A transvers wave traveling on a rope is given by
y=0.25 sin(0.3 radX-40radt), where y and X is expressed in meter and t is in seconds. Determine
a-Amplitude.
B-frequency
C-Direction of motion.
e-Displacement at X=0.6 m and t=2.3 s.
Please help me
To determine the amplitude, frequency, direction of motion, and displacement at specific values of X and t, we will use the given equation:
y = 0.25 sin(0.3 radX - 40 radt)
a) Amplitude:
The amplitude represents the maximum displacement of the wave from its equilibrium position. In our equation, the coefficient in front of the sine function is the amplitude. Therefore, the amplitude in this case is 0.25.
b) Frequency:
The frequency represents the number of complete oscillations the wave makes per unit of time. In our equation, the coefficient of X (0.3 rad) represents the angular frequency (ω), which is related to the frequency (f) by the equation ω = 2πf. Therefore, the frequency can be calculated as f = 0.3 rad / (2π) ≈ 0.0477 Hz.
c) Direction of motion:
To determine the direction of motion, we need to look at the sign of the coefficient of t (-40 rad). A negative sign indicates that the wave is moving in the negative direction (opposite of positive x-axis), while a positive sign would indicate movement in the positive direction.
Therefore, since we have a negative sign in our equation, the direction of motion is in the negative x-direction.
d) Displacement at X = 0.6 m and t = 2.3 s:
To find the displacement at a particular point (X = 0.6 m) and time (t = 2.3 s), we substitute the values into the given equation:
y = 0.25 sin(0.3 rad × 0.6 - 40 rad × 2.3)
Evaluating this expression gives us the displacement of the wave at that specific point and time. To obtain the numerical value, you can use a calculator or software to perform the calculations.