Maximizing Sound Output from a Tube with Frequency of 444Hz

[DimSum]

Sound waves move from the left(R) to right(L) from a tube.
In the tube, the sound waves are split into 2 w/ radius R (half circled shaped)
a) if sound emitted has a freq of 444Hz, what is the min value of R that will lead to max L?
b) what is the smallest R leads to min sound at L?

Homework Statement

freq. of 444Hz

Homework Equations

f=(mv)/2L
lambda=V/freq

The Attempt at a Solution

I tried using the first eqn to solve for L, then using the 2nd solving for lambda and thinking it would be one of the two. but I am completely lost now.
I dun get this question at all...

Max sound is constructive.. soo...
attached is the picture w/ the Question

 

[DimSum]

i really need hints please =s

i have a midterm on this this week =s

 

[Astronuc]

Yes - this would be a problem of max (constructive) and min (destructive) interference.

The length of the curve is $\pi$R, and one has find the R such that the sounds add or cancel each other. The straight path has a length 2R.

What is the condition for interference with respect to difference between the two lengths, i.e. when is interference constructive/destructive?

lambda=V/freq is correct - so what is the wavelength of a 440 Hz wave?

Here is a reference - http://hyperphysics.phy-astr.gsu.edu/hbase/sound/interf.html

 

[DimSum]

ah I see
Thanks. i figured it out soon afterwards.

i thought we didnt learn that section. so i tried to solve it bying the phase eqn for construction and destruction waves x_x

THANKS.