Answer:
The speed of the wave on the longer wire is 580m/s
Explanation:
The velocity possessed by a stretched string is directly proportional to the tension in the string and inversely proportional to the mass per unit length of the string. Mathematically,
V = √T/m
Where V is the velocity of wave in the wire
T is the tension in the wire
M is the mass per unit length of the wire
Let m1 and m2 be the mass per unit length of the wires
Let T1 and T2 be their respective tensions
Since the tension and mass of the wire is the same
m1= m2= m.
T1=T2=T
Let m1 =M/l
m2 =M/4l( since the second is tour times as far apart)
V1 = 290m/s(velocity in shorter wire)
V2 is the velocity of the longer wire.
V1 = √T/(m/l)
290 = √Tl/m
290² = Tl/m... 1
V2 = √4Tl/m
V2²= 4Tl/m... 2
Dividing equation 1 by 2 we have;
290²/V2² = {Tl/m}/{4Tl/m}
290²/V2² = Tl/m × m/4Tl
290²/V2² = 1/4
Cross multiplying we have;
V2² = 290²×4
V2 = √290²×4
V2 = 290×2
V2 = 580m/s
