The equation y=5sin(3x-4) where y is in millimeters,x is in metres and t in seconds,represent motion. Find;
Frequency
Period
Speed of the wave
SHOW ME THE WORKING
0.64HZ, 1.56s, 1.34
Y=5sin (3x-4y) where y is mm, x in meters find the frequency, speed and period
sadbs
To find the frequency, period, and speed of the wave represented by the equation y = 5sin(3x - 4), let's break down these components and explain how to find them.
1. Frequency: The frequency of a wave represents how many complete cycles occur in a given unit of time. In our equation, the coefficient of x inside the sine function represents the angular frequency, which is related to the frequency. To find the frequency, we need to divide the angular frequency by 2π.
- In this case, the angular frequency can be calculated as 3 since it is the coefficient in front of x.
- So, the frequency (f) can be found using the formula f = angular frequency / (2π).
- Therefore, f = 3 / (2π).
2. Period: The period of a wave is the amount of time it takes for one complete cycle to occur. It is reciprocal to the frequency and is denoted by the symbol T. The period can be calculated using the formula T = 1 / f, where f represents the frequency.
- In our case, we have already found the frequency in step 1 as f = 3 / (2π).
- Hence, the period (T) can be calculated as T = 1 / f, which is T = 1 / (3 / (2π)).
- Therefore, T = 2π / 3.
3. Speed of the wave: The speed of a wave can be determined by multiplying the wavelength with the frequency. However, we need additional information to calculate the speed, such as the wavelength or the wave velocity. Unfortunately, the given equation does not provide us with that information. Hence, we cannot directly calculate the speed of the wave using the provided equation.
In summary:
- Frequency (f) = 3 / (2π)
- Period (T) = 2π / 3
- Speed of the wave cannot be calculated without additional information.