Wave Speed, Frequency & Wavelength: Complete Guide with Formula
Learn the fundamental relationship between wave speed (v), frequency (f) and wavelength (λ) with the formula v = fλ. Includes derivations, real examples, and step-by-step calculations.
The Key Relationship
Wave Speed = Frequency × Wavelength
This equation applies to all types of waves, including transverse waves, sound waves, and electromagnetic waves.
Wave Speed (v)
How fast the wave travels through the medium. Unit: meters per second (m/s).
Frequency (f)
Number of complete waves passing a point per second. Unit: Hertz (Hz).
Wavelength (λ)
Distance between two consecutive crests or troughs. Unit: meters (m).
How the Formula is Derived
In one second, f waves pass a point. Each wave has a length of λ.
Therefore, the total distance covered by the wave in one second (which is the speed) is:
v = f × λ
Solved Examples
Example 1: A transverse wave has a frequency of 5 Hz and a wavelength of 2 meters. What is its speed?
Solution: v = f × λ = 5 × 2 = 10 m/s
Example 2: A wave travels at 340 m/s with a wavelength of 0.85 m. Calculate its frequency.
Solution: f = v / λ = 340 / 0.85 = 400 Hz
Example 3: Light (electromagnetic wave) travels at 3 × 10⁸ m/s. If its frequency is 5 × 10¹⁴ Hz, what is its wavelength?
Solution: λ = v / f = (3×10⁸) / (5×10¹⁴) = 6 × 10⁻⁷ m (600 nm – orange light)
Real-Life Applications
Sound Waves
Higher frequency = higher pitch. Speed of sound in air is approximately 340 m/s.
Light & Colors
Different wavelengths of light appear as different colors (red has longer wavelength than blue).
Radio Waves
FM radio stations use different frequencies. Speed is the speed of light.
Seismic Waves
Earthquake waves have different speeds depending on frequency and medium.
Connection to Transverse Waves
In transverse waves (like light or waves on a string), the particles move perpendicular to the direction of wave travel, but the relationship v = f × λ still holds perfectly.
This formula helps calculate how fast a wave on a guitar string travels or how different colors of light behave.
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