Frequency – the physical quantity reflecting number of fluctuations in mechanical, electromagnetic or other process. Besides usual linear frequency, consider cyclic (angular) frequency at rotation of bodies. Finding of these sizes in various tasks is carried out with use of the known formulas, ratios of parameters of bodies and indicators of their movement.
Instruction
1. At the beginning of the solution of any task lead all known sizes to units accepted in the SI system. Linear frequency is measured in hertz (Hz), cyclic – in radians in one second.
2. At the solution of a task on distribution of waves with the known length and speed of fluctuations calculate their frequency on a formula: F=v/λ, where λ - wavelength (m), v - the speed of distribution of fluctuations in the environment of (m/s). If in a task only T period is set (c) the fluctuations made by a body, frequency is from a ratio: F=1/T (Hz).
3. To learn the linear frequency of fluctuations of F through set cyclic at the time of rotation of a body, use the following expression: F=ω / (2*π), where ω - cyclic frequency (I am glad / c), π – the constant approximately equal 3.14. From here it is possible to remove also the return formula of finding of cyclic frequency on a preset value of linear: ω=2*π*F.
4. It is admissible the oscillatory system consisting of the suspended cargo of the known weight of M (m) and a spring with a certain rigidity of k (N/m) is set. Calculate the frequency of fluctuations of cargo of F, having carried out the following actions. Find the period of fluctuations on a formula T=2*π √ (M/k), substitute the known values and calculate the period in seconds. On above to the given formula determine the frequency of fluctuations of the suspended body: F=1/T (Hz).
5. At the solution of tasks from the section of electrodynamics the electromagnetic oscillatory contour is considered. Let it consist of pair in parallel of the connected condensers capacity With (T) and coils of inductance of L (Gn). It is possible to calculate the frequency of own fluctuations on a formula: ω = 1 / √ (L*C) (c is glad/).
6. If the value of current of I (A) is set by the following equation of i = 0.28*sin70*π*t (t - is expressed in seconds) and at the same time it is required to calculate cyclic ω and linear frequency F fluctuations, perform the following operations. In a general view the equation of sinusoidal current looks so: i = Im*sin(ωt+φ0). Therefore in this case it is known that amplitude of fluctuations of Im = 0.28 A, the initial phase φ0 is equal to zero, angular (cyclic) frequency ω = 70*π c as it is in the set equation coefficient at t is glad/. From here calculate the linear frequency of F = ω / (2*π) = 70*π / (2*π) = 35 Hz.