Two waves with different periods are described mathematically by:
y3 = (7.0 m)cos[ 2£kt/(3.0 ms) - £k/2 ]
y4 = (2.0 m)cos[ 2£kt/(3.1 ms) ¡V 3£k/2]
What is the beat frequency for these two waves?
To find the beat frequency for two waves, we need to find the difference in their frequencies. The formula for beat frequency is:
Beat Frequency = |f1 - f2|
Where f1 and f2 are the frequencies of the two waves.
In this case, the frequencies can be found by taking the inverse of the periods. The period T is the time it takes for one complete cycle of the wave, and frequency f is the number of cycles per second (or hertz, Hz), given by:
f = 1/T
For the first wave:
Period T3 = 3.0 ms = 3.0 × 10^(-3) s
Frequency f3 = 1 / T3 = 1 / (3.0 × 10^(-3) s)
For the second wave:
Period T4 = 3.1 ms = 3.1 × 10^(-3) s
Frequency f4 = 1 / T4 = 1 / (3.1 × 10^(-3) s)
Once we have the frequencies, we can calculate the beat frequency using the formula:
Beat Frequency = |f3 - f4|
Now we can substitute the values and solve for the beat frequency.