The speed of a wave doubles as it passes from one medium to the next. How will this affect the frequency of the wave?
speed = wavelength*frequency
So, if speed doubles you know nothing about the frequency.
If the wavelength is unchanged, then the frequency doubles.
But, if the wavelength doubles, the frequency remains unchanged.
To understand how the speed of a wave affects its frequency, we need to know the relationship between speed, frequency, and wavelength.
The speed of a wave (v) is given by the formula: v = λf
where λ represents the wavelength of the wave, and f represents the frequency of the wave.
If the speed of a wave doubles while passing from one medium to another, it means that v₂ = 2v₁, where v₁ is the initial speed of the wave and v₂ is the final speed.
Substituting these values into the formula, we get:
2v₁ = λf
Now, let's consider the relationship between frequency and wavelength. For a wave, the product of its frequency and wavelength is constant (c) when the wave is traveling in a single medium. Mathematically, this can be represented as:
λ₁f₁ = c
If the frequency (f₁) remains constant, but the speed doubles (2v₁), we can rewrite the equation as:
λ₂f₁ = 2v₁
We know that 2v₁ = λf (from the initial equation), so substituting this value into the new equation:
λ₂f₁ = λf
Now, it is clear that the wavelength (λ₂) of the wave passing through the new medium is the same as the wavelength (λ) in the initial medium, since it is constant. Therefore, the frequency (f₁) of the wave passing through the new medium will also remain the same as the initial frequency (f).
In conclusion, when the speed of a wave doubles as it passes from one medium to another, the frequency of the wave remains unchanged.