The beat wavelength lbeat is much longer than that of either superposed wave , l1 and...

The beat wavelength lbeat is much longer than that of either superposed wave , l1 and l2. Demonstrate this. They relate as lbeat-1 = (1/2)( l1-1 - l2-1) (hint: remember the condition for the formation of beats, and state it mathematically. If it takes more than a couple of lines, you are on the wrong track)

Expert Solution

Given the relation , we get

Now one of the fundamental requirement for the formation of beats is that the 2 waves must have nearly equal frequencies, this means that their wavelengths must also be nearly equal, since where is the frequency and is the wavelength and is the speed of propogation of the wave in that medium. Since both the waves are assumed to be travelling in the same medium, their are same. Hence, if their are nearly equal, their would also be nearly equal. Coming back to the relation, this would mean that the denominator

Becomes very large. Hence, becomes very large compared to either superposed wave.

genius_generous answered 2 years ago

which wave has the shorter wavelength, and which has the longer wavelength

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