The frequency of a wave is doubled. How does this affect its wavelength if the speed of the wave remains constant? (2022)

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Q: The frequency of a wave is doubled. How does this affect its wavelength if the speed of the wave remains constant? (2022)

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

Steps: 8

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 in this question, the speed (v) of the wave remains constant.
Step 3: Note that the frequency (f) of the wave is doubled, meaning it becomes 2f.
Step 4: Substitute the new frequency into the wave equation: v = (2f)λ.
Step 5: Since the speed (v) is constant, we can set the original equation equal to the new one: fλ = (2f)λ'.
Step 6: Cancel out f from both sides (assuming f is not zero): λ = 2λ'.
Step 7: Rearrange the equation to find the new wavelength: λ' = λ/2.
Step 8: Conclude that if the frequency is doubled and the speed remains constant, the wavelength must halve.