AS A WAVE TRAVELS FROM ONE MEDIUM TO ANOTHER, ITS WAVELENGTH TRIPLES. WHAT IS THE SPEED AND FREQUENCY IN THE NEW MEDIUM?
To find the speed and frequency in the new medium, we first need to understand the relationship between wavelength, frequency, and speed of a wave. The equation that relates these three quantities is:
v = fλ
where:
v = speed of the wave
f = frequency of the wave
λ = wavelength of the wave
Given that the wavelength triples as the wave travels from one medium to another, we can say that the ratio of the wavelength in the new medium to the wavelength in the original medium is 3. Therefore, λnew = 3λoriginal.
Since the speed of a wave is constant in a vacuum, we can say that the speed of the wave remains the same in both media. Let's denote the speed in the original and new medium as voriginal and vnew, respectively.
From the equation v = fλ, we can rewrite it as f = v/λ.
For the original medium:
foriginal = voriginal/λoriginal
For the new medium:
fnew = vnew/λnew
= vnew/(3λoriginal)
Since the speed of the wave remains the same in both media, we can set vnew = voriginal.
Therefore, fnew = voriginal/(3λoriginal)
= foriginal/3
This means that the frequency in the new medium is one-third of the frequency in the original medium.