Inteference Pattern Question

[Sarah0001]

Homework Statement

A loudspeaker L is placed between a microphone M and a screen S reflecting
sound waves as sketched below. The loudspeaker emits sound of fixed wavelength
λ in all directions. When the screen is moving slowly, to the right along the
x direction (slowly in comparison with the speed of sound), the microphone
records minima and maxima of the sound intensity.

What is the distance between two screen positions giving two successive maxima? Would the
microphone record minima and maxima if
(a) the loudspeaker or
(b) the microphone is moving along x direction instead of the screen?

Relevant Equations

.

a) When the loudspeaker is moving along the x direction instead of the screen, I understand that the phase of which the of the reflected wave meets the loudspeaker is changing, and so when the reflected wave interferes with waves behind the loudspeaker reaching microphase, the phase of the reflected wave meeting microphone also changes as L(loudspeaker moves). However I am slightly sceptical of this as I cannot visualise how the reflected waves phase changes as L moves towards the screen because surely the incident wave's phase would change too in order for the reflected waves phase to change?
(Q1) Would it be possible to draw a diagram to visualise how the phase of the reflected wave (or both waves if infact phase of both waves) changes relative to loudspeaker, as the loudspeaker moves towards the screen?

(b) For B I understand there is a constant phase difference as the wave indicent to the screen and the reflected waves are not being shifted, but I don't understand how this means the Microphone will not record a maxima or minima.
Qimg.attached

 

[BvU]

Hi,

Did you answer

What is the distance between two screen positions giving two successive maxima?

?

for (a) I wouldn't worry about indirect or downstream interference : just look at the path difference of direct wave and reflected wave. Same for (b).

 

[Sarah0001]

Hi,

Did you answer ?

for (a) I wouldn't worry about indirect or downstream interference : just look at the path difference of direct wave and reflected wave. Same for (b).

Yes, distance between adjacent maxima is lambda/2. Also, I don't understand how the path difference leads to the solution that it is (a) Yes and for (b) No for recording minimia and maxima, the solution given itself is in terms of changing phases, so I would like to understand the solution further.

 

[BvU]

If , when you move the speaker away from the microphone, the distance between microphone and speaker changes by +1 cm, what happens to the other path (speaker-screen-microphone) ? So what happens to the path difference ?

(b) Same question, but now move the microphone.