The Speed of a transverse wave

In summary, a copper wire with a cross sectional area of 1.1 x 10^-6 m^2 and a linear density of 7.0 x 10^-3 Kg/m 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. By using formulas for wave speed and tension, we can calculate the speed of the wave when the temperature is lowered by 14 C. To find the speed, we must first calculate the initial tension in the wire and then
  • #1
golriz
43
0
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.
 
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  • #2
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
 

What is the definition of the speed of a transverse wave?

The speed of a transverse wave is the rate at which the wave moves through a medium in a transverse direction, perpendicular to the direction of the wave's propagation.

How is the speed of a transverse wave calculated?

The speed of a transverse wave can be calculated using the equation v = fλ, where v is the speed, f is the frequency, and λ is the wavelength of the wave.

What factors affect the speed of a transverse wave?

The speed of a transverse wave is affected by the properties of the medium it is traveling through, such as density, elasticity, and temperature. It is also affected by the frequency and wavelength of the wave.

What is the relationship between the speed of a transverse wave and its frequency and wavelength?

The speed of a transverse wave is directly proportional to its frequency and inversely proportional to its wavelength. This means that as the frequency increases, the speed of the wave also increases, while a longer wavelength results in a slower wave speed.

Why is the speed of a transverse wave important to understand in science?

The speed of a transverse wave is important because it affects many aspects of wave behavior, including how waves interact with each other and how they propagate through different mediums. It is also a fundamental concept in understanding the properties of light, sound, and other types of waves.

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