Relationship Between Period, Wave Speed, Frequency and Wavelength

Definition:	Explanation
Period, T is the time taken by each point on the wave to complete one oscillation SI unit is second (s) PhysicsDefinitions	period is equivalent to the time taken for the wave to travel through a distance equal to one wavelength (you can also use the distance between 1st time it hits the mean and the 2nd time it returns bac to the mean position)
Frequency f is the number of oscillations each point completes per second SI unit is hertz (Hz) PhysicsDefinitions Wavelength $\lambda$ is the shortest distance between 2 successive crests of troughs SI unit is meter (m)	Frequency of a wave is also the number of crests (or troughs) that go past a point per second Frequency and period are also related by this equation $f=\frac{1}{T}$ physicsFormulae ⇒ T here is the period of the wave. 3 wave cycles are produced and move away from the source in 1s Frequency f = 3Hz Period T = $\frac{1}{3}s$
wave speed v is the distance travelled by the wave per second. SI unit is meter/second (m/s)	Recall that speed = $\frac{distance}{time}$. since every crest advances by 1 wavelength in one period, T the speed of the wave is given by $V=\frac{\lambda }{T}$ where v = wave speed (m/s) $\lambda$ = wavelength (m) T = period (s) physicsFormulae Since $f=\frac{1}{t}$, $v=f\lambda$ in the above figure ⇒ wavelength of the wave is 0.5m Wave speed: $v=0.5÷\frac{1}{3}=1.5m/s$ to conclude, relationship between v, f and $\lambda$ is $v=f\lambda$ physicsFormulae

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Wave speed v is determined by properties of the medium Wave speed on a rope is determined by factors like tension and thickness of rope. Therefore for a wave that stays in the same medium , v is fixed. equation $v=f\lambda$ tells us that if the frequency f of the wave generator is increased, $\lambda$ will decrease

sometimes waves can travel into a diff medium and its speed in a new medium can be higher or lower however ⇒ frequency of wave will always remain the same as a wave travels from one medium to another if wave travels into a different medium such that v decreases, then $\lambda$ will decrease since f remains the same

⇒ this is the figure to understand why frequency of wave remains the same as a wave travels from 1 medium to another. At point J where 2 sections of ropes are joined ⇒ oscillation of first section is passed on to the next section. ⇒ hence frequency f of oscillation in the second rope must be the same as in the first rope.

compare the wavelength in the second section to the first section and applying the formula $v=f\lambda$.

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