To find the wavelength of a wave at a Grade 10 level, you typically use the fundamental relationship between wave speed, frequency, and wavelength. The most common way is using the wave equation:
Wavelength (λ) = Wave Speed (v) / Frequency (f)
Understanding the Wave Equation
The wave equation connects three key properties of a wave:
- Wavelength (λ): This is the distance between two consecutive identical points on a wave, such as from crest to crest or trough to trough. It is usually measured in meters (m).
- Wave Speed (v): This is how fast the wave is traveling through a medium. It is measured in meters per second (m/s). For light and other electromagnetic waves traveling in a vacuum, this speed is the speed of light, denoted by 'c' (approximately 3 x 10⁸ m/s). For sound waves, the speed depends on the medium (e.g., air, water, solid).
- Frequency (f): This is the number of complete waves that pass a point in one second. It is measured in Hertz (Hz), which is equivalent to cycles per second (1/s).
Using the Formula λ = v / f
To find the wavelength (λ), you need to know the wave's speed (v) and its frequency (f).
- Identify the Wave Speed (v): This might be given in the problem, or you might know it based on the type of wave and the medium it's traveling through (like using 'c' for light in a vacuum).
- Find the Frequency (f): The frequency might be given directly, or you might have to calculate it from other information. As demonstrated in the reference video snippet, one way to find frequency, particularly for electromagnetic waves, is if you know the energy (E) of a photon and Planck's constant (h). The relationship is f = E / h. The snippet shows calculating frequency as f = (4.3 x 10⁻¹⁹ J) / (6.626 x 10⁻³⁴ J⋅s). Once you have the frequency from this or another method, you can use it in the main wavelength formula.
- Plug the Values into the Formula: Divide the wave speed (v) by the frequency (f).
Example:
Let's say you have a wave traveling at a speed (v) of 343 m/s (the approximate speed of sound in air at room temperature) and a frequency (f) of 440 Hz (the musical note A₄).
Using the formula:
λ = v / f
λ = 343 m/s / 440 Hz
λ ≈ 0.78 meters
So, the wavelength of this sound wave is approximately 0.78 meters.
Alternatively, if you calculated the frequency using the method from the reference (f = 6.49 x 10¹⁴ Hz) and knew it was light traveling in a vacuum (v = c ≈ 3 x 10⁸ m/s), you would find the wavelength like this:
λ = c / f
λ = (3 x 10⁸ m/s) / (6.49 x 10¹⁴ Hz)
λ ≈ 4.62 x 10⁻⁷ meters
This second example shows how calculating frequency, as shown in the reference, is a crucial step before applying the wavelength formula.
Summary Table
Here’s a quick summary of the formula and terms:
| Property | Symbol | Unit | How to Find (Common) | Relationship to Wavelength |
|---|---|---|---|---|
| Wavelength | λ | meters (m) | λ = v / f | Inversely proportional to f |
| Wave Speed | v | m/s | v = f × λ | Proportional to λ & f |
| Frequency | f | Hertz (Hz) | f = v / λ OR f = E / h (for light) | Inversely proportional to λ |
Understanding and applying the formula λ = v / f is the primary method for finding the wavelength of a wave in Grade 10 physics.
