Part a a microphone is located on the line connecting two speakers hat are 0 932 m apart and oscillating in phase. the microphone is 2 83 m from the midpoint of the two speakers what are the lowest two trequencies that produce an interflerence maximum at the microphone's location? enter your answers numerically separated by a comma

a)

b)

Explanation:

Given:

The distance between two speakers (d) = 0.932 m

The distance of the microphone from the midpoint = 2.83 m

Thus, distance of microphone from the nearest speaker (L) = 2.83 - (0.932/2) = 2.364 m

also, the distance of the microphone from the farther speaker (L') = 2.83 + (0.932/2) = 3.296 m

Now,

The path difference is calculated as

L' - L = d = 0.932 m

Now,for a maxima to be produced at the microphone, the waves must constructively interfere.

for this to happen the path difference should be integral multiple of the wavelength.

thus,

hence, the largest wavelength will be for n = 1,

therefore,

0.932 = 1 × λ

or

λ = 0.932 m

now, the velocity of sound is given as c = 343 m/s

thus, the frequency will be

on substituting the values, we get

now, the 2nd largest wavelength will be for n = 2

0.932 = 2 × λ

or

λ = 0.466

thus, the frequency will be

hence, these are the lowest first two frequencies.