4400 Higher June 2007 Paper 3 Q15
15 The frequency, \(f\) kilohertz, of a radio wave is inversely proportional to its wavelength, \(w\) metres.
When \(w = 200\), \(f = 1500\)
(a)
(i) Express \(f\) in terms of \(w\).
(ii) On the axes, sketch the graph of \(f\) against \(w\).
(b) The wavelength of a radio wave is 1250 m.
Calculate its frequency. (2)
Calculate its frequency. (2)
| Scheme | Marks |
|---|---|
(i) \(f = \dfrac{k}{w}\) | M1 |
| \(f = \dfrac{300000}{w}\) | A1 |
| (ii) Answer:  | B2 |
| (4) |
Notes
M1: May be implied by \(1500 = \dfrac{k}{200}\)
A1: Also award if answer is \(f = \dfrac{k}{w}\) but \(k\) is evaluated as 300 000 in (a) or (b)
B2: B1 for graph with negative gradient (increasing or constant) even if it touches or crosses one or both axes e.g.
| Scheme | Marks |
|---|---|
| \(f = \dfrac{300000}{1250}\) | M1 |
| 240 | A1 |
| (2) | |
| (6 marks) |
Notes
M1: for substitution in \(f = \dfrac{k}{w}\)
A1: ft from \(k\)