tex]
[tex]\dfrac{v_A}{v_B}=\sqrt{\dfrac{440}{820}\times \dfrac{1^2}{0.5^2}}[/tex]
[tex]\dfrac{v_A}{v_B}=1.47[/tex]
ratio of the wave speed Va/Vb is 1.47
