Why Is Frequency Selection Critical in Sound Interference Experiments?

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1)
In an experiment on Interference of sound, 2 loudspeakers are 0.8m apart and are driven in phase. The microphone is 1m from the loudspeakers. The frequency of the sound is set to be 500Hz. Explain why it is unsuitable to use sound of frequency, say 200Hz or 20kHz in this experiment.

Is it because the distance between the loudspeakers and the microphone is too large? Or the separation between the loudspeakers is too small?


2)
Two waves have the same frequency. Wave 1 has an amplitude of 1cm. Wave 2 has an amplitude of 2cm and leads wave 1 by 1/4 pi .

Find the amplitude of the resultant wave.

Can I simply add 1cm and 2 cm together?


3)
A transverse progressive wave of frequency 50Hz and amplitude 3cm is traveling to the right. The progressive wave is reflected and a stationary wave is formed. Now the stationary wave is illuminated witha stroboscope set at 53Hz. Find the apparent frequency of the stationary wave.

Attempt: 50 + 53 = 103Hz
I am not sure whether it is correct.

Thank you so much.

 

[denverdoc]

For the first part, assume the speakers are both facing the same direction and the mic can be anywhere on a line one meter away and parallel to a line thru the speakers. Using geometry can you figure out how the path length would vary say from the case its directly in front of the left speaker to the one in which is in the middle? Hows does path length difference relate to interference as a function of wavelength?

2) Careful here, if the two waves are ninety degrees apart, will they both be both of maximal amplitude at the same time?

3)What if the strobe was set for 50Hz? what would you see?