Question

Jack and jill blow their whistles at the same time producing sound waves at frequencies of 400 hz and 404 hz respectively. how many beats per second are heard from the superposition of the two waves

Answer 1

Two beat sounds are produced, at the sum and difference of the two waves that produce them.

When Jack and Jill blow their whistles at the same time, their father Joe, at the bottom of the hill, hears four sounds ... the sound from Jack's whistle at 400 Hz, the sound from Jill's whistle at 404 Hz, and two more sounds that have no apparent source ... one at 804 Hz and another at 4 Hz.

Joe may not even notice the sound at 804 Hz, and the 4 Hz won't actually sound like a sound ... it'll sound to Joe like a rapid pulsing fluctuation in the loudness of the sounds from the whistles.

As long as the sounds of the whistles and their beats continue, Joe knows that the kids are OK, but they're not doing the job he sent them up the hill to do. Clearly, they're standing there whistling, and no pail of water is being fetched.

Answer 2

When two sound waves of similar frequency interfere with each other, there is a fluctuating sound heard which is periodic and repeating. This fluctuating sound is called beat. Beat frequency( number of beats per second) is equal to the difference of the frequency of the two sound waves.

So, sound waves of frequency 400 Hz and 404 Hz will produce 4 beats per second.