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 can use the formulas related to wave properties. Let's break down each question step by step:
a) What is the velocity of the waves?
The formula to calculate the velocity of a wave in a given medium is v = λ * f, where v represents velocity, λ represents wavelength, and f represents frequency.
Since we are given the distance between the crests (wavelength) and the time it takes for the wave to move across the pond (15 seconds), we need to convert the unit of time to frequency. Frequency is the number of cycles (waves) per unit of time.
To find the frequency, we can use the formula f = 1 / T, where f represents frequency, and T represents the period. Considering period is the time it takes for one complete cycle, we know T = 15 seconds.
b) What is the frequency of the waves?
Using f = 1 / T, we can substitute f = 1 / 15 seconds.
c) What is the period of the waves?
The period of the waves is T = 15 seconds.
Now, let's calculate the answers to these questions.
a) Velocity of the waves:
We are given the distance between two successive waves (wavelength) as 60.0 cm. To ensure the units are consistent, let's convert it to meters by dividing by 100 (1 meter = 100 centimeters).
λ = 60.0 cm / 100 = 0.6 meters
Now, substituting the given values into the equation v = λ * f, we have:
v = 0.6 meters * f
b) Frequency of the waves:
From the given information, we know T = 15 seconds. Using f = 1 / T, we substitute T = 15 seconds.
f = 1 / 15 seconds
c) Period of the waves:
The period of the waves is T = 15 seconds.
Calculating the frequency and velocity of the waves depends on the given information. Once you have the values for wavelength and time, you can use the formulas mentioned above to find the answers.