The ratio of frequencies of three different sounds in the same medium is 1:2:3.
The relationship between frequency (f), wavelength (λ), and the speed of sound (v) in a medium is given by the equation:
v = f × λ
Since the speed of sound remains constant within a medium, we can conclude that the product of frequency and wavelength will be constant for each sound wave.
Let's assume the ratio of wavelengths for the three sounds is a:b:c. Then we have:
(1f) × (aλ) = (2f) × (bλ) = (3f) × (cλ)
Simplifying, we can cancel out the common factor of f:
aλ = 2bλ = 3cλ
Now, let's cancel out the common factor of λ:
a = 2b = 3c
Therefore, the ratio of wavelengths for the three different sounds will be 1:2:3, which is the same as the ratio of their frequencies.