Two waves with different periods are described mathematically by:
y1 = (7.0 m)cos[ 2£kt/(3.0 ms)-£k/2 ]
y2 = (2.0 m)cos[ 2£kt/(3.1 ms)-3£k/2]
What is the beat frequency for these two waves?
To find the beat frequency between two waves, we need to identify the difference in their frequencies. The beat frequency (fbeat) is the absolute difference between the frequencies of the two waves. In this case, we can determine the frequencies of the waves by using the formula:
f = 1 / T
Where f is the frequency and T is the period.
For y1:
Period (T1) = 3.0 ms = 3.0 x 10^(-3) s
f1 = 1 / T1 = 1 / (3.0 x 10^(-3)) = 333.33 Hz
For y2:
Period (T2) = 3.1 ms = 3.1 x 10^(-3) s
f2 = 1 / T2 = 1 / (3.1 x 10^(-3)) = 322.58 Hz
Now, we can find the beat frequency (fbeat):
fbeat = |f1 - f2| = |333.33 - 322.58| = 10.75 Hz
Therefore, the beat frequency for these two waves is 10.75 Hz.