The time needed for a water wave to change from the equilibrium level to the crest is 0.20 s.
(a) What fraction of a wavelength is this?
(b) What is the period of the wave?
(c) What is the frequency of the wave?
I don't understand any of this. help appreciated
Think of the graph of a sine wave.
one period of the wave proceeds as follows
equilibrium → maximum → equilibrium → minimum → equilibrium
Each stage is 1/4 of the period. So,
(a) 0.20 s = 1/4 of the period T
(b) T = 4*0.20 = 0.8 s
(d) f = 1/T = 1.25 Hz
Sure, let's break down each part of the problem step-by-step:
(a) To find the fraction of a wavelength, we need to know the velocity of the wave. However, if this information is not provided, we cannot compute the fraction directly. Please double-check if any additional information is given in the problem.
(b) The period of a wave (T) is the time it takes for one complete cycle. In this case, the time needed for the water wave to change from the equilibrium level to the crest is given as 0.20 s, which is the time for half a cycle. Since one complete cycle is equal to the time for two halves, the period can be calculated as:
T = 2 * 0.20 s
T = 0.40 s
Therefore, the period of the wave is 0.40 s.
(c) The frequency of a wave (f) is the number of cycles that occur per second. It can be calculated by taking the reciprocal of the period:
f = 1 / T
f = 1 / 0.40 s
f = 2.5 Hz
Hence, the frequency of the wave is 2.5 Hz.
If you have any further questions or need clarification, please let me know!
Of course, I can help explain these concepts to you!
First, let's start with some basic definitions:
- A water wave is a disturbance that propagates through water, causing the water's surface to oscillate up and down.
- The equilibrium level of a wave refers to the undisturbed or flat surface of the water.
- The crest of a wave is the highest point of the wave.
Now, let's break down the problem step by step:
(a) What fraction of a wavelength is the time needed for the wave to change from the equilibrium level to the crest?
To understand this, we need to know the speed of the wave. Unfortunately, the problem statement doesn't provide that information. So, let's assume the wave speed is constant for now.
The time needed for the wave to change from the equilibrium level to the crest is given as 0.20 s. Let's call this time interval "T_e2c."
The distance from the equilibrium level to the crest is half of the wavelength (λ/2) because the wave oscillates up and down symmetrically. So, the fraction of a wavelength that T_e2c represents is:
Fraction of wavelength = T_e2c / Period (T)
(b) What is the period of the wave?
The period of a wave is the time taken for one complete cycle of the wave. In other words, it is the time interval required for the wave to repeat its shape.
To find the period, we can use the relationship between the wave speed (v), wavelength (λ), and period (T):
v = λ / T
Since we need to find the period, we rearrange the equation to:
T = λ / v
However, we still don't have the wave speed (v), so we can't find the exact period without that information.
(c) What is the frequency of the wave?
The frequency of a wave represents the number of complete cycles per unit time. It is the reciprocal of the period:
Frequency (f) = 1 / T
Again, since we don't have the exact period, we can't find the frequency without the wave speed.
So, in summary:
(a) Without knowing the wave speed, we can't determine the fraction of a wavelength represented by the time interval.
(b) Without the wave speed, we can't find the period.
(c) Without the wave speed, we can't determine the frequency either.
To solve this problem accurately, we would need the wave speed. If you have any additional information or any other questions, please let me know!