A boat is wrecked by waves of speed 30m/s whose successive crest are 10m apart. Calculate the speed at which the boat receives the waves.
To determine the speed at which the boat receives the waves, we can use the formula for wave speed:
Wave Speed = Frequency x Wavelength
Given that the crests of the waves are 10 meters apart, we can calculate the wavelength. However, we need to find the frequency first.
The frequency can be calculated using the formula:
Frequency = Speed / Wavelength
In this case, the speed of the waves is given as 30 m/s and the wavelength is 10 m. Plugging these values into the formula, we can compute the frequency:
Frequency = 30 m/s / 10 m = 3 Hz
Now, we can substitute the frequency value into the wave speed formula:
Wave Speed = 3 Hz x 10 m = 30 m/s
Therefore, the speed at which the boat receives the waves is 30 m/s.
To calculate the speed at which the boat receives the waves, we can use the concept of wave velocity. The wave velocity is given by the formula:
Wave velocity = Frequency × Wavelength
In this case, the wavelength is given as 10m because the successive crests are 10m apart. We need to find the frequency of the waves first.
The frequency of the waves can be calculated by using the formula:
Frequency = Speed / Wavelength
We are given that the speed of the waves is 30m/s and the wavelength is 10m. Substituting these values into the formula, we have:
Frequency = 30m/s / 10m = 3 Hz
Now that we have the frequency and the wavelength, we can find the wave velocity:
Wave velocity = Frequency × Wavelength = 3 Hz × 10m = 30 m/s
Therefore, the speed at which the boat receives the waves is 30 m/s.