Describing progressive waves
Section: Waves | Syllabus: Cambridge AS Level Physics 9702
What is a Progressive Wave? A progressive wave is a periodic disturbance that transfers energy without transferring matter. This periodic disturbance is usually the regular vibration, or oscillation, of particles of the medium (material) through which the wave travels.
Key Concept You can make a progressive wave using a rope. If you move one end rapidly from side to side, the wave moves from your hand towards the other end of the rope, but the rope itself does not move this way.
You are using the wave to transfer energy, but not matter, from your hand to the other end. Transverse Waves In a transverse wave , the oscillations are perpendicular to the direction of energy transfer.
When a wave is produced in a rope by moving the hand from side to side, the particles oscillate from side to side, passing through the equilibrium position. The particles do not move along the rope, only from side to side.
The distance of a particle from the equilibrium position at any point in time is called its displacement . FIG 7.1: Transverse Wave Properties Show a sinusoidal transverse wave with clearly labelled features: wavelength (λ) measured between two adjacent crests, amplitude (A) measured from equilibrium to crest, equilibrium position (horizontal line), direction of oscillation (vertical arrows), and direction of energy transfer (horizontal arrow).
Mark crests (peaks) and troughs. Examples of Transverse Waves Waves in vibrating strings of musical instruments Surface water waves Electromagnetic waves (light, radio waves) Waves on a rope Wavelength and Amplitude We can describe the form of all waves using the terms wavelength and amplitude .
Wavelength (λ) The distance between any two adjacent equivalent points on the wave. Usually measured from one wave peak to the next, but it could be measured from any point on the wave to the next equivalent point.
SI unit: metre (m) Amplitude (A) The maximum displacement of the wave from the equilibrium position. The equilibrium position is the location of the particles when there is no disturbance due to the wave.
SI unit: metre (m) Important On a diagram, the amplitude of a wave is measured from the mid-point line of the wave to the top of a peak or the bottom of a trough. It is not the peak-to-trough distance.
Speed, Frequency and Period Wave Speed (v) v = distance coveredtime SI unit: m s⁻¹ Frequency (f) The number of complete oscillations per unit time. SI unit: s⁻¹ or hertz (Hz) Period (T) The time taken for one complete oscillation to pass a fixed point.
SI unit: second (s) Speeds of Different Waves Wave and Medium Speed / m s⁻¹ Water waves caused by wind 2.5 – 15 Sound waves in air at sea level at 20°C 343 Sound waves in sea water at 4 m depth at 20°C 1500 EM waves in optical (fibre optic) cable 2.00 × 10⁸ EM waves in air or vacuum 3.00 × 10⁸ Key Point The speed of electromagnetic waves in a vacuum is one of the fundamental constants in the Universe, often denoted by c .
This is the maximum possible speed in the Universe. The Wave Equation The frequency of a wave is proportional to the speed of the wave when all other factors are constant. For a wave moving at a particular speed, the longer its wavelength, the fewer complete waves will pass a point each second.
The Wave Equation: v = fλ speed of a wave = frequency × wavelength where: v = wave speed (m s⁻¹) f = frequency (Hz or s⁻¹) λ = wavelength (m) Relationship Between Period and Frequency f = fraction and T = fraction For example, if the frequency is 10 Hz (10 complete oscillations per second), then one oscillation takes 1/10 s to pass a fixed point.
Important The speed of electromagnetic waves and sound in air (at a particular temperature and density) is the same for all frequencies. When waves change speed in different media, their frequency remains constant (since this depends on the wave source), so their wavelengths will change according to the medium.
The Ripple Tank The ripple tank is a transparent glass or plastic tray filled with water, used to show wave behaviour of surface water ripples. Images of the water waves can be projected onto a screen for viewing.
A round 'dipper' dips into the water and vibrates up and down to produce circular water waves A rectangular 'paddle' generates plane (straight) waves The vibrations are generated using an electric motor Can demonstrate reflection, refraction, and diffraction Phase Points on a wave that have the same displacement and are moving in the same direction are said to be oscillating in phase .
Instead of using arbitrary position numbers, we can use an angle from 0° to 360° to refer to a point on a wave. This is called the phase angle . A phase angle of 360° is equivalent to: A distance of one wavelength A time interval of one period Phase Difference Phase difference is the difference in phase angle between two waves at the same time.
Phase Difference (degrees) Phase Difference (radians) Description 0° 0 In phase 90° π/2 Quarter cycle difference 180° π In antiphas…
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