Two loudspeakers are set 3.0 m apart in a room.  A microphone connected to a CRO is placed at the apex of a triangle 4 m from the line separating the two loudspeakers as shown below:

The microphone picks up sound waves of a very large amplitude.  If the microphone is moved along the line AB by 10 cm either side of the central point, a point of minimum amplitude is found.  What is the wavelength of the waves?  What is the frequency of the signal?  Speed of sound is 340 m/s  (Hint - you will need to do some geometry!)                                        

Move the microphone to the right by 10 cm. What is the path difference?

Path difference = X – Y (P)

X² = 4² + 1.6² = 16 + 2.56 = 18.56

X = 4.31 m (P)

Y² = 4² + 1.4² = 16 + 1.96 = 17.96

Y = 4.24 m (P)

The path difference = 4.31 – 4.24 = 0.07 m (P)

Since this is cancellation, the path difference is half a wavelength (P). 

Therefore the wavelength = 0.14 m (P)

Frequency = speed  ÷ wavelength = 340 m/s ÷ 0.14 m = 2400 Hz (P)