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Physics - phase difference question

Got stuck on a question, please see the link for the diagram *link removed*
q5a
Two loudspeakers are one metre apart, and are connected to the same signal. A listener is two metres away from the left speaker on a line which is perpendicular to the line joining the two speakers (see above diagram). Speed of sound in air 340m/s.

a) When both speakers generate a 1000Hz signal what is the phase difference between them?

Sorry if working is hard to follow having been typed up.

Path difference = √1² + √2² = √5

Wavelength = speed/frequency = 340/1000 = 0.34

Using this equation ∅=2πX/wavelength,
(2xπx√5)/0.34 = 41.32243959

The actual answer is 4.435π Radians - can someone please explain where I went wrong?

(edited 11 years ago)

Reply 1

Qwertish

I think X is meant to be "difference in path"... i.e., √(5)-2.

But that still gives the wrong answer :s-smilie:

(1.389π)

Reply 2

Joinedup

Original post by Qwertish

I think X is meant to be "difference in path"... i.e., √(5)-2.

But that still gives the wrong answer :s-smilie:

(1.389π)

I think you were right... all the possible answers look wrong to me.

4.435 is close... 4.435 pi is miles out - why greater than 2pi?

Reply 3

Qwertish

Original post by Joinedup

I think you were right... all the possible answers look wrong to me.

4.435 is close... 4.435 pi is miles out - why greater than 2pi?

Oh yes, you're right... I didn't notice that :h:

, phase difference can't be greater than 2pi... haha

So the answer would be 1.389π, except they did 1.389π² in the answers for some reason lol

(edited 11 years ago)

Reply 4

Ketchup!

Original post by Qwertish

I think X is meant to be "difference in path"... i.e., √(5)-2.

But that still gives the wrong answer :s-smilie:

(1.389π)

Original post by Qwertish

Oh yes, you're right... I didn't notice that :h:

, phase difference can't be greater than 2pi... haha

So the answer would be 1.389π, except they did 1.389π² in the answers for some reason lol

Thanks so much to both of you, but 1.389π isn't an option though? Or have they made a mistake?

also, where did the "-2" come from?

And Qwertish, what do you mean by "except they did 1.389π² in the answers for some reason"

Reply 5

Joinedup

1.389 pi = 4.364

I think they put the pi in the multi choice by mistake

Reply 6

Qwertish

Original post by Ketchup!

The '-2' is the 2m of the straight path, because X is the difference between the two paths :smile:

.

I meant:
The answer they wrote is "4.435π Radians", except the actual answer just "4.435 Radians", without the pi. So, they must have made a mistake and done 1.389π², which simplifies to 4.435π :P.

Reply 7

Ketchup!

Original post by Joinedup

1.389 pi = 4.364

I think they put the pi in the multi choice by mistake