Relation between frequency and wavelength
The main relation between frequency and wavelength is frequency is inversely proportional to the wavelength. that means if frequency of the wave increases then wavelength decreases and if the frequency decreases then wavelength increases. that is given by,
f ∝ 1/λ
Hence, the formula of relation between frequency and wavelength is f ∝ 1/λ.
Now, as we know that the relation between frequency and wavelength is frequency is inversely proportional to the wavelength. but we have to deep analysis about frequency and wavelength. we should also know about How frequency and wavelength are related to each other? so In this article we discussed more about frequency and wavelength in the later below. and also we solve derivation of relation between frequency and wavelength.
Wavelength
The minimum distance in which a sound wave repeats itself is called its wavelength. In most simple words, it is the length of one complete wave. It is denoted by λ . In a sound wave, the combined length of a compression and an adjacent rarefaction is called its wavelength. In a sound wave, the distance between the center of two consecutive compression and two consecutive rarefaction is also called its wavelength. S.I unit of wavelength is meter (m).
Please note that the distance between the center of a compression and an adjacent rarefaction is equal to the half of the wavelength. λ/2.
Frequency
The term frequency tells us the rate at which the waves are produced by their source. in other words frequency is the number of cycles produced in one second is called the frequency of the wave. Since the one complete wave is produced by one full vibration of the vibrating body, so we can say that the number of vibration per second is also called frequency of the wave. it is denoted by f. S.I unit of frequency is Hertz (Hz).
Derivation of relation between frequency and wavelength.
for a given light wave,
Distance = Speed × Time
Speed (Velocity) = Distance traveled by wave / Time period
Velocity of light = Wavelength/ Time period
V = λ/T
V= λ × 1/T
V = λ × f ∵ [ 1/T = f ]
or, f ∝ 1/λ ,
we can say that the relation between frequency and wavelength is f ∝ 1/λ .
relation between frequency and wavelength explain in detailed
Imagine a beam of light wave travels in a medium with very small velocity. (assume speed of light is less than 3 × 10^8 m/s). So according to our imagination, light beam looks like this,
So in this case frequency of the light wave is very small due to low velocity. Now imagine the velocity of the light goes faster, more faster, even more faster. Then the beam of light wave looks like this,
Frequency ∝ velocity ∝ Amplitude
Now after looking deep in the second experiment, we will observe that the all three waves say something. That is if we calculate the length of the first wave, the second wave and the third wave. We will find that the as we increases the speed of light wave the length of the wave decreases. i.e, if we compare the first wave and third wave in second experiment we will notice that the length of the third wave is smaller than that of the first wave due to the increase in velocity of the wave.
Conclusion
so we conclude that after increasing in velocity of the wave the wavelength decrease. But frequency increases. therefore the relation between frequency, wavelength and velocity is, Frequency ∝ velocity ∝ 1/wavelength. That means frequency is inversely proportional to the wavelength but directly proportional to the velocity of the wave.
Relation between frequency, wavelength, and velocity:-
If we increase the velocity of the wave then frequency also increases but wavelength of the wve decreases.
Distance = speed
Distance = Speed × Time
Speed (Velocity) = Distance traveled by wave / Time period
Velocity of light = Wavelength/ Time period
V = λ/T
V= λ × 1/T
V = λ × f
Hence, the relation between frequency, velocity and wavelength is V = λ × f.
Also Read
FAQ on relation between frequency and wavelength
Are wavelength and frequency directly or inversely related?
wavelength and frequency is inversely proportional to each other. i.e, f ∝ 1/λ.
What is the relation between speed of sound frequency and wavelength?
the relation between speed of sound frequency and wavelength is V = λ × f .
Is frequency directly proportional to wavelength?
No,frequency is inversely proportional to wavelength.
What happens to wavelength as frequency increases?
When frequency increases then wavelength decreases.
