Final answer:
By using the concept of beats and the fundamental frequency formula for closed organ pipes, we can calculate the velocity of sound to be approximately 300 m/s, given that two pipes produce 16 beats in 20 seconds.
Step-by-step explanation:
To calculate the velocity of sound based on the given information about two closed organ pipes producing beats, we need to first understand the concept of beats. Beats occur when two sound waves of slightly different frequencies interfere with each other, leading to a periodic variation in intensity. The number of beats per second is equal to the absolute difference in frequencies of the interfering waves.
In this case, the two closed organ pipes of 100 cm and 101 cm are producing 16 beats in 20 seconds, which means they are producing 0.8 beats per second (16 beats / 20 s).
The fundamental frequency (f) of a closed organ pipe is given by f = v / (4L), where v is the velocity of sound and L is the length of the pipe. Since we have two pipes with lengths L1 = 100 cm and L2 = 101 cm, their fundamental frequencies f1 and f2 can be represented as:
f1 = v / (4 × 1.00 m)
f2 = v / (4 × 1.01 m)
The beat frequency is the absolute difference between f1 and f2, which we know is 0.8 Hz. So, |v / (4 × 1.00 m) - v / (4 × 1.01 m)| = 0.8 Hz. From this equation, we can solve for v, the velocity of sound.
After performing the algebra, we find that the velocity of sound (v) is approximately 300 m/s.