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Question

The diagram shows waves set up in a rope by a student moving the free end up and down at a steady rate. What is the wavelength of the waves shown, and what will be the wavelength when the student doubles the frequency at which the free end is moved up and down?

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A
Wavelength as shown- 0.50m , Wavelength when frequency doubled- 1.00m
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B
Wavelength as shown- 0.50m, Wavelength when frequency doubled- 0.50m
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C
Wavelength as shown- 1.00m, Wavelength when frequency doubled- 1.00m
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D
Wavelength as shown- 1.00m, Wavelength when frequency doubled- 0.50m
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Solution

The correct option is D Wavelength as shown- 1.00m, Wavelength when frequency doubled- 0.50m
Answer is D - 4.

Wavelength is the distance between two successive points on a wave that are in the same state of oscillation.
The frequency of a wave is the number of full wave forms generated per second. This is the same as the number of repetitions per second or the number of oscillations per second.
For a particular distance, if the frequency is doubled, the wavelength will be decreased by half.
Hence, when the wavelength is 1.00 m, and the frequency is doubled, the wavelength becomes 1/2 = 0.50 m.

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