Sound will first disappear when sound waves originating from center and from either end of the slit are out of phase. This will occur when the path difference for waves originating from the center and from either end of the slit is , where is the wavelength of the sound wave. This path difference will be at an angle of if the following condition is satisfied
The relationship between , the frequency , and the speed of sound , is
So, the condition for destructive interference at in terms of the frequency is
Plugging in and solving for gives
Therefore, answer (D) is correct.