y(x,t) = (6.50 mm)sin2pi((t/0.0360 s)-(x/0.280m))
Determine the wave's (a) amplitude (b) wavelength (c) frequency (d) speed of propagation and (e) direction of propagation
To determine the properties of the given wave equation y(x,t) = (6.50 mm)sin2π((t/0.0360 s)-(x/0.280 m)), we can analyze each property separately.
(a) Amplitude:
The amplitude of a wave is the maximum displacement from the equilibrium position. In the given equation, the amplitude is already provided as 6.50 mm.
(b) Wavelength:
The wavelength of a wave is the distance between two adjacent points in phase. To determine the wavelength, we need to identify the term that represents the spatial variation in the wave equation. In this case, it is the term (x/0.280 m). The wavelength can be found by taking the inverse of the coefficient, so the wavelength is 0.280 m.
(c) Frequency:
The frequency of a wave is the number of complete cycles per unit of time. In the given equation, the term that represents the temporal variation is (t/0.0360 s). To determine the frequency, we need to take the inverse of the coefficient, so the frequency is 1/0.0360 Hz.
(d) Speed of Propagation:
The speed of propagation of a wave can be determined using the equation: speed = frequency × wavelength. In this case, we already have the values for frequency and wavelength. Therefore, we can calculate the speed of propagation as follows:
Speed = (1/0.0360 Hz) × 0.280 m
= 7.78 m/s
The speed of propagation of the given wave is 7.78 m/s.
(e) Direction of Propagation:
To determine the direction of propagation, we need to examine the arguments inside the sine function. The wave equation is y(x,t) = (6.50 mm)sin2π((t/0.0360 s)-(x/0.280 m)).
From the arguments, we notice that the term (t/0.0360 s) appears with a positive sign, while the term (x/0.280 m) appears with a negative sign. This indicates that the wave is propagating in the positive x-direction (along the negative x-axis).
In summary, the properties of the given wave equation are:
(a) Amplitude: 6.50 mm
(b) Wavelength: 0.280 m
(c) Frequency: 1/0.0360 Hz
(d) Speed of Propagation: 7.78 m/s
(e) Direction of Propagation: Positive x-direction (along the negative x-axis)