The crests on a long surface water wave are 22 m apart, and in 1 minute 8 crests pass by. What is the speed of this wave?
speed=distance/time= 8*22/60sec
To find the speed of a wave, we can use the formula:
Speed = Wavelength × Frequency
In this case, we are given the distance between the crests (wavelength) and the number of crests passing in a given time (frequency).
The distance between the crests is given as 22 m, so the wavelength is 22 m.
The number of crests passing by in 1 minute is given as 8. Since frequency is the number of cycles (crests) per unit time, the frequency is 8 crests/minute.
It's important to convert the time unit to seconds before calculating the speed, as the SI unit of frequency is Hertz (Hz), which corresponds to cycles per second.
There are 60 seconds in a minute, so we can convert the frequency to 8 crests/60 seconds.
Now we can substitute the values into the formula:
Speed = Wavelength × Frequency
= 22 m × (8 crests / 60 seconds)
To simplify the calculation, we can cancel out the units:
Speed = 22 m × (8 / 60)
= 22 m × (2 / 15)
= 44 / 15 m/s
Therefore, the speed of the wave is approximately 2.93 m/s.