State what is meant by the terms ray and wavefront and state the relationship between them.

The diagram shows three wavefronts, A, B and C, of a wave at a particular instant in time incident on a boundary between media X and Y. Wavefront B is also shown in medium Y.

(i) Draw a line to show wavefront C in medium Y.

(ii) The refractive index of X is n_X and the refractive index of Y is n_Y. By making appropriate measurements, calculate \(\frac{{{n_{\rm{X}}}}}{{{n_{\rm{Y}}}}}\).

Describe the difference between transverse waves and longitudinal waves.

The graph below shows the variation of the velocity v with time t for one oscillating particle of a medium.

(i) Calculate the frequency of oscillation of the particle.

(ii) Identify on the graph, with the letter M, a time at which the displacement of the particle is a maximum.

ray: direction of wave travel / energy propagation;
wavefront: line that joins points with same phase/of same crest/trough;
ray normal/at right angles/perpendicular to wavefront;

(i) line parallel to existing line in Y and continuous at boundary; (both needed)

(ii) measures “wavelength” correctly in media X and Y; } (by eye)
(look for ratio of 0.5: 1 in responses)
\(\frac{{{n_{\rm{X}}}}}{{{n_{\rm{Y}}}}} = \frac{{{\lambda _{\rm{Y}}}}}{{{\lambda _{\rm{X}}}}}\);
0.5:1; (accept answers in the range of 0.47 to 0.53)

or

justification that angles needed for calculation are either pair of i and r as shown and angles measured correctly;
\(\frac{{{n_{\rm{X}}}}}{{{n_{\rm{Y}}}}} = \frac{{\sin r}}{{\sin i}}\);
0.5:1;

mention of perpendicular/right angle/90° angle for transverse and parallel for longitudinal;
clear comparison between direction of energy propagation and direction of vibration/oscillation of particles for both waves;

(i) time period=6.0ms;
167Hz;

(ii) M where line crosses x-axis;

(iii) counts rectangles (14±2) to first peak;
one rectangle equivalent to 0.5 mm;
7.2 mm;

or

\(\omega  = \left( {2\pi f = } \right)330\pi \);
\(a = \left( {\frac{v}{w} = } \right)\frac{{7.5}}{{330\pi }}\);
7.2 mm;
Allow any valid algebraic method, eg \(v = \omega \sqrt {\left( {{x_0}^2 - {x^2}} \right)} \).