Final answer:
To calculate speed using beat frequency, apply the Doppler effect formula, where the absolute difference between the observed frequency and the source frequency gives the beat frequency. This principle is used in applications like police radar to determine vehicle speed by analyzing the frequency shift due to motion.
Step-by-step explanation:
Understanding Beat Frequency and Speed Calculation
To find speed using beats per second (the beat frequency) and frequency, we need to understand the concept of the Doppler effect, which relates frequency change to relative motion. The formula for beat frequency is given by fB = |fobs - fs|, where fB is the beat frequency, fobs is the observed frequency and fs is the source frequency.
For example, police radar uses this principle by sending out a frequency, such as 1.50×109 Hz microwaves, and then measures the frequency of the returning wave to determine the speed of a motor vehicle.
A higher or lower observed frequency would indicate motion towards or away from the radar source, respectively. The difference in these frequencies is used to calculate the beat frequency, which can be converted to a vehicle's speed.
If you have a heart rate of 150 beats per minute during exercise, the time per beat is calculated by dividing 60 seconds by 150, which equals 0.400 seconds per beat. For tuning forks and other applications, if it takes 2.50×10-3 seconds to complete an oscillation, the frequency is the inverse of the time, which means the frequency is 400 Hz.