explain the relationship between wave velocity, frequency and wavelength
OR
derivation of
wave velocity = frequency×wavelength
Answers
#BAL
When analysing a wave(longitudnal or transverse), there are two different kinds of properties to keep track of:
Properties of the oscillation(the disturbance that generates the energy propagation). The frequency of oscillation is one such property.
Properties of the energy propagation itself. The wavelength and velocity of the wave are two such properties.
Let’s first try to understand what these three terms mean.
Wave velocity
Wave velocity refers to the phase velocity i.e the velocity at which a particular phase of oscillation is replicated in space. For example, in the figure below, you see two identical phases of oscillation at x0 and x. The phase velocity is the velocity with which the phase at x0 ‘travels’ to x.
Wavelength
Next lets look at wavelength.Wavelength is the spatial frequency of phase. For example, in the figure below you can see two peaks of energy propagation. The wavelength is the frequency, with which these peaks are distributed in space.
The inverse of wavelength(i.e the spatial variation of phase k=dθdx)is called the wavenumber.
Frequency
Next lets look at frequency.Frequency is the time rate of change of the phase of the oscillation. For example, in the figure below, you can see a spring propagating a transverse wave and a longitudnal wave. For the transverse wave, the frequency is the rate at which the hand(disturbance) goes up and down, while for the longitudnal wave, it is the rate at which the hand moves back and forth.
Mathematically,
f=dθdt
Multiplying the spatial frequency of phase with the time rate of change of the phase of oscillation, gives us the phase velocity of the wave:
f.λ=dθdt.dxdθ=dxdt=υ
or
υ=f.λ
which is the equation relating the phase velocity, frequency and wavelength of a wave.
Answer:
velocity= distance /time
suppose a wave travels a distance Lambda which is its wavelength in time T then:
Explanation:
velocity is equals to wavelength upon time
/T here it is time taken by one wave we know that 1/T becomes the number of waves per second and this is known as frequency of the wave so we can write f in place of 1 I n the above relation. Thus,
velocity is equal to frequency into Lambda
where, v= velocity of the wave
f= frequency
lambda= wavelength
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