Two identical loudspeakers separated by distance triangle x each emit sound waves of wavelength lambda and amplitude a along the and amplitude a along the x-axis. What is the minimum value of the ratio triangle x/lambda for which the amplitude of their superposition is also a?

zapri4j 2022-09-27 Answered
Two identical loudspeakers separated by distance x each emit sound waves of wavelength λ and amplitude a along the and amplitude a along the x-axis.
What is the minimum value of the ratio x / λ for which the amplitude of their superposition is also a?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Jamari Morgan
Answered 2022-09-28 Author has 10 answers
We know that the amplitude of the superposition A will be given by
A = 2 a cos ( ϕ 2 )
On the other hand, the phase difference is given by
ϕ = 2 π x λ
Combining these two results, we have
A = 2 a cos ( π x λ )
Therefore, for A=a we will have
2 a cos ( π x λ ) = a cos ( π x λ ) = 1 2 ( π x λ ) m i n = π 3
Finally,
x λ = 1 3
Result:
1/3
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in