Physics: wavelength of sound waves

[YMMMA]

Homework Statement

Stated in the attached file.

Homework Equations

Wavelength = 2 times length divided by harmonic
I don’t know if it’s the relevant equation

The Attempt at a Solution

I used the equation I wrote. So, if the left side is 10cm longer, I guess it might be 2(10).

 

[mfb]

20 cm is right, but I'm not sure you used the right formula.
10 cm corresponds to one of 1/2, 3/2, 5/2, ... times the wavelength, only the first option leads to a possible answer.

 

[YMMMA]

I used this formula, is it the right one?

 

[mfb]

No. That looks like something for constructive interference.

 

[YMMMA]

20 cm is right, but I'm not sure you used the right formula.
10 cm corresponds to one of 1/2, 3/2, 5/2, ... times the wavelength, only the first option leads to a possible answer.

I think that’s the same rule. If wavelength=2*length / n, where n can be 1,2,3,4,5,6,...(the one wrote in the picture)
It’s basically the same as you said but solving for length not wavelength. I mean, length =1/2 *n*wavelength.
Right?

 

[mfb]

For destructive interference you want the length difference to be (n+1/2) wavelengths where n is an integer: L = (n+1/2)λ or 2L = (2n+1)λ or $\lambda = \frac{2L}{2n+1}$. Your formula works if you require n in it to be odd.

 

[YMMMA]

I am confused now. That’s a little bit different from I have learned. Or is this rule for these type of questions?

 

[mfb]

You do not have a standing wave here. You have two waves from different tubes interfering.

 

[YMMMA]

You do not have a standing wave here. You have two waves from different tubes interfering.

Yes, okay then. Thanks!