A wire is stretched between two posts. Another wire is stretched between two posts that are twice 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 249 m/s. What would be the speed of the wave on the longer wire?

Answer: 996m/s

Explanation:

Formula for calculating velocity of wave in a stretched string is

V = √T/M where;

V is the velocity of wave

T is tension

M is the mass per unit length of the wire (m/L)

Since the second wire is twice as far apart as the first, it will be L2 = 2L1

Let V1 and V2 be the speed of the shorter and longer wire respectively

V1 = √T/M1 ... 1

V2 = √T/M2 ... 2

Since V1 = 249m/s, M1 = m/L1 M2 = m/L2 = m/2L1

The equations will now become

249 = √T / (m/L1) ... 3

V2 = √T / (m/2L1) ... 4

From 3,

249² = TL1/m ... 5

From 4,

V2² = 2TL1/m ... 6

Dividing equation 5 by 6 we have;

249²/V2² = TL1/m*m/2TL1

{249/V2}² = 1/2

249/V2 = (1/2) ²

249/V2 = 1/4

V2 = 249*4

V2 = 996m/s

Therefore the speed of the wave on the longer wire is 996m/s