Question

The diagram in Figure 2 shows three identical strings that have been put under tension by suspending masses of 5 kg each. What is the wave speed for each of the figures in terms of the linear density ρ?

Figure 2. Strings under tension

Answer 1

wave speed = sqrt(T/mu) =sqrt(T/ ρ)

linear density ρ kg/meter

mu = mass per unit length = M/L =  ρ*L/L =  ρ

in one the string are holding a mass of 5 kg so T=5*9.8 N

in 3, two strings holding two masses of same mass, so T is again= 5*9.8 N

but in two two ropes are holding 5 kg so 2T=5*9.8 ,T=5*4.9 N

so finally wave speed  

wave speed = sqrt(T/mu) =sqrt(T/ ρ)  

and u alredy know T so u can find out wave speed in terms of ρ