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Year of the natural sciences course of the University of Cambridge

Year 1 of the natural sciences course of the University of Cambridge

Physics course of the year 1 of the natural sciences course of the University of Cambridge

Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge

2024

Paper 1

Section B

Use the dimensionless coordinate $u=x/L$:
$$
P=\int_{0.45}^{0.55}2\sin^2(2\pi u)\,du=\left[u-\frac{\sin4\pi u}{4\pi}\right]_{0.45}^{0.55}.
$$
Therefore
$$
\boxed{P=0.1-\frac{\sin(\pi/5)}{2\pi}=0.00645\simeq0.645\%.}
$$
The central interval surrounds a node, which explains why the <probability> is much smaller than its ten-percent share of the well's length.

Solution

Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2024 / Paper 1 / Section B / 9 / e / Solution

Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2024 / Paper 1 / Section B / 9 / e / Solution

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Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2024 / Paper 1 / Section B / 9 / e / Solution

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