What is the relationship among frequency, wavelength, and velocity?

Suppose you shake a rope up and down at a constant rate. The rate or frequency is the number of times your hand is at the top of its motion per second. As the waves move along the rope, the distance between the crests of the rope, the wavelength, will remain the same. The wavelength depends both on the frequency of oscillation and on the velocity of the wave along the rope. The relationship is velocity = frequency x wavelength (v = λ) or wavelength = velocity/frequency (λ = v/f). Therefore, if the frequency of a wave increased, the wavelength decreases while the velocity, being a property of the medium (rope) doesn’t change. The frequency and wavelength are inversely proportional to each other.

The following table shows the relationship between frequency and wavelength for a sound wave in 0°C air:

Velocity of Sound Frequency (Hz) Wavelength (m)
331 128 2.59
331 256 1.29
331 512 0.65
331 768 0.43


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