How to calculate the path difference in this question

[Ajaroy]

1. Homework Statement
Two speakers S₁
and S₂ derived by the same amplifier and placed at y=1
and y = - 1.The speakers vibrate in phase at 600 Hz. A man stands on the x-axis at a very large distance from the origin and starts moving parallel to the Y - axis. The speed of sound in air is 330ms^-1

at what angle will the sound drop to a minimum for the first time?

Homework Equations

The Attempt at a Solution

as minimun occurs at destructive interferenc
Δx = S₂Y - S₁Y = (2n-1)λ/2

for the first minima Δx = λ/2
but how to calculate Δx in terms of θ ,i an not able to from the geomentry of problem[/B]

 

[kuruman]

Hi Ajaroy and welcome to PF.

Make a drawing. The man is moving parallel to the line joining the two speakers. To find Δx formally you need to use the Pythagorean theorem. You also need to consider that he is far from the speakers, so some kind of approximation will be required in terms of his angular displacement from the x-axis.

 

[drvrm]

1. Homework Statement
Two speakers S1
and S2 derived by the same amplifier and placed at y=1
and y = - 1.The speakers vibrate in phase at 600 Hz. A man stands on the x-axis at a very large distance from the origin and starts moving parallel to the Y - axis. The speed of sound in air is 330ms-1

at what angle will the sound drop to a minimum for the first time?

drop a normal from s1 on s2 Y ...the angle between s1-s2 line and the normal is say theta then its the angle between the normal to s1 s2
and the radial line to Y...this i am saying as x is very large compared to s1 s2 length.

so theta = Y/x and nearly equal to sin(theta)= (s2Y- s1y) /s1s2 as theta is small.

 

[Ajaroy]

drop a normal from s1 on s2 Y ...the angle between s1-s2 line and the normal is say theta then its the angle between the normal to s1 s2
and the radial line to Y...this i am saying as x is very large compared to s1 s2 length.

so theta = Y/x and nearly equal to sin(theta)= (s2Y- s1y) /s1s2 as theta is small.

drop a normal from s1 on s2 Y ...the angle between s1-s2 line and the normal is say theta then its the angle between the normal to s1 s2
and the radial line to Y...this i am saying as x is very large compared to s1 s2 length.

so theta = Y/x and nearly equal to sin(theta)= (s2Y- s1y) /s1s2 as theta is small.

What are X and Y
Als how sin theta = y/x

 

[Ajaroy]

Hi Ajaroy and welcome to PF.

Make a drawing. The man is moving parallel to the line joining the two speakers. To find Δx formally you need to use the Pythagorean theorem. You also need to consider that he is far from the speakers, so some kind of approximation will be required in terms of his angular displacement from the x-axis.

I drew a perpendicular from Y to s1 s2line

 

[Ajaroy]

s2line

I drew a perpendicular from Y to s1 s2line

Then by Pythagoras theorem
OY₂+OS1²=S1Y²
And
OY²+OS2² =S2Y²

Then by solving
(OS1 +OS2) *2/S2Y+S1Y = DELTA X
What should I do nnex?

 

[Ajaroy]

What are X and Y
Als how sin theta = y/x

Oh!
Thanks I got it