Question

Beat phenomenon of class 11 explain in full details ??

Answer 1

The difference is frequencies that produces a special type of sound is called beats.

Beats=F1-F2.

Answer 2

Here is the answer

Beats:-

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Beats is the phenomenon caused by two sound waves of nearly same frequencies and amplitudes travelling in the same direction.

For example:-

Tuning of musical instruments like piano, harmonium etc. Before we start playing on these musical instruments they are set against the standard frequency. If it is not set a striking noise will keep on coming till it is set.

Mathematically

Consider only the time dependent and not the position dependent part of the wave.

i) s1=a cos ω1t and s2=a cos ω2t; where amplitude and phase of the waves are same,but the frequencies are varying. Also considering ω1> ω2.

ii) When these 2 waves superimpose s= s1+ s2=a[cos ω1t + cos ω2t]

iii) By simplifying , 2a (cos(ω1 - ω2)/2)t cos(ω1 + ω2)/2)t)

=>ω1 - ω2 is very small as ω1> ω2.Let (ω1 - ω2 )=ωb

=>ω1 + ω2 is very large. Let (ω1 + ω2 )=ωas= 2a cos ωbt cos ωatcosωat will vary rapidly with time and 2acosωbt will change slowly with time.

Therefore we can say 2acosωbt = constant. As a result 2acosωbt = amplitude as it has small angular variation.