The oscillations of two points x1 and x2 at x = 0 and x = 1 m respectively are modelled as
follows:
y1 = 0.2 sin 3pt
and y2 = 0.2 sin (3pt +
8
p
)
Calculate the wavelength and speed of the associated wave.
To calculate the wavelength and speed of the associated wave, we need to first understand the relationship between wavelength, speed, and frequency.
The wavelength (λ) is the distance between two consecutive points in a wave that are in phase. It is usually measured in meters (m).
The speed (v) of a wave is the distance it travels per unit time. It is usually measured in meters per second (m/s).
The frequency (f) of a wave refers to the number of complete oscillations or cycles that occur in a given time period. It is usually measured in hertz (Hz), which represents cycles per second.
Now, to calculate the wavelength and speed of the associated wave, we need to extract the frequency from the given equations.
For the equation y1 = 0.2 sin(3pt):
The frequency (f1) can be found by inspecting the coefficient in front of the t term in the argument of the sine function. In this case, the coefficient is 3p. Since the coefficient in front of t is the angular frequency (ω = 2πf), we can divide it by 2π to get the frequency:
f1 = (3p) / (2π)
For the equation y2 = 0.2 sin(3pt + (8/√π)):
Similarly, the frequency (f2) can be found by inspecting the coefficient in front of the t term in the argument of the sine function, which is still 3p. So, we have:
f2 = (3p) / (2π)
The wavelength (λ) can be calculated using the formula:
λ = v / f
Since both waves have the same frequency, their wavelengths will be the same. So, we can calculate the wavelength of either wave.
However, to calculate the speed, we need additional information. If we have the time taken for a wave to travel a certain distance, we can divide that distance by the time to get the speed.
Please provide any additional information you may have, such as the time taken or any other relevant details, so that we can calculate the speed as well.
Umaga = 3π rad/s
k(x) = k(1)=8π
The wavelength:
Lamda =2π/k
= 2π/8π = 0.25m
The speed of the associated wave
V= Umaga/k
= 3π/8π = 0.75m/s.