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
To determine the wave's amplitude, you can refer to the equation. The amplitude of a wave is the maximum displacement from the equilibrium position. In this case, the amplitude is given as 6.50 mm. So, the answer to part (a) is 6.50 mm.
To find the wavelength, you can compare the equation to the general form of a transverse wave:
y(x,t) = A sin(2π((t/T) - (x/λ)))
In the equation, λ represents the wavelength. By comparing the given equation to the general form, you can see that the coefficient in front of x/0.280 m is the wavelength. Therefore, the wavelength is 0.280 m. So, the answer to part (b) is 0.280 m.
The frequency of a wave is the number of complete oscillations it makes in one second. To find the frequency, you can use the formula:
f = 1/T
where T is the period of the wave. In the given equation, the coefficient in front of t/0.0360 s (remember that 2π is just a constant value) is the period. Thus, the period is 0.0360 s. By substituting the period in the formula, you get:
f = 1/0.0360 s
Simplifying this gives:
f = 27.8 Hz
So, the answer to part (c) is 27.8 Hz.
To calculate the speed of propagation, you can use the formula:
v = λf
where v represents the speed of propagation, λ is the wavelength, and f is the frequency. By substituting the given values, you get:
v = (0.280 m)(27.8 Hz)
Calculating this gives:
v ≈ 7.78 m/s
So, the answer to part (d) is approximately 7.78 m/s.
The direction of propagation can be determined by examining the equation. In this case, the sine function has a positive coefficient (1), which means the wave is propagating in the positive direction along the x-axis. Therefore, the answer to part (e) is the positive direction along the x-axis.