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IGCSE · 3 · structured

Waves · Question 7

Waves · Original GioPhysics question with a detailed, mark-by-mark answer guide.

Demand
demanding
Marks
7
Topics
1
Answer
Complete
Straight water waves meeting the boundary of a shallow region30°boundarydeep watershallow water
Fig. 7.1Plan view of the ripple tank, seen from above. A straight boundary runs right across the tank, dividing it into deep water in the upper part and shallow water in the lower part, each region labelled. Twelve straight parallel wavefronts, evenly spaced, fill the deep water and slope up to the right so that each one makes an angle of 30° with the boundary; that angle is marked with an arc where one front meets the boundary. The shallow region is drawn empty.
structured7 marks

Straight water waves in a ripple tank travel from a deep region into a shallow region. The boundary between the regions is a straight line, and the wavefronts meet it at 30° to the boundary. In the deep region the waves have a wavelength of 1.8 cm and a frequency of 8.0 Hz. In the shallow region the wavelength is 1.2 cm.

  1. (a)

    Calculate Calculate the speed of the waves in the deep region.

    2 marks
  2. (b)

    Determine Determine the speed of the waves in the shallow region.

    2 marks
  3. (c)

    Describe The wavefronts meet the boundary at an angle. Describe and explain what happens to the direction in which the waves travel as they cross into the shallow region.

    3 marks
Ready to self-mark?Reveal the detailed answer guide
Answer overviewKey answer: v = fλ = 8.0 × 1.8 v = 14.4 cm/s the frequency is unchanged at 8.0 Hz as the waves cross the boundary
01

(a)

2 marks

Calculate Calculate the speed of the waves in the deep region.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    v = fλ = 8.0 × 1.8

  2. 2

    v = 14.4 cm/s

02

(b)

2 marks

Determine Determine the speed of the waves in the shallow region.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    the frequency is unchanged at 8.0 Hz as the waves cross the boundary

  2. 2

    v = 8.0 × 1.2 = 9.6 cm/s

03

(c)

3 marks

Describe The wavefronts meet the boundary at an angle. Describe and explain what happens to the direction in which the waves travel as they cross into the shallow region.

How to approach it

Answer the command word directly and use precise physical vocabulary. Include only the distinct features or facts that earn marks, without burying them in unrelated background information.

  1. 1

    the direction of travel changes — the waves bend towards the normal to the boundary

  2. 2

    because the part of each wavefront that reaches the shallow water first slows down before the rest of it does

  3. 3

    so the wavefront pivots, and refraction has occurred

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