Wave Features and the Wave Equation
In 1877, Thomas Edison recorded the first sound wave on a cylinder at 261.6 Hz, proof that wave features can be captured, measured, and replayed.
At the start of this lesson you were shown Middle C vibrating at 261.6 Hz with a wavelength of 1.32 m, and how one equation connects every measurable feature of every wave in the universe.
Now that you've worked through the lesson, how has your thinking shifted? Can you explain that hook idea more precisely using what you've learned today?
Answers
▾MCQ 1
CFrequency is measured in hertz (Hz), which means cycles per second.
MCQ 2
BPeriod T = 1/f = 1/4 = 0.25 seconds.
MCQ 3
AUsing v = f × λ, rearranged: f = v / lambda = 6 / 3 = 2 Hz.
MCQ 4
DSince v = f × λ and v is constant in a given medium, if f doubles, lambda must halve to keep the product the same.
MCQ 5
BAmplitude is the maximum displacement from the rest position (centre line), not the total distance from crest to trough. Crest to trough would measure twice the amplitude.
Short Answer 1
Model answer: Amplitude is the maximum displacement of a particle from its rest position. It is measured as the distance from the centre line of the wave to either a crest or a trough. Its unit is metres (m). Wavelength is the distance between two consecutive corresponding points on a wave, such as from one crest to the next crest, or one trough to the next trough. It is measured in metres (m).
Short Answer 2
Model answer: Wavelength: lambda = v / f = 340 / 440 = 0.77 m (to 2 decimal places). Period: T = 1/f = 1/440 = 0.0023 s (or 2.3 milliseconds). The wavelength tells us the physical length of each sound wave in air, while the period tells us how long each wave takes to pass a point.
Short Answer 3
Model answer: In the deep ocean, tsunami waves travel very fast (over 800 km/h) with extremely long wavelengths (often over 100 km). Their amplitude is small (less than 1 m) because the energy is spread over a vast depth. According to the wave equation (v = f × λ), as the wave approaches shallow water, the wave speed decreases because the water depth is shallower. Since the frequency remains constant, the wavelength must also decrease. However, the total energy of the wave is conserved, so as the wavelength shortens and speed drops, the amplitude must increase dramatically. This is why a barely noticeable wave in deep water can become a devastating wall of water near the coast.
Wave Jumper
Jump through the wave platforms while testing your knowledge of wave features and the wave equation. Can you solve them all?
Model answers (click to reveal)
Answers
▾MCQ 1
CFrequency is measured in hertz (Hz), which means cycles per second.
MCQ 2
BPeriod T = 1/f = 1/4 = 0.25 seconds.
MCQ 3
AUsing v = f × λ, rearranged: f = v / lambda = 6 / 3 = 2 Hz.
MCQ 4
DSince v = f × λ and v is constant in a given medium, if f doubles, lambda must halve to keep the product the same.
MCQ 5
BAmplitude is the maximum displacement from the rest position (centre line), not the total distance from crest to trough. Crest to trough would measure twice the amplitude.
Short Answer 1
Model answer: Amplitude is the maximum displacement of a particle from its rest position. It is measured as the distance from the centre line of the wave to either a crest or a trough. Its unit is metres (m). Wavelength is the distance between two consecutive corresponding points on a wave, such as from one crest to the next crest, or one trough to the next trough. It is measured in metres (m).
Short Answer 2
Model answer: Wavelength: lambda = v / f = 340 / 440 = 0.77 m (to 2 decimal places). Period: T = 1/f = 1/440 = 0.0023 s (or 2.3 milliseconds). The wavelength tells us the physical length of each sound wave in air, while the period tells us how long each wave takes to pass a point.
Short Answer 3
Model answer: In the deep ocean, tsunami waves travel very fast (over 800 km/h) with extremely long wavelengths (often over 100 km). Their amplitude is small (less than 1 m) because the energy is spread over a vast depth. According to the wave equation (v = f × λ), as the wave approaches shallow water, the wave speed decreases because the water depth is shallower. Since the frequency remains constant, the wavelength must also decrease. However, the total energy of the wave is conserved, so as the wavelength shortens and speed drops, the amplitude must increase dramatically. This is why a barely noticeable wave in deep water can become a devastating wall of water near the coast.