Betty is sitting on of her surfboard out in the ocean. She is waiting for the perfect wave to come along so she can ride it in to shore. As she waits, she notices that the waves roll by in patterns, or sets. As Betty waits, she counts the number of waves that pass her during a 1-second period; she counts just 1. She estimates that the distance between crests is 6 meters. Betty sees the perfect wave and begins paddling. She pushes herself up, stands on the surfboard and rides the wave all the way in to shore, a distance of about 60 meters. It takes her about 10 seconds to ride the wave in. Use two methods to calculate the speed of the wave based on the information presented. Are they the same? Explain how you got your answers.
Question
Betty is sitting on of her surfboard out in the ocean. She is waiting for the perfect wave to come along so she can ride it in to shore. As she waits, she notices that the waves roll by in patterns, or sets.
As Betty waits, she counts the number of waves that pass her during a 1-second period; she counts just 1. She estimates that the distance between crests is 6 meters. Betty sees the perfect wave and begins paddling. She pushes herself up, stands on the surfboard and rides the wave all the way in to shore, a distance of about 60 meters. It takes her about 10 seconds to ride the wave in. Use two methods to calculate the speed of the wave based on the information presented. Are they the same? Explain how you got your answers.
Solution
Method 1: Using the wave frequency and wavelength
The speed of a wave can be calculated using the formula: speed = frequency * wavelength. In this case, the frequency of the wave is 1 wave per second (since Betty counted 1 wave passing her in a 1-second period) and the wavelength is 6 meters (the distance between crests).
So, speed = 1 wave/second * 6 meters/wave = 6 meters/second.
Method 2: Using the distance and time it took Betty to ride the wave
The speed of an object (or in this case, a wave) can also be calculated using the formula: speed = distance / time. Here, the distance Betty traveled on the wave is 60 meters and the time it took her is 10 seconds.
So, speed = 60 meters / 10 seconds = 6 meters/second.
In both methods, we find that the speed of the wave is 6 meters/second. Therefore, they are the same.
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