Interference - Q done, is it right?

[Flucky]

Hi all, I have a question here that I've done but it hasn't got an answer provided. I'm sure it's easy stuff but haven't looked at this material in a while so
just want to double check.

(The things in red are what I added to the original diagram)

RE-DONE

d = √17

d + λ/2 = 2√5

λ/2 = 2√5 -d

λ = 4√5 -2(√17)

λ = 0.698m

Using v=fλ

∴f = 340/0.698 = 487 Hz

Is this correct?

Thanks in advance

 

[szynkasz]

$d=\sqrt{1^2+4^2}=\sqrt{17}$

 

[Flucky]

$d=\sqrt{1^2+4^2}=\sqrt{17}$

Woops, muppet at work. No idea how that came about, thanks.

Looking over it I've done a couple of very stupid errors such as line 4.

First post RE-DONE

 

[szynkasz]

Correct, but you get more frequencies:

$(2n-1)\frac{\lambda}{2}=d\Rightarrow f=(2n-1)\frac{v}{2d},\,n=1,2,3,...$

 

[Flucky]

Correct, but you get more frequencies:

$(2n-1)\frac{\lambda}{2}=d\Rightarrow f=(2n-1)\frac{v}{2d},\,n=1,2,3,...$

Thanks a lot, big help