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# Coincidence Calculator

The minimum frequency of a vertically directed radio wave which will penetrate a particular layer in the ionosphere; for example, all vertical radio waves with frequencies greater than the E-layer critical frequency will pass through the E layer. The critical frequency is also known as penetration frequency.

Table of Contents:

Formula

**f _{c}= [ sqrt(3)c^{2}/pi*d ] * [ sqrt(ρ/Y) ]**

**Where,**

f_{c} = Coincidence Frequency [Hz]

c = Speed of sound in air [ms^{-1}]

d = Thickness of panel [m]

ρ = Density of panel [kgm^{-3}]

Y = Young\'s modulus of panel [Nm^{-2}]

Coincidence frequency is defined as the Optimum efficiency that is achieved when the plate is vibrated such that the wavelength of flexural waves in the plate is equal to the wavelength of acoustic waves in the air, also called critical frequency.

**Example:**

Calculate the coincidence frequency or critical frequencies for the given details.

Speed of sound, c = 25 ms^{-1}

Thickness of panel, d = 20 m

Density of panel, ρ = 15 kgm^{-3}

Young\'s modulus, Y = 10 Nm^{-2}

**Solution:**

**Apply Formula:**

f_{c} = [ sqrt(3)c^{2}/pi*d ] * [ sqrt(ρ/Y) ]

f_{c} = [sqrt (3)25 2 / 3.14*20] * [sqrt (15/10)]

f_{c} = [sqrt 3* 625 / 62.8] * [sqrt(1.5)]

f_{c} = [1.73*625/62.8] * [1.22]

f_{c} = [1081.25/62.8] * 1.22

f_{c} = 17.217*1.22

f_{c} = 21.1118 Hz

**Coincidence frequency, f _{c} = 21.1118 Hz**