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
Question 18
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) is equal to twice the length of the rope. Therefore, λ1=2L=2×1.0 m=2.0 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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Answer
The wavelengths for standing waves on a rope fixed at both ends can be calculated using the formula λn=n2L, where n is the harmonic number. For n=5, the wavelength is λ5=52×1.0=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.