Cambridge O Level Physics · Syllabus 5054 · Waves
Frequency
What is Frequency?
Frequency is the number of wavelengths that pass a point per unit time; symbol f, unit hertz, where one hertz is one wave per second. Frequency is fixed by the source and does not change when a wave crosses a boundary.
This definition is part of the Waves chapter in Cambridge O Level Physics.
Frequency in context
A wave is a disturbance that travels, carrying energy away from a source while the material it passes through only oscillates about fixed positions. Describe the disturbance with wavelength, frequency and amplitude; link them with \(v = f\lambda\). Every wave can reflect, refract and diffract. Light is an electromagnetic wave, so mirrors, blocks, prisms, fibres and lenses are all the same three behaviours applied to rays. Sound is a longitudinal mechanical wave, so it needs a medium, its pitch follows frequency and its loudness follows amplitude, and its echoes measure distance.
A wave is a disturbance that travels through space or a material, transferring energy from a source to a receiver without transferring matter. The particles of the medium oscillate about fixed equilibrium positions and end up where they began. Describe the wave with its wavelength, frequency and amplitude, and link them to the speed with \(v = f\lambda\). Waves of every kind can be reflected at a plane surface, refracted when their speed changes, and diffracted at a gap or an edge.
White light is a mixture of all the visible frequencies. A glass prism separates them because the refractive index of glass is slightly different for each frequency: violet is refracted (and so deviated) most, red least. The colours therefore emerge along slightly different directions and spread out into a spectrum. The prism does not create the colours — it separates colours that were in the white light all along.
The electromagnetic spectrum is one continuous family of transverse waves that all travel at \(3.0 \times 10^{8}\) m/s in a vacuum (and at approximately the same speed in air), transfer energy, and need no material medium. In order of increasing frequency and therefore decreasing wavelength the main regions are: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma. Each region is used for the jobs its particular frequency and wavelength suit, and the hazards rise sharply at the high-frequency end, where the radiation becomes ionising.
Sound is produced by a vibrating source and travels as a longitudinal mechanical wave: the particles of the medium oscillate back and forth parallel to the direction of energy transfer, creating compressions (particles closer together, pressure above normal) and rarefactions (particles further apart, pressure below normal). Because it needs particles to pass the disturbance on, sound cannot travel through a vacuum. Its frequency sets the pitch, its amplitude sets the loudness, and its waveform shape sets the quality or timbre.
Common mistakes with Frequency
- 4. “Frequency changes when a wave crosses a boundary.” Why wrongIf fewer crests left the boundary each second than arrived at it, crests would have to pile up there without limit. They do not. CorrectFrequency is fixed by the source. Speed changes at the boundary, and since \(v = f\lambda\) with \(f\) fixed, the wavelength changes in the same ratio. Say this“The frequency is unchanged because it is determined by the source; the speed and wavelength both change.” CheckA 500 Hz sound passes from air into water where it travels about four times faster. State what happens to \(f\) and to \(\lambda\).
- 15. “A prism creates the colours.” Why wrongIsolate one colour and send it through a second prism: it stays that colour. Nothing new is manufactured. CorrectWhite light is already a mixture of frequencies; the prism separates them because glass refracts each frequency by a slightly different amount. Say this“The prism separates the colours already present in white light, because the refractive index of glass is slightly different for each frequency.” CheckWhat is seen if a second, inverted prism is placed after the first?
- 18. “All electromagnetic waves are equally dangerous.” Why wrongThe hazard depends on frequency, intensity and exposure time. Radio waves at everyday intensities have no measurable effect; gamma rays ionise molecules in cells. CorrectExcessive exposure to any region heats tissue and can burn. Ultraviolet, X-rays and gamma rays are additionally ionising: ultraviolet is linked to skin cancer and cataracts, X-rays and gamma rays to cell mutation and cancer. Say this“Excessive exposure to any electromagnetic radiation can heat tissue and cause burns, but only ultraviolet, X-rays and gamma rays are ionising.” CheckState one hazard of microwaves and one of gamma rays, and say which is ionising.
- 19. “Pitch depends on amplitude.” Why wrongPlay the same guitar string harder: it sounds louder, not higher. The note is unchanged. CorrectPitch is set by frequency. Higher frequency gives higher pitch. Say this“A higher frequency gives a higher pitch.” CheckTwo traces have the same height but one has twice as many waves. Which sound is higher in pitch?
- 20. “Loudness depends on frequency.” Why wrongThe mirror image of the previous error. A high whistle can be barely audible and a low drum deafening. CorrectLoudness is set mainly by amplitude. Greater amplitude gives a louder sound. Say this“A larger amplitude gives a louder sound.” CheckWhich measurement on an oscilloscope trace tells you the loudness?
- 22. “Ultrasound means very loud sound.” Why wrongIt confuses the two axes of a trace. “Ultra” here refers to frequency, not amplitude. A dog whistle is ultrasonic and very quiet. CorrectUltrasound is sound of frequency above 20 kHz, beyond the upper limit of human hearing. Its loudness is a separate matter entirely. Say this“Ultrasound is sound with a frequency higher than 20 kHz.” CheckIs a 30 kHz sound necessarily loud? Explain.
Questions students ask about Frequency
Why does the frequency of a wave stay the same when it crosses into a different medium?
Frequency is fixed by the source, not by the medium the wave is travelling through. If fewer wave crests left a boundary each second than arrived at it, crests would pile up there without limit, which does not happen. Crossing into a new medium changes the wave's speed, and since \(v = f\lambda\) with \(f\) fixed, the wavelength changes in the same ratio as the speed.