Olympiad question on destructive interference

[Glenn G]

Hello all, I have been working through a number of past Olympiad questions for fun. This one, though, I find very strange - even after looking at the answer i'm confused. I know when the path difference from the two speaker is lambda/2 you would get destructive interference (typical A level answer) - the answer given on the mark scheme doesn't even completely correlate with the question. I don't get the first marking point, also with the second marking point, 2 waves are collinear with the centre of the speaker, so this means that it is as if both speakers are sending waves from the centre point? BUT then there'd be no path difference and no destructive interference - would apprecate any help so I can understand this.

 

[Steve4Physics]

The question/answer appear (IMO) to be badly written for the following reasons:

1. The question seems to ask what “orientation of the radio” is needed for destructive interference. But the radio’s orientation is irrelevant.

2. The question asks for the “maximum wavelength $l$”but the answer supplied is the minimum speaker separation. And a different symbol ($\lambda$) is used for wavelength.

3. The question asks about ‘complete destructive interference’. But (being picky) any destructive interference will not be complete due to amplitude differences between the two interfering waves

So things seem a bit muddled.

I’d guess the intended question is equivalent to this:

A and B are in-phase, point, single frequency wave sources separated by a distance $d$.

a) In terms of $d$, what it is maximum wavelength for destructive interference (2 waves meeting exactly in antiphase) to be possible?

b) For this maximum value of wavelength, where does destructive interference occur?

Minor edits.

 

[haruspex]

2 waves are collinear with the centre of the speaker, so this means that it is as if both speakers are sending waves from the centre point?

No, that's not what it says. It is saying that the paths of the waves are along the straight line through the two speakers.

 

[Glenn G]

Thanks Steve,

Ah so makes sense that if d is less than half a wavelength then at no point on that line between the 2 speakers can there be a point where there is complete destructive interference since they won’t ever be out of phase by half a cycle … ok if I’ve got that correct it makes sense now, certainly not clear to me from the question that that is what they were getting at,

The question/answer appear (IMO) to be badly written for the following reasons:

1. The question seems to ask what “orientation of the radio” is needed for destructive interference. But the radio’s orientation is irrelevant.

2. The question asks for the “maximum wavelength $l$”but the answer supplied is the minimum speaker separation. And a different symbol ($\lambda$) is used for wavelength.

3. The question asks about ‘complete destructive interference’. But (being picky) any destructive interference will not be complete due to amplitude differences between the two interfering waves

So things seem a bit muddled.

I’d guess the intended question is equivalent to this:

A and B are in-phase, point, single frequency wave sources separated by a distance $d$.

a) In terms of $d$, what it is maximum wavelength for destructive interference (2 waves meeting exactly in antiphase) to be possible?

b) For this maximum value of wavelength, where does destructive interference occur?

Minor edits.