If the frequency of a wave is doubled, what happens to its wavelength, assuming the speed of the wave remains constant?
Correct Answer: Wavelength will be halved.
- Step 1: Understand the wave equation, which is v = fλ, where v is the speed of the wave, f is the frequency, and λ is the wavelength.
- Step 2: Identify that if the frequency (f) is doubled, it means f becomes 2f.
- Step 3: Since the speed (v) of the wave remains constant, we can rewrite the equation as v = (2f)λ.
- Step 4: To keep the equation balanced, if frequency is doubled, the wavelength (λ) must change to maintain the same speed.
- Step 5: Rearranging the equation gives us λ = v / (2f). This shows that the new wavelength is half of the original wavelength.
- Step 6: Conclude that if the frequency is doubled, the wavelength must halve.
- Wave Equation – The relationship between wave speed (v), frequency (f), and wavelength (λ) is described by the equation v = fλ.
- Inverse Relationship – There is an inverse relationship between frequency and wavelength when wave speed is constant.
