Pepe and Alfredo are resting on an offshore raft after a swim. They estimate that 3m separates a trough and an adjacent crest of surface waves on the lake. They count 14 crests that pass by the raft in 20 seconds. Calculate how fast the waves are moving.
wavelength=6m
freq=14/20 sec
freq*wavelengt=speed
14/20*6=84/20=4.2m/s
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Well, well, well, Pepe and Alfredo seem to be catching some waves! Let's see if we can ride this wave of calculations together.
We know that the distance between the trough and crest is 3 meters. So, in 20 seconds, 14 crests pass by. That means 14 crests travel a distance of 3 meters in 20 seconds.
To find the distance traveled by one crest, we can divide the total distance (3 meters) by the number of crests (14). So each crest travels a distance of 3 meters / 14 crests = 0.214 meters.
Now, since we have the distance traveled by one crest, we can determine how fast each crest is moving by dividing this distance by the time it takes to travel that distance. In this case, it's 0.214 meters / 20 seconds.
Using our trusty calculator, the speed of each crest turns out to be approximately 0.01 meters per second.
So, Pepe and Alfredo, these waves are moving at a leisurely pace of 0.01 meters per second. Enjoy the calm ride!
To calculate the speed of the waves, we need to know the wavelength (distance between two crests). We can calculate the wavelength by dividing the total distance (3m) by the number of crests that pass by the raft.
Wavelength = Total distance / Number of crests
Wavelength = 3m / 14 crests
Wavelength ≈ 0.214 m/crest
Next, we use the formula for wave speed:
Wave speed = Wavelength / Time
Wave speed = 0.214 m/crest / 20 s
Wave speed ≈ 0.0107 m/s
Therefore, the waves are moving at approximately 0.0107 m/s.
To calculate the speed of the waves, we need to determine the distance traveled by each wave crest in a given time frame.
First, let's find the distance between two consecutive crests. We are given that the distance between a trough and an adjacent crest is 3m. Since one complete wave consists of one trough and one crest, the distance between two consecutive crests is twice the given distance: 2 * 3m = 6m.
Next, we need to determine the time it takes for 14 crests to pass by the raft. We are given that 14 crests pass in 20 seconds.
Now, we can calculate the distance traveled by the crests in 20 seconds. Since 14 crests pass in this time, the total distance traveled by the crests is 14 * 6m = 84m.
Finally, we can find the speed of the waves by dividing the total distance traveled by the time taken:
Speed = Distance / Time
Speed = 84m / 20s
Speed = 4.2 m/s
Therefore, the waves are moving at a speed of 4.2 meters per second.