# What causes TV static interference meaning

## Mechanical waves

The superposition of waves is called **interference** designated. If there are only two transmitters (sources) from which waves emanate, one speaks of two-source interference (ZQI). Examples of transmitters are two swabs in a water wave tub, two loudspeakers or two columns from which elementary waves emanate.

#### Assumptions

To simplify matters, we want to assume that the waves under consideration are harmonic and have the same amplitude, frequency and direction of oscillation.

Imagine a calm lake in which two swabs (transmitter S_{1} and S._{2}) and create two circular wave systems, as well as a cork (receiver E) some distance away, which is captured by the waves and excited to vibrate. When the waves are superimposed, the following two extreme cases occur:

#### Constructive interference

A mountain of wave 1 meets a mountain of wave 2 or a valley of wave 1 meets a valley of wave 2. In this case there is a maximum deflection (e.g. of the cork).

Constructive interference always occurs when the path difference \ (\ Delta s = \ left | {\ overline {{S_2} E} - \ overline {{S_1} E}} \ right | \) applies

\ [\ Delta s = k \ cdot \ lambda \; \; \; \ rm {with} \; \; \; k \ in \ left \ {{\ color {Red} {0} \ ;; \; 1 \ ;; \; 2 \ ;; \; ...} \ right \} \]

One speaks for \ (k = 0 \ Rightarrow \ Delta s = 0 \ cdot \ lambda = 0 \) of the maximum of 0th order.

For \ (k = 1 \ Rightarrow \ Delta s = 1 \ cdot \ lambda = \ lambda \) there is a maximum of 1st order.

#### Destructive interference

A mountain of wave 1 meets a valley of wave 2 or a valley of wave 1 meets a mountain of wave 2. In this case, extinction occurs (e.g. no deflection of the cork).

Destructive interference always occurs when the path difference \ (\ Delta s = \ left | {\ overline {{S_2} E} - \ overline {{S_1} E}} \ right | \) the values \ (\ frac {\ lambda} {2} \), \ (3 \ cdot \ frac {\ lambda} {2} \), \ (5 \ cdot \ frac {\ lambda} {2} \) etc. Mathematically elegant, this can be written in the following form:

\ [\ Delta s = \ left ({k - \ frac {1} {2}} \ right) \ cdot \ lambda \; \; \; \ rm {with} \; \; \; k \ in \ left \ {{\ color {Red} {1} \ ;; \; 2 \ ;; \; 3 \ ;; \; ...} \ right \} \]

One speaks for \ (k = 1 \ Rightarrow \ Delta s = \ left ({1 - \ frac {1} {2}} \ right) \ cdot \ lambda = \ frac {\ lambda} {2} \) of the minimum 1st order.

#### Angular width \ (\ alpha \)

The calculation of the angular width \ (\ alpha \) below which a maximum or minimum appears is particularly easy if the distance \ (a \) of the receiver E is very large compared to the distance \ (b \) of the two transmitters ( \ (b \ ll a \)). In this case the lines \ (\ overline {\ rm {S_1 E}} \) and \ (\ overline {\ rm {S_2 E}} \) almost parallel and the angle \ (\ alpha \) very small.

From the drawing it can be seen that \ (\ Delta s \) applies to the path difference

\ [\ sin \ left (\ alpha \ right) = \ frac {{\ Delta s}} {b} \ Leftrightarrow \ Delta s = b \ cdot \ sin \ left (\ alpha \ right) \ quad (1) \ ]

and that \ (\ alpha \) applies to the angular width

\ [\ tan (\ alpha) = \ frac {d} {a} \ quad (2) \]

If \ (\ alpha \) is very small (i.e. in school practice \ (\ alpha <5 ^ \ circ \)), then the sine and tangent of an angle agree well, i.e. \ (\ tan (\ alpha) \ approx \ sin (\ alpha) \); this is called the **Small angle approximation**. With this approximation it follows from \ ((1) \) and \ ((2) \)

\ [\ Delta s = b \ cdot \ tan \ left (\ alpha \ right) = b \ cdot \ frac {d} {a} \]

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