A group of swimmers is resting in the sun on an off shore raft. They estimate that 2.9 meters separates a trough and an adjacent crest of surface waves on the lake. In addition, they count 12 crests that pass by the raft in 16 seconds.
What is the Period of these waves?
P = 16/12 = 1.333 s.
To find the period of the waves, we need to understand what period represents. The period is the time it takes for one complete wave cycle to pass by a certain point.
Given that the swimmers counted 12 crests passing by the raft in 16 seconds, we can determine the number of crests passing by the raft in 1 second. We can calculate this by dividing the total number of crests (12) by the total time (16 seconds):
Number of crests per second = 12 crests / 16 seconds = 0.75 crests/second
Next, we can find the distance between two adjacent crests. It is given that 2.9 meters separate a trough and an adjacent crest. Since one complete wave cycle consists of one trough and one crest, the distance between two adjacent crests is half of this value:
Distance between two adjacent crests = 2.9 meters / 2 = 1.45 meters/crest
Now, we have the number of crests passing by the raft in 1 second and the distance between adjacent crests. The product of these two values will give us the speed of the waves:
Wave speed = Number of crests per second × Distance between adjacent crests
= 0.75 crests/second × 1.45 meters/crest
By canceling out the units, we can simplify the calculation:
Wave speed = 0.75 × 1.45 meters/second
= 1.0875 meters/second
The period of the waves represents the time it takes for one complete wave cycle to pass by the raft. To find the period, we can use the formula:
Period = Distance / Speed
Since we want to find the period in seconds, we need to divide the distance between adjacent crests by the wave speed:
Period = Distance between adjacent crests / Wave speed
= 1.45 meters / 1.0875 meters/second
Now, by dividing the distance by the speed, we can calculate the period of the waves:
Period = 1.33 seconds
Therefore, the period of these waves is approximately 1.33 seconds.