Question

A theme park creates a new kind of water wave pool with large waves caused by constructive interference. There are two wave generators in phase with each other along either side of a pool that is 24.0 m wide. A swimmer that is 9.0 m from one generator and 14.0 m from the other notices that she is in a region with almost no wave amplitude, but there are large-amplitude waves on either side of her.
What is the longest wavelength that will produce this interference pattern?
Express your answer to three significant figures and include appropriate units.

Answer 1

Answer:

10.0 m

Explanation:

Since there is no amplitude at the point of the swimmer, we have destructive interference.

So, the path difference ΔL = L₂ - L₁ where L₁ = swimmer's shorter distance from one generator = 9.0 m and L₂ = swimmer's longer distance from the other generator = 14.0 m.  ΔL = 14.0 m - 9.0 m = 5.0 m

Also, since we have destructive interference, ΔL = (n + 1/2)λ where n = number of wavelengths and λ = wavelength of waves

For maximum wavelength, n = 0

So, ΔL = (n + 1/2)λ

ΔL = (0 + 1/2)λ

ΔL = λ/2

λ/2 = ΔL

λ = 2ΔL

λ = 2 × 5.0 m

λ = 10.0 m

So,  the longest wavelength that will produce this interference pattern is λ = 10.0 m