A wire is stretched between two posts. Another wire is stretched between two posts that are four times as far apart. The tension in the wires is the same, and they have the same mass. A transverse wave travels on the shorter wire with a speed of 290 m/s. What would be the speed of the wave on the longer wire?

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