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Stationary waves are set up on a rope of length 1.0 m fixed at both ends - AQA - A-Level Physics - Question 18 - 2020 - Paper 1

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Stationary waves are set up on a rope of length 1.0 m fixed at both ends. Which statement is not correct? A The first harmonic has a wavelength of 2.0 m. B The midp... show full transcript

Worked Solution & Example Answer:Stationary waves are set up on a rope of length 1.0 m fixed at both ends - AQA - A-Level Physics - Question 18 - 2020 - Paper 1

Step 1

A The first harmonic has a wavelength of 2.0 m.

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Answer

The length of the rope is 1.0 m. For the first harmonic (fundamental frequency), the wavelength (λ1\lambda_1) is equal to twice the length of the rope. Therefore, λ1=2L=2×1.0 m=2.0 m\lambda_1 = 2L = 2 \times 1.0 \text{ m} = 2.0 \text{ m}. This statement is correct.

Step 2

B The midpoint of the rope is always stationary for even-numbered harmonics.

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Answer

In even-numbered harmonics, the midpoint is indeed a node where there is no displacement, making this statement correct.

Step 3

C A harmonic of wavelength 0.4 m can be set up on the rope.

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The wavelengths for standing waves on a rope fixed at both ends can be calculated using the formula λn=2Ln\lambda_n = \frac{2L}{n}, where nn is the harmonic number. For n=5n = 5, the wavelength is λ5=2×1.05=0.4\lambda_5 = \frac{2 \times 1.0}{5} = 0.4 m. This statement is correct.

Step 4

D There are five nodes on the rope for the fifth harmonic.

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Answer

For the fifth harmonic, there are a total of 6 nodes (at each end and at 5 evenly spaced points along the length of the rope). Therefore, this statement is not correct.

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