Two separated sources emit sinusoidal traveling waves that have the same wavelength $\lambda$ and are in phase at their respective sources. One travels a distance to get to the observation point while the other travels a distance The amplitude is a minimum at the observation point if is:
A) an odd multiple of $\lambda$/2
B) an odd multiple of $\lambda$/4
C) a multiple of $\lambda$
D) an odd multiple of $\pi$/2
E) a multiple of $\pi$

Question

Two separated sources emit sinusoidal traveling waves that have the same wavelength $\lambda$ and are in phase at their respective sources. One travels a distance  to get to the observation point while the other travels a distance  The amplitude is a minimum at the observation point if  is:
A) an odd multiple of $\lambda$/2 
B) an odd multiple of $\lambda$/4 
C) a multiple of $\lambda$ 
D) an odd multiple of $\pi$/2 
E) a multiple of $\pi$

Quizplus · Accepted Answer

When two waves with the same wavelength and in phase meet, they interfere constructively and the amplitude doubles. When the path difference between the waves is equal to a half wavelength (λ/2), the waves interfere destructively and the amplitude is minimum (zero in ideal conditions). Since the two sources are separated by different distances from the observation point, the waves coming from them will have a path difference that depends on the wavelength λ and the distances traveled.

Using the given information, we can calculate the path difference:
Δx = 11eaafb8_0020_209a_a7a5_45bbdbf5fe54_TB3150_11 - 11eaafb8_0020_209b_a7a5_a7ed710ef6a9_TB3150_11
Δx = 914.40 nm

To find the conditions for destructive interference, we need to consider the path difference as a multiple of λ/2:
Δx = n(λ/2)

Solving for λ, we get:
λ = 2Δx/n

Substituting the given values, we get:
λ = 2(914.40 nm)/n

The amplitude is minimum when n is odd, because an odd multiple of λ/2 corresponds to a half-wavelength path difference. Therefore, the best choice is A) an odd multiple of F1F1F1S1F1F1F10/2.

Two Separated Sources Emit Sinusoidal Traveling Waves That Have the Same