Waves and frequency
Verify the fundamental wave relationship v = λ × f by varying the frequency and measuring the wavelength with the FizziQ Web Waves on a Lake simulation.
Throw a pebble into a lake and watch the circular ripples spread across the surface. Does their propagation speed depend on the frequency? On the amplitude? The Waves on a Lake simulation in FizziQ Web lets you answer these questions by systematically varying the frequency while keeping the speed fixed, and measuring the wavelength from the pattern of concentric circles. You will discover the universal relationship that connects three fundamental wave quantities.
Activity overview:
The student uses the FizziQ Web Waves on a Lake simulation to observe circular wave propagation. By fixing the propagation speed and varying the frequency, they measure the wavelength and verify that the product λ × f equals the wave speed.
Level:
High school
FizziQ
Author:
Duration (minutes) :
25
What students will do :
- Observe the propagation of mechanical waves on a water surface
- Measure the wavelength from the simulation
- Experimentally verify the relationship v = λ × f
- Understand that propagation speed depends on the medium, not on frequency
- Establish that wavelength and frequency are inversely proportional at constant speed
Scientific concepts:
- Mechanical wave
- Frequency (Hz)
- Wavelength (m)
- Propagation speed (wave velocity)
- Fundamental relationship v = λ × f
- Circular propagation
Sensors:
- FizziQ Web Waves on a Lake simulation
Material needed:
- Computer, tablet, or smartphone with FizziQ Web
Experimental procedure:
Open the Waves on a Lake simulation in FizziQ Web (Experiment → Simulations → Waves on a Lake).
Fix the propagation speed to a given value (for example 2 m/s) and the amplitude to 0.5 m. These parameters will not change during the experiment.
Set the frequency to 0.5 Hz. Start the simulation (START). Observe the circular waves propagating on the surface.
Observe the distance between two successive crests: this is the wavelength λ. Measure it or note it from the data display.
Stop the simulation. Change the frequency to 1.0 Hz, then restart. Has the distance between crests changed? In which direction?
Repeat for frequencies 1.5 Hz, 2.0 Hz, 2.5 Hz, and 3.0 Hz. For each frequency, note the wavelength λ in a table.
Create a table with three columns: Frequency f (Hz), Wavelength λ (m), and Product λ × f (m/s).
Calculate the product λ × f for each row. What do you notice? Is this product constant?
Plot the graph of λ versus 1/f. If the relationship v = λ × f holds, you should get a straight line through the origin with slope v.
Verify that the slope matches the propagation speed you set at the beginning. Conclusion: v = λ × f.
Expected results:
For v = 2 m/s: λ = 4.0 m (f = 0.5 Hz), λ = 2.0 m (f = 1.0 Hz), λ = 1.33 m (f = 1.5 Hz), λ = 1.0 m (f = 2.0 Hz), λ = 0.8 m (f = 2.5 Hz), λ = 0.67 m (f = 3.0 Hz). The product λ × f is constant and equals 2 m/s (the propagation speed). The graph λ(1/f) is a straight line through the origin with slope 2 m/s.
Scientific questions:
- If you double the frequency, what happens to the wavelength? And to the speed?
- Does the wave amplitude affect the propagation speed or the wavelength?
- Why do waves on deep water travel faster than waves on shallow water?
- Could you determine the propagation speed using only a float and a stopwatch?
- What is the difference between the speed of a wave and the speed of a float?
- Does the v = λf relationship also apply to electromagnetic waves like light?
Scientific explanations:
A mechanical wave is a disturbance that propagates through a material medium without transporting matter. On a lake, a float bobs up and down but does not travel with the wave.
Three quantities characterize a wave. The frequency f (in Hz) is the number of oscillations per second. The wavelength λ (in m) is the distance between two consecutive crests. The speed v (in m/s) is the distance traveled by the wavefront per second.
These three quantities are linked by the fundamental relationship: v = λ × f. This relationship is universal: it applies to water waves, sound waves, light waves, and seismic waves.
The propagation speed depends on the medium and not on the frequency. On a lake, it depends on the water depth. In air, sound speed depends on temperature. When you change the frequency, only the wavelength adjusts (λ = v/f).
The amplitude is the maximum height of the wave (the crest). It is independent of frequency and wavelength. A high-frequency wave and a low-frequency wave can have the same amplitude.
Extension activities:
- If you double the frequency, what happens to the wavelength? And to the speed?
- Does the wave amplitude affect the propagation speed or the wavelength?
- Why do waves on deep water travel faster than waves on shallow water?
- Could you determine the propagation speed using only a float and a stopwatch?
- What is the difference between the speed of a wave and the speed of a float?
- Does the v = λf relationship also apply to electromagnetic waves like light?
Frequently asked questions:
Q: How do I measure the wavelength in the simulation?
R: The wavelength is the distance between two successive crests visible on the screen. You can also calculate it: λ = v/f if you know the speed and frequency.
Q: The wavelength seems to change during the simulation.
R: Make sure the frequency and speed settings are not changing. The visual appearance may vary as the wavefront spreads, but the actual wavelength remains constant.
Q: Does changing the amplitude affect the wavelength?
R: No. Amplitude and wavelength are independent. Changing the amplitude makes the waves taller or shorter but does not change the spacing between crests.
Q: Why is the product λ × f not perfectly constant in my data?
R: Small discrepancies are due to measurement precision. If you are reading wavelength from the visual display, there is inherent imprecision. The theoretical product should be exactly equal to v.