Question

Two fire alarms are placed in a building, one 2.3 m north of the other. A person sitting at a desk which is 67.2 m east and 8.4 m north of the point mid-way between the alarms does not hear them when they sound. What is the lowest frequency that the alarms can be sounding at assuming that the alarms are both perfectly in phase?
[speed of sound in air=330m/s]

Answer 1

half a wavelength path difference

8.4 - 1.15 = 7.25
d1^2 = 67.2^2 + 7.25^2
d1 = 67.589958

8.4^2 + 1.15 = 9.55
d2^2 = 67.2^2 + 9.55^2
d2 = 67.875198

d2 - d1 = .2852 meters
which is half a wavelength
so wavelength = .5705

.5705 = 330 m/s * 1/f
so
f = 578 Hz

Answer 2

solution checks out but they made a typo in line 4 it should be 8.4 not 8.4^2