How can one recognise the beat frequency from a graph?
Why is the beat frequency equal to the difference of the frequency of the two waves?
To recognize the beat frequency from a graph, you can follow these steps:
1. Start by examining the graph representing the superposition of two waves.
2. Look for the regions on the graph where the amplitude of the combined wave is maximum, i.e., where the peaks are highest.
3. Measure the distance between consecutive maximum points in time (horizontal axis).
4. Calculate the inverse of this distance to find the frequency.
5. The calculated frequency corresponds to the beat frequency of the two waves.
Now, let's dive into why the beat frequency is equal to the difference of the frequency of the two waves.
When two waves of slightly different frequencies interfere, they create a phenomenon known as beats. This occurs when the waves are in a state of constructive and destructive interference periodically.
The beat frequency is defined as the difference between the frequencies of the two waves. Mathematically, it can be represented as follows:
Beat Frequency = |Frequency1 - Frequency2|
Let's understand why this is the case:
1. Constructive Interference: When the two waves are in phase (peaks align with peaks, and troughs align with troughs), they add up and create a wave with higher amplitude. The frequency of this resultant wave is the average frequency of the two waves.
2. Destructive Interference: When the two waves are exactly out of phase (peaks align with troughs), they subtract and cancel each other out, resulting in a wave with lower amplitude. The frequency of this resultant wave is again the average frequency of the two waves.
3. Beats: As the waves interfere, they go through cycles of constructive and destructive interference. This leads to periodic fluctuations in the amplitude of the resultant wave. The beat frequency represents how many times these fluctuations occur per second.
Since the frequency of a wave is the number of cycles it completes per second, the beat frequency is the difference between the number of cycles completed by the two waves in the same time period.
Therefore, the beat frequency can be seen as the difference between the frequencies of the two waves, as it reflects the periodic variations caused by their interference.