From topics on linear motion, speed v is usually given as rate of change of distance with time. i.e. speed (v) =distance(s)/time(t)
Speed of a wave is the distance covered by a wave in one second.
The SI unit of a wave speed is metres per second.
Consider a particle on a wave motion that gets displaced from point A to B such that distance AB makes one wavelength as shown
For the particle to cover a distance of exactly one wavelength, it means it has completed exactly one oscillation.
The time taken to complete one oscillation is called the periodic time (T) and so the speed of the particle can be expressed in terms of wavelength (λ) and periodic time T as in the equation below.
λ is a greek letter known as lambda which means wavelength in english.
but T = 1/f. hence
Multiplying both numerator and denominator by f, we get v=fλ.
v=fλ is a relationship that helps determine speed of a wave given it’s frequency and wavelength.
In a given media, the speed of a wave motion is constant and so frequency is inversely proportional to the the wavelength such that:
The above equation shows that an increase in frequency results in decrease of wavelength.
The relationship between frequency and wavelength is represented graphically as shown in figure below.
If a wavelength covers λ distance, then the total distance covered by the wave profile can be determined as λ x number of oscillations and the total time taken as periodic time x number of oscillations..
Example Question
The figure below shows a wave form in a string.The wave is moving at 30.0ms-1 and the grid is in centimeters.
Detrmine:
(a) Amplitude
(b) Wavelength
(c) frequency
(d) Period
solution
(a) amplitude is the largest displacement of the wave profile. It is the crest in the wave motion. In our diagram, the largest displacement is ±5. hence the amplitude of the wave is 5.0 cm
(b) we can determine wavelength by determining distances between two points that are in phase. (40-0)cm or (50-10)cm or (60-20)cm. Hence the wavelength is 40cm.
(c) v=fλ
hence
v= 30.0ms-1 and λ = 40 cm = 0.4m
hence
(d) Period T = 1/f
Practice Question 1
Waves on a spring are produced at the rate of 200 wavelengths every 10 seconds.
(a) Find the frequency of the wave motion. (Answer: 20 Hz)
(b) If the wavelength of the waves is 0.15m, find the speed of the waves (Answer: 3ms-1)
(c) Find the period of the waves (Answer: 0.05s)
Practice Question 2
A water wave travels at 24m in 3 s. If source of the water waves vibrates at 5Hz, determine:
(a) The speed of the wave (Answer: 8 ms-1)
(b) The wavelength (Answer: 1.6m)
Related Topics
- Angular displacement
- Angular velocity
- Types of waves
- Characteristics of a wave motion
- Trigonometric ratios
- Equation of a circle