Waves are produced when an oscillating or vibrating system transfers energy from one point to another without transferring matter. By exploring progressive and stationary waves, mechanical and electromagnetic waves, as well as transverse and longitudinal waves, students can analyze wave characteristics, sketch displacement graphs, and apply the wave formula \(v = f\lambda\).
Distinguish transverse waves from longitudinal waves, and learn how to read amplitude, period and wavelength from displacement graphs.
A wave is a disturbance that travels through a medium or vacuum, carrying energy from one point to another without carrying the matter itself.
Waves are generated by an oscillating or vibrating system. An oscillating iron bob at the end of a spring produces water waves, while a vibrating tuning fork produces sound waves.
When a medium vibrates at a fixed position, wave propagation transfers energy from one place to another without transferring the matter of the medium. A ribbon tied to a slinky spring only vibrates about a fixed position; it does not move along the direction of propagation.
A progressive wave has a wave profile that propagates with time. A stationary wave has a wave profile that does not propagate with time, formed when two identical progressive waves moving in opposite directions collide.
Wave Characteristics and Wave Formula
Frequency is the reciprocal of period.
Wave speed equals frequency multiplied by wavelength.
Amplitude (\(A\)): Maximum displacement of a particle from its equilibrium position.
Period (\(T\)): Time taken by a particle to make one complete oscillation. SI unit: s.
Frequency (\(f\)): Number of complete oscillations made by a particle in one second. SI unit: Hz or s⁻¹.
Wavelength (\(\lambda\)): Distance between two consecutive points in phase. SI unit: m.
Wave speed (\(v\)): Distance travelled per second by a wave profile.
Displacement against time graph: Gives amplitude (\(A\)) and period (\(T\)). Frequency is found using \(f = \frac{1}{T}\).
Displacement against distance graph: Gives amplitude (\(A\)) and wavelength (\(\lambda\)).
Combine frequency from the displacement-time graph with wavelength from the displacement-distance graph to calculate wave speed using \(v = f\lambda\).
A ripple tank consists of a perspex/glass water tank, ripple generator, digital xenon stroboscope, mirror, glass screen and dippers. A plane dipper produces plane waves, while a spherical dipper produces circular waves.
Switch on the plane dipper and adjust the stroboscope frequency until the wave pattern appears stationary. Read the frequency, \(f\), from the stroboscope. Measure the distance between consecutive bright fringes to obtain the wavelength, \(\lambda\). Calculate wave speed using \(v = f\lambda\).
The same wave read two ways: against time it gives amplitude and period, against distance it gives amplitude and wavelength.
The time axis gives the period directly. Here one complete oscillation takes \(T = 0.50\text{ s}\), so the frequency is \(f = \dfrac{1}{T} = 2\text{ Hz}\). The amplitude is the maximum displacement from the equilibrium position, \(A = 3\text{ cm}\).
The distance axis gives the wavelength directly, \(\lambda = 16\text{ cm}\), measured between two consecutive points in phase. The amplitude read from this graph is the same, \(A = 3\text{ cm}\).
Combining the two graphs gives the wave speed: \(v = f\lambda = 2\text{ Hz} \times 16\text{ cm} = 32\text{ cm s}^{-1} = 0.32\text{ m s}^{-1}\). Note that the two graphs have the same shape but different horizontal axes, so a period must never be read off a displacement-distance graph, nor a wavelength off a displacement-time graph.
Answer in your mind, then press “Check Answer”.
Based on a displacement-time graph, a crest is at \(3\text{ cm}\) and one complete wave cycle takes \(0.4\text{ s}\). Find the amplitude, period, and frequency of the wave.
State the primary difference between a progressive wave and a stationary wave in terms of wave profile propagation.
In a ripple tank experiment, a plane dipper produces water waves with a frequency of \(5\text{ Hz}\). If the distance between two consecutive bright fringes is \(1.5\text{ cm}\), calculate the wave speed.
Matter travels together with the wave from source to destination.
Only energy is transferred. Medium particles merely vibrate about their fixed equilibrium positions, as proven by the vibrating ribbon on a slinky spring.
All waves require a physical medium to propagate.
Only mechanical waves require a medium. Electromagnetic waves consist of oscillating electric and magnetic fields and can travel through a vacuum.
Longitudinal waves have crests and troughs just like transverse waves.
Longitudinal waves consist of alternating compressions and rarefactions, with vibrations parallel to wave travel.
Objective: Test your understanding of wave types, wave characteristics and the wave formula.
1 Which of the following statements correctly differentiates a transverse wave from a longitudinal wave?
2 A wave has a frequency of \(20\text{ Hz}\) and a wavelength of \(0.3\text{ m}\). What is the speed of the wave?
3 The formula relating wave speed \(v\), frequency \(f\), and wavelength \(\lambda\) is \(v =\) .
4 A wave where the profile of the wave does not propagate with time is called a wave.
Match each wave term to its correct textbook definition. If using a phone, tap the answer first, then tap the matching box.
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