Electromagnetic radiation (light) consists of waves. More than a century ago, scientists thought that light, like other waves, required a medium (called the ether) to support its transmission. Glass, having a typical mass density of ρ = 2770 kg/m3, also supports the transmission of light. What would the elastic modulus of glass have to be to support the transmission of light waves at a speed of v = 2.27 · 108 m/s? (For comparison: the actual elastic modulus of window glass is 5 · 1010 N/m2.)
To determine the required elastic modulus of glass to support the transmission of light waves, we can use the formula relating the speed of sound in a material to its density and elastic modulus.
The formula for the speed of sound in a material (v) is given by:
v = sqrt(E / ρ)
Where:
v is the speed of sound
E is the elastic modulus
ρ is the mass density
We are given that the speed of light (which travels at the same speed as electromagnetic waves) is v = 2.27 · 10^8 m/s, and the mass density of glass is ρ = 2770 kg/m^3.
Rearranging the formula, we can solve for the elastic modulus (E):
E = ρ * v^2
Plugging in the given values:
E = 2770 kg/m^3 * (2.27 · 10^8 m/s)^2
Calculating:
E ≈ 1.42 * 10^21 N/m^2
Therefore, the elastic modulus of glass would need to be approximately 1.42 * 10^21 N/m^2 to support the transmission of light waves at a speed of 2.27 · 10^8 m/s.
To determine the elastic modulus of glass required to support the transmission of light waves at a specific speed, we can use the relationship between the speed of a wave, the density of the medium, and the elastic modulus.
The speed of a wave in a medium is given by the equation:
v = √(E/ρ)
Where:
v = speed of the wave
E = elastic modulus of the medium
ρ = density of the medium
We can rearrange this equation to solve for the elastic modulus:
E = v^2 * ρ
Now, let's plug in the given values:
v = 2.27 * 10^8 m/s
ρ = 2770 kg/m^3
E = (2.27 * 10^8 m/s)^2 * 2770 kg/m^3
E = 12.99 * 10^19 N/m^2
Therefore, the elastic modulus of glass required to support the transmission of light waves at a speed of 2.27 * 10^8 m/s would need to be approximately 12.99 * 10^19 N/m^2.
It's important to note that this value is significantly higher than the actual elastic modulus of window glass (5 * 10^10 N/m^2). This suggests that glass alone is not solely responsible for the transmission of light waves and that other factors, such as the atomic structure of glass, play a significant role.