Question

O
Prove that the beat frequency produced by superposition of two waves is equal to difference
of frequencies of the two waves.

Answer 1

Answer:

amplitude of vibration of particle at any point changes simple harmonically with frequency equal to one half of the difference between the component waves

Explanation:

component waves

y

1

=Asinω

1

t,y=Asinω

2

t

y

1

+y

2

=A(sinω

1

t+sinω

2

t)

=2Asin(

2

ω

1

+ω

2

)+cos(

2

ω

1

−ω

2

)t

in case of beats

∣ω

1

−ω

2

∣<<∣ω

1

+ω

2

∣

∴y

1

+y

2

=A

1

sinω

1

t

ω

1

=(

2

ω

1

+ω

2

)

A

1

=2Acos(

2

ω

1

−ω

2

)t