A certain transverse wave is described by the equation
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
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can I Have some help on where to start?
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 wave's properties, we can extract information from the given equation:
y(x,t) = (6.50 mm)sin(2π)((t/0.0360 s)-(x/0.280m))
(a) Amplitude:
The amplitude of a wave is the maximum displacement of any particle of the wave from its undisturbed position. In this equation, the coefficient before the sine function gives us the amplitude:
Amplitude = 6.50 mm
(b) Wavelength:
The wavelength of a wave is the distance between two identical points on the wave, such as two consecutive crests or two consecutive troughs. It is given by the equation:
Wavelength = 2π/ |k|
where k represents the wave number. In this equation, k is the coefficient in front of x:
k = 2π/0.280 m = 22.46 m^(-1)
Wavelength = 2π/ |22.46 m^(-1)|
(c) Frequency:
The frequency of a wave is the number of complete cycles passing through a given point in one second. It is reciprocally related to the period of the wave. The period, represented by T, is given as 0.0360 s in this equation.
Frequency = 1 / T = 1 / 0.0360 s
(d) Speed of propagation:
The speed of wave propagation is given by the equation:
v = ω / k
where ω is the angular frequency. In this equation, ω equals 2π/T:
v = (2π / T) / k
(e) Direction of propagation:
To determine the direction of wave propagation, we need to examine the sign of the x coefficient within the sine function. If the coefficient is positive, the wave propagates in the positive x direction, and if it is negative, the wave propagates in the negative x direction.
Now, using the given values, we can calculate the requested properties.