Water waves in a shallow dish are 5.0 cm long. At one point, the water moves up and down at a rate of 5.2 oscillations per second.
(a) What is the speed of the water waves?
(b) What is the period of the water waves?
To solve this problem, we can use the formulas:
(a) Speed of wave (v) = Frequency (f) x Wavelength (λ)
(b) Period (T) = 1 / Frequency (f)
Given:
Wavelength (λ) = 5.0 cm
Frequency (f) = 5.2 oscillations per second
(a) To find the speed of the water waves, substitute the given values into the formula:
v = f x λ
= 5.2 oscillations per second x 5.0 cm
To calculate the speed, we need to convert cm to m:
1 cm = 0.01 m
v = 5.2 oscillations per second x 5.0 cm x 0.01 m/cm
= 0.26 m/s
Therefore, the speed of the water waves is 0.26 m/s.
(b) To find the period of the water waves, substitute the given frequency into the formula:
T = 1 / f
= 1 / 5.2 oscillations per second
T = 0.192 s
Therefore, the period of the water waves is 0.192 seconds.
To answer these questions, we need to understand the relationship between speed, wavelength, and frequency. The speed of a wave can be calculated using the formula:
Speed = Wavelength x Frequency (v = λf)
Where:
- Speed (v) is measured in meters per second (m/s)
- Wavelength (λ) is measured in meters (m)
- Frequency (f) is measured in hertz (Hz)
(A) Calculating the speed of the water waves:
We are given the wavelength (λ) as 5.0 cm. However, the formula requires the wavelength to be in meters. So, we need to convert the wavelength from centimeters to meters.
1 meter = 100 centimeters
Therefore, the wavelength in meters (λ) is:
λ = 5.0 cm ÷ 100 = 0.05 m
We are also given the frequency (f) as 5.2 oscillations per second.
Now, we can use the formula to calculate the speed (v):
v = λf
v = 0.05 m x 5.2 Hz
v = 0.26 m/s
Therefore, the speed of the water waves is 0.26 m/s.
(B) Calculating the period of the water waves:
The period of a wave is the time it takes for one complete oscillation. It can be calculated using the formula:
Period (T) = 1 / Frequency (f)
So, to find the period of the water waves, we can use the frequency (f) given as 5.2 Hz:
T = 1 / 5.2 Hz
T = 0.192 s
Therefore, the period of the water waves is 0.192 seconds.
speed=frequency*wavelength.
period=1/frequency