On the diagram above, identify

(i) with an arrow, the direction of movement of marker P at the instant in time shown.

(ii) the wavelength of the wave.

The wavelength of the wave is 25mm and its speed is 18mms^–1.

(i) Calculate the time period T of the oscillation of the wave.

(ii) On the diagram above, draw the displacement of the string at a time \(\frac{T}{3}\) later than that shown in the diagram.

Marker P undergoes simple harmonic motion. The amplitude of the wave is 1.7×10^–2m and the mass of marker P is 3.5×10^–3kg.

(i) Calculate the maximum kinetic energy of marker P.

(ii) Sketch a graph to show how the kinetic energy E_K of marker P varies with time t from t=0 to t=T, where T is the time period of the oscillation calculated in (b). Annotate the axes of the graph with numerical values.

The right-hand edge of the wave AB reaches a point where the string is securely attached to a second string in which the speed of waves is smaller than that of the first string.

(i) On the diagram above, draw the shape of the second string after the complete wave AB is travelling in it.

(ii) Explain the shape you have drawn in your answer to (d)(i).

(i) downward arrow at P;

(ii) clear single wavelength marked;

(i) frequency=\(\frac{{18}}{{25}}\)(Hz)=0.72(Hz);
period=\(\left( {\frac{1}{{0.72}} = } \right)1.4{\rm{s}}\);
Award [2] for a bald correct answer.

(ii) wave moved to right by one-third of a cycle by eye;

(i) \(\omega  = \frac{{2\pi }}{{1.4}}\);
\(\left( {\frac{1}{2} \times 3.5 \times {{10}^{ - 3}} \times \left[ {\frac{{4{\pi ^2}}}{{{{1.4}^2}}}} \right] \times {{\left[ {1.7 \times {{10}^{ - 2}}} \right]}^2}} \right) = 1.0 \times {10^{ - 5}}{\rm{J}}\);
Award [2] for a bald correct answer.

(ii)

correct shape (sin²) ; (allow any phase for this graph)
varying between 0 and 1.0×10^–5J; { (allow ECF from (c)(i) but do not allow E to be negative)
one period takes \(\frac{T}{2}\);

(i) reduced wavelength;
reduced amplitude;

(ii) speed reduced and frequency constant;
therefore wavelength reduced;
some energy reflected at boundary / second string is denser/greater mass per unit length;
therefore amplitude reduced;