Tuesday, January 6, 2015

Beats and Its Applications

The phenomenon in which to sound notes of slightly different frequency travelling together in the same direction are superimposed and produce alternate waxing and waning s called beats.

When the two waves are met in the same phase, they produces a maximum resultant intensity and it is called waxing. When the two waves are met in the opposite phase, they producers minimum resultant intensity and it is called waning.

We have derived a mathematical equation for beat frequency here.It is number of beats per one second.The time taken for completion of one beat that is one waxing and one waning is called time period of beat.A mathematical equation is derived for both of them as shown below.

The time interval between two maximum intensities as well as the two minimum intensities is always fixed. This is called Beat time period. The reciprocal of this time period is called beat frequency. We can derive the equation for them as shown below.

The diagrammatic view of the phenomena is as shown below.We can see one two waves are met in same phase,their resultant intensity is maximum and it is called waxing.As the time progresses,the phase difference increases and minimum intensity is produced and it is called waning.

The interval between two waxings and wanings is regular and systamatic.

Every ordinary human being needs a time interval of 0.1 second between the two successes sounds to understand the sound properly. This is called persistence of hearing. Hence difference between the frequencies of two sources shall not be greater than 10 to hear the beats.

Problem and solution

A tuning fork A has a frequency 5% more than the standard fork K and another tuning fork B has a frequency 3% less than the standard fork K. When this two tuning forks are vibrated together calculate the number of the beats generated?

Number of the beats generated is equal to difference between the frequencies.We can solve the problem as shown below.

Problem and solution

Solving problems in the concepts of beat is very simple.Just follow the concept given and comment if any clarification is required.

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