The mathematical solution initially explains how to find the maximum and minimum values of f(x) = 5sin x + 2cos x and how to find, in radians to 2 decimal places, the smallest positive values of x at which they occur. f(x) is written in the form Rcos(x + α). Explanation is then given as to how the maximum and...

The mathematical solution explains how to use the identity sin2x + cos2x≡ 1 to form a quadratic equation which can then be solved in a given range. The method of 'splitting the middle term' is used in order to help factorise the resulting quadratic in sin2x. The two resulting equations are then considered...

Physicists are involved in a wide range of activities, including electronics, energy, space, transport, medicine and materials. Their work can involve designing and conducting experiments, simulating real-life problems and conditions in laboratories, or making a series of observations which are written up in...

CK's job is helping people under the impact of the conflict ongoing in Yemen. In Yemen, he is managing a water and sewer programme which requires lots of engineering skill and also project management skill.

Comparing two sine waves of different amplitudes, this video shows that the intensity of a wave is proportional to the square of the amplitude.  The intensity is given I = ^P/_A, i.e., power per cross-sectional area.

This video summarises the properties of waves, i.e., reflection, refraction, diffraction and polarisation using a free App called Ripple free by Paul Falstad.  The App is very effective and versatile. 

This video uses a jelly baby wave machine to introduce the motional properties of progressive and standing waves and to introduce key terminology.

A displacement – distance graph is used to define wavelength (λ) and the phase of a wave.  A complete wave cycle is 360⁰ and from this the position of a particle...