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In the diagram, P is the source of a wave of frequency 50 Hz - AQA - A-Level Physics - Question 15 - 2018 - Paper 1

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In the diagram, P is the source of a wave of frequency 50 Hz. The wave travels to R by two routes, P → Q → R and P → R. The speed of the wave is 30 m s⁻¹. What is ... show full transcript

Worked Solution & Example Answer:In the diagram, P is the source of a wave of frequency 50 Hz - AQA - A-Level Physics - Question 15 - 2018 - Paper 1

Step 1

Calculate the wavelength of the wave

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Answer

The wavelength (λ) can be calculated using the formula:

ext{wavelength} = rac{ ext{speed}}{ ext{frequency}} = rac{30 ext{ m/s}}{50 ext{ Hz}} = 0.6 ext{ m}

Step 2

Calculate the distances for both paths

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Answer

  1. The distance for the path P → Q → R:

    • PQ = 20 m
    • QR = 18 m
    • Distance = 20 m + 18 m = 38 m

  2. The distance for the path P → R:

    • PR = 30 m

Step 3

Calculate the path difference

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Answer

The path difference (Δd) between the two paths is:

extPathdifference=∣38extm−30extm∣=8extm ext{Path difference} = |38 ext{ m} - 30 ext{ m}| = 8 ext{ m}

Step 4

Express the path difference in terms of wavelength

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Answer

To express the path difference in terms of wavelength, we can do the following:

ext{Path difference in λ} = rac{8 ext{ m}}{0.6 ext{ m}} = rac{80}{6} = 13.33λ

Thus, the path difference can be said to be approximately 13.3λ.

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