A pond is 12 metres across. The crests of two successive waves are 60.0 cm apart and they each move across the pond in 15 seconds.
a)What is the velocity of the waves?
b)What is the frequency of the waves?
c)What is the period of the waves?
To find the answers to these questions, we need to understand the relationship between velocity, frequency, and period in wave motion.
a) The velocity of a wave can be calculated by dividing the distance traveled by the time taken. In this case, the distance traveled is the distance between two successive crests, which is given as 60.0 cm. The time taken is given as 15 seconds.
So, to find the velocity of the waves, we can use the formula:
Velocity = Distance/Time
Velocity = 60.0 cm/15 s
Make sure to convert the distance to meters and the time to seconds if necessary.
b) The frequency of a wave represents the number of wave crests passing a given point in one second. It is measured in Hertz (Hz). We can calculate the frequency using the formula:
Frequency = 1/Period
In this case, the period is equivalent to the time it takes for one wave to pass a given point, which is given as 15 seconds.
Frequency = 1/15 Hz
c) The period of a wave is the time it takes for one complete cycle of the wave to pass a given point. It is the inverse of the frequency, as mentioned earlier. So, the period can be calculated using the formula:
Period = 1/Frequency
Using the calculated frequency from part (b), we have:
Period = 1/(1/15) s
Simplifying, we get:
Period = 15 s
Therefore, the answers are:
a) The velocity of the waves is 4.0 m/s
b) The frequency of the waves is 1/15 Hz
c) The period of the waves is 15 seconds