# The Speed of a transverse wave

1. Aug 9, 2010

### golriz

A copper wire, whose cross sectional area is 1.1 x 10 ^ -6 m^2, has a linear density of 7.0 x 10^-3 Kg/m and is strung between two walls. At the ambient temperature, a transverse wave travels with a speed of 46 m/s on this wire. The coefficient of linear expansion for copper is 17 x 10^-6 , and Youngs modulus for copper is 1.1 x 10^11 N/m^2. What will be the speed of the wave when the temperature is lowered by 14 C?

v = √(F/(m⁄L)) (1)
F = Y(∆L/L0)A (2)
∆L = α.L0.∆T ⇒ ∆L/L0 = α.∆T (3)

A = 1.1 x 10^-6 m^2
m/L = 7 x 10^-3 Kg/m
α = 17 x 10^-6
Y = 1.1 x 10^11 N/m^2
v = 46 m/s

We can write formula (1) such this:

v = √((Y.α.∆T.A)/(m/L))

and now substitute all the variables in the above formula for finding ∆T.
But now I don't know what do I have to do, ∆T2 to find the speed of the wave.

2. Aug 11, 2010

### Andrew Mason

Work out the initial tension in the wire. Then work out the tension after cooling 14 deg. Think of the wire shrinking due to the decrease in temperature but additional tension stretches it back to the original length.

AM