If the frequency of a wave is halved, what happens to its wavelength? (2015)

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Question: If the frequency of a wave is halved, what happens to its wavelength? (2015)

Options:

Correct Answer: Doubles

Solution:

Wavelength is inversely proportional to frequency. If frequency is halved, wavelength doubles.

If the frequency of a wave is halved, what happens to its wavelength? (2015)

If the frequency of a wave is halved, what happens to its wavelength? (2015)

Step 1: Understand that frequency and wavelength are related in a wave.
Step 2: Remember the formula that connects frequency (f) and wavelength (λ): Speed of wave (v) = Frequency (f) × Wavelength (λ).
Step 3: If the frequency is halved, it means the new frequency is f/2.
Step 4: Since the speed of the wave remains constant, we can rewrite the formula: v = (f/2) × λ'.
Step 5: To find the new wavelength (λ'), rearrange the formula: λ' = v / (f/2) = (2v) / f.
Step 6: This shows that the new wavelength (λ') is double the original wavelength (λ).
Step 7: Therefore, if the frequency is halved, the wavelength doubles.

Wave Properties – Understanding the relationship between frequency and wavelength, specifically that they are inversely proportional.