If the frequency of a wave is doubled, what happens to its wavelength, assuming the speed of the wave remains constant?

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Q: If the frequency of a wave is doubled, what happens to its wavelength, assuming the speed of the wave remains constant?

Solution: According to the wave equation v = fλ, if frequency (f) is doubled and speed (v) remains constant, the wavelength (λ) must halve.

Steps: 6

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.