IB Physics HL C.2 Wave model Notes

A wave is a travelling disturbance that transfers energy. In a material medium, such as a rope, water, or air, the particles of the medium oscillate about equilibrium positions as the wave passes. The particles do not have a net displacement along with the wave, so matter is not transported overall. The wave speed describes how fast the disturbance or wave pattern moves, not how fast one medium particle travels. This distinction matters when interpreting wave diagrams: follow the marked particle separately from the moving crest, compression, or pulse.

A cork floating on water bobs up and down as ripples pass across the surface. Explain how this demonstrates energy transfer without net transfer of matter.

Wave quantities depend on what the graph axes show. A displacement-distance graph is a snapshot of the wave at one instant, so the horizontal spacing between adjacent points in phase is wavelength λ. A displacement-time graph follows one point in the medium, so the time between repeated states is the period T. Amplitude A is the maximum displacement from equilibrium and can be read from either graph. Frequency is f = 1/T, and wave speed is the speed of the disturbance, not the speed of an individual particle oscillating in the medium.

A displacement-distance graph shows adjacent crests 0.75 m apart and maximum displacement 0.020 m. A displacement-time graph for the same wave shows adjacent crests 0.25 s apart. State the wavelength, amplitude, period, and frequency.

The wave equation comes directly from the definitions of period and wavelength. In the time for one complete oscillation, T, the wave pattern moves forward by one wavelength, λ. Therefore wave speed is v = λ/T. Since frequency is f = 1/T, this becomes v = fλ. In many wave problems the medium determines the wave speed, so if the source frequency increases while the medium is unchanged, the wavelength decreases. Always check units before substituting: hertz means s^-1.

A wave travels at 340 m s^-1 in air. Its frequency is increased from 170 Hz to 340 Hz while it remains in air. Determine the new wavelength and explain your reasoning.

Transverse and longitudinal waves are distinguished by particle motion relative to wave travel. In a transverse wave, each particle oscillates perpendicular to the direction in which the wave transfers energy. Waves on a string and electromagnetic waves are transverse. In a longitudinal wave, particles oscillate parallel to the direction of wave travel, creating alternating compressions and rarefactions. Sound in air is longitudinal. The same displacement graph idea can represent either type, so always ask what direction the particles move, not just what the drawing looks like.

A sound wave travels through air. Describe the motion of the air molecules and name the regions of high and low pressure.

Sound and electromagnetic waves are both waves, but their physical nature is different. Sound is a mechanical longitudinal wave: air molecules or particles in another medium oscillate parallel to the direction of travel, producing compressions and rarefactions. Without a medium, sound cannot travel. Electromagnetic waves are transverse oscillations of electric and magnetic fields, so they can travel through vacuum. In vacuum all electromagnetic waves travel at the same speed, c = 3.00 × 10^8 m s^-1, and the wave equation becomes c = fλ.

Compare sound waves in air with electromagnetic waves in vacuum, including wave type, medium requirement, and speed.

C.2 is secure when the student can separate the wave pattern from the particle motion, read the correct quantity from the graph axis, and choose the right comparison. A wave carries energy; particles in a medium oscillate locally. Distance graphs give wavelength, time graphs give period, and v = fλ links wave speed, frequency, and wavelength. Transverse and longitudinal waves are classified by particle motion, while sound and electromagnetic waves differ mainly by medium requirement and wave type.