A grasshopper floating in water generates waves at a rate of three per second with a wavelength of two centimeters. (a) What is the period of these waves in seconds? (b) What is the wave velocity in m/s?
T = 1/f = 1/3 second
distance = rate * time
.02 = c * 1/3
c = .06 m/s
(a) The period of the waves can be calculated using the formula: period = 1/frequency. Since the frequency of the waves is given as three per second, the period can be calculated as 1/3, which is approximately 0.333 seconds.
(b) The wave velocity can be determined using the equation: velocity = frequency x wavelength. Given that the frequency is three per second and the wavelength is two centimeters (which is equivalent to 0.02 meters), we can calculate the wave velocity as 3 x 0.02 = 0.06 m/s.
So, the period of the waves is approximately 0.333 seconds and the wave velocity is 0.06 m/s.
To calculate the period of the waves, use the formula:
Period (T) = 1 / Frequency (f)
Given that the frequency is 3 waves per second, we can substitute the value into the formula:
T = 1 / 3
The period of the waves is 1/3 seconds.
To calculate the wave velocity, use the formula:
Wave velocity (v) = Frequency (f) × Wavelength (λ)
Given that the frequency is 3 waves per second and the wavelength is 2 centimeters, we need to convert the wavelength to meters:
1 centimeter = 0.01 meters
Therefore, the wavelength is 2 × 0.01 = 0.02 meters.
Now we can substitute the values into the formula:
v = 3 × 0.02
The wave velocity is 0.06 m/s.
To calculate the period of the waves, we need to know that the period is the time it takes for one complete wave cycle. It can be calculated using the formula:
Period (T) = 1 / Frequency (f)
In this case, the frequency of the waves is given as three per second, so:
(a) Period (T) = 1 / Frequency (f) = 1 / 3 = 0.33 seconds
To calculate the wave velocity, we need to use the formula:
Wave velocity (v) = Frequency (f) × Wavelength (λ)
In this case, the frequency is given as three per second, and the wavelength is given as two centimeters. However, it is more convenient to work with SI units, so we need to convert centimeters to meters by dividing by 100:
(b) Wave velocity (v) = Frequency (f) × Wavelength (λ) = 3 × (2/100) = 0.06 m/s
So, the period of these waves is 0.33 seconds, and the wave velocity is 0.06 m/s.