Calculating slit separation for sound two-slit interference?

[fwFAWFSERG]

SOLVED

Homework Statement

A two-slit interference set-up with slit separation d =0.30 mm produces interference fringes at a particular set of angles THETAm (where m = 0, 1, 2,) for red light of frequency f = 4.9×10^14 hz.

If one wishes to construct an analogous two-slit interference set-up that produces interference fringes at the same set of angles THETAm for room-temperature sound of middle-C frequency f = 262 hz, what should the slit separation distance be for this analogous set-up?
this particular problems answer is 640 but i can't seem to arrive at that

Homework Equations

sin(theta)= m(wavelength)/d

The Attempt at a Solution

i believe sin(theta) is equalin both, so i don't see why it wouldn't come down to wavelenth/d is proprotional to wavelenth/d, or converting to frequency 1/fd = 1/fd or fd=fd.

 

[nickjer]

You know \lambda = v/f, but they both have different velocities so you can't use fd = fd.

 

[fwFAWFSERG]

arent their velocities equal at c, being the speed of light?

 

[nickjer]

room-temperature sound of middle-C frequency f = 262 hz

Sound doesn't travel at the speed of light. At least not where I live at.

 

[fwFAWFSERG]

oh that is quite true, shouldn't have overlooked that, so i can now say the formula is
c/fd = 343/fd?

edit: yes i can, thanks a lot nickjer, i got it now.