A wave is travelling to the right at 50.0 m/s. What is the amplitude if the maximum displacement is 38.0 cm and the total distance travelled by the wave is 16.0 m?
To find the amplitude of the wave, we need to understand the relationship between the maximum displacement and the amplitude.
Amplitude is defined as the maximum displacement of a wave from its equilibrium position. It represents the maximum extent to which particles of the medium carrying the wave are displaced. It is usually represented by the symbol 'A'.
In this case, we are given that the maximum displacement is 38.0 cm. However, we also need to consider the total distance travelled by the wave. Since the wave is traveling to the right, the distance traveled will be positive.
The total distance traveled by the wave is given as 16.0 m. We can use this information to find the wavelength of the wave.
The wavelength is the distance between two consecutive points on a wave that are in phase with each other. It represents the distance covered by one complete cycle of the wave. It is usually represented by the symbol 'λ' (lambda).
To find the wavelength, we can use the equation:
wavelength = total distance / number of cycles
In this case, since the total distance traveled is 16.0 m and the wave is traveling at 50.0 m/s to the right, we can calculate the number of cycles as follows:
number of cycles = total distance / velocity
number of cycles = 16.0 m / 50.0 m/s
number of cycles = 0.32 cycles
This means that the wave completes 0.32 cycles in its total distance of 16.0 m.
Now, we know that the maximum displacement occurs at the crest or trough of the wave. Since one complete cycle consists of a crest and a trough, the maximum displacement of 38.0 cm occurs over half a cycle.
Therefore, the amplitude (A) can be calculated as follows:
Amplitude = Maximum displacement / 0.5
Amplitude = 38.0 cm / 0.5
Amplitude = 76.0 cm
Thus, the amplitude of the wave is 76.0 cm.