Waves

A water wave travels at 0.60 m s⁻¹ and has frequency 4.0 Hz. What is its wavelength?

1. A

   0.15 m

2. B

   0.24 m

3. C

   1.5 m

4. D

   2.4 m

1. a

   Select and show Select the correct wavelength and show the calculation.

   3
   Ready to self-mark?Reveal the detailed answer3 marks+

   Mark-by-mark answer

   Correct choiceA

   1. 1

      Selects option A: the water-wave wavelength is 0.15 m.

   2. 2

      Uses wavelength = wave speed ÷ frequency.

   3. 3

      Calculates 0.60 ÷ 4.0 = 0.15 m.

A ripple tank has constant water depth. A student changes the source frequency and measures wavelength.

1. a

   Calculate Calculate the wave speed for the first four rows.

   3
   Ready to self-mark?Reveal the detailed answer3 marks+

   Mark-by-mark answer

   1. 1

      Uses v = fλ and converts centimetres to metres.

   2. 2

      Obtains 0.24 m s⁻¹ for the 5.0 Hz and 6.0 Hz rows.

   3. 3

      Obtains 0.24 m s⁻¹ for the 8.0 Hz and 10.0 Hz rows.

2. b

   Evaluate Evaluate the 12.0 Hz result against the constant-speed model.

   3
   Ready to self-mark?Reveal the detailed answer3 marks+

   Mark-by-mark answer

   1. 1

      Calculates the 12.0 Hz speed as 12.0 × 0.021 = 0.252 m s⁻¹.

   2. 2

      Compares it with 0.24 m s⁻¹ and identifies a difference of 0.012 m s⁻¹ or 5%.

   3. 3

      Concludes that it is a possible anomalous or uncertain point, but one point alone does not establish a real speed change.

3. c

   Improve Propose one improvement that reduces wavelength-measurement uncertainty.

   2
   Ready to self-mark?Reveal the detailed answer2 marks+

   Mark-by-mark answer

   1. 1

      Proposes measuring across several complete wavelengths, using a strobe image, or repeating independent readings.

   2. 2

      Explains that a longer measured distance or repeated mean reduces the percentage uncertainty in one wavelength.

Two coherent ripple sources create alternating regions of large and small amplitude. A student claims that increasing the source separation makes the nodal regions closer together at a fixed distance from the sources.

1. a

   Formulate State the variables needed to test the claim and one suitable dependent measurement.

   3
   Ready to self-mark?Reveal the detailed answer3 marks+

   Mark-by-mark answer

   1. 1

      Identifies source separation as the independent variable.

   2. 2

      Identifies nodal spacing at a fixed observation line, or number of nodal lines across a fixed width, as the dependent variable.

   3. 3

      Controls source frequency, water depth, source phase, amplitude, and observation distance.

2. b

   Design Describe a method that would produce evidence strong enough to test the claim.

   3
   Ready to self-mark?Reveal the detailed answer3 marks+

   Mark-by-mark answer

   1. 1

      Uses at least five measured source separations and records a frozen or stroboscopic pattern for each.

   2. 2

      Measures across several nodal spacings and divides by the number of intervals, with repeats.

   3. 3

      Plots mean nodal spacing against source separation and uses uncertainty or spread when judging the trend.

3. c

   Evaluate Explain why judging nodal positions by eye is a limitation and propose a linked improvement.

   2
   Ready to self-mark?Reveal the detailed answer2 marks+

   Mark-by-mark answer

   1. 1

      Explains that low-amplitude regions have finite width or fluctuate, making the chosen centre subjective.

   2. 2

      Proposes video/image analysis, a fixed grid, or an amplitude probe with a stated threshold to define positions consistently.