If the frequency of a periodic wave is cut in half while the speed remains the same, what happens to the wavelength
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Ответ:
The wavelength becomes twice the original wavelength
Explanation:
Recall that for regular waves, the relationship between wavelength, velocity (i.e speed) and frequency is given by
v = fλ
where,
v = velocity,
f = frequency
λ = wavelength
Before a change was made to the frequency, we have: v₁ = f₁ λ₁
After a change was made to the frequency, we have: v₂ = f₂ λ₂
We are told that the speed remains the same, so
v₁ = v₂
f₁ λ₁ = f₂ λ₂ (rearranging this)
f₁ / f₂ = λ₂/λ₁ (1)
we are given that the frequency is cut in half.
f₂ = (1/2) f₁ (rearranging this)
f₁/f₂ = 2 (2)
if we substitute equation (2) into equation (1):
f₁ / f₂ = λ₂/λ₁
2 = λ₂/λ₁
λ₂ = 2λ₁
Hence we can see that the wavelength after the change becomes twice (i.e doubles) the initial wavelength.
Ответ: