The speed of a wave is determined by the product of its frequency and wavelength. Mathematically, the speed of a wave (v) is given by the equation:
v = f * λ
where: v = speed of the wave f = frequency of the wave λ = wavelength of the wave
If the frequency of a wave triples (becomes three times larger) and its wavelength doubles (becomes two times larger), let's denote the original frequency as f₀ and the original wavelength as λ₀.
According to the given information, we have: f = 3f₀ (frequency triples) λ = 2λ₀ (wavelength doubles)
To find the new speed of the wave (v'), we can substitute the new values into the wave speed equation:
v' = f * λ = (3f₀) * (2λ₀) = 6f₀λ₀
Therefore, the new speed of the wave (v') is six times the original speed (v₀). In other words, the speed of the wave increases by a factor of six.