Question

Two cellists, one seated directly behind the other in an orchestra, play the same 220-Hz note for the conductor who is directly in front of them. What is the smallest non-zero separation that produces constructive interference?

Answer 1

Answer:

d= 1.56 m

Explanation:

In order to have a constructive interference, the path difference between the sources of the sound, must be equal to an even multiple of the semi-wavelength, as follows:

⇒ d = d₂ - d₁ = 2n*(λ/2)

The minimum possible value for this distance, is when n=1, as it can be seen here:

dmin = λ

In any wave, there exists a fixed relationship between the wave speed, the frequency and the wavelength:

v = λ*f

If v = vsound = 343 m/s, and f = 220 1/s, we can solve for λ:

λ =$\frac{v}{f} = \frac{343 m/s}{220(1/s)} = 1.56 m$

⇒ dmin =λ = 1.56 m