A snapshot graph of a travelling wave is shown. The wave is travelling to the right at 10.4m/s. What is the amplitude if the maximum displacement is 26.6cm and the total distance travelled by the wave is 18.4m?
Max displacement is the amplitude =>
A=26.6 cm
To find the amplitude of the travelling wave, we can use the formula:
Amplitude (A) = Maximum displacement/2
Given that the maximum displacement is 26.6 cm, we can convert it to meters by dividing by 100:
Maximum displacement = 26.6 cm = 26.6/100 m = 0.266 m
So,
Amplitude (A) = 0.266 m / 2 = 0.133 m
Therefore, the amplitude of the travelling wave is 0.133 meters.
To find the amplitude of the wave, we need to understand a few key concepts: the maximum displacement, the total distance travelled, and the relationship between them.
First, let's define some terms:
- Maximum displacement: This refers to the maximum height or depth of the wave from its equilibrium position.
- Amplitude: It is the maximum displacement from the equilibrium position of a wave.
Now, let's determine the amplitude using the given information:
1. Convert the maximum displacement from centimeters to meters:
Maximum displacement = 26.6 cm = 26.6 / 100 m = 0.266 m.
2. The total distance travelled by the wave is twice the wavelength (one full cycle). Therefore, the wavelength can be calculated as:
Total distance travelled = 2 * wavelength.
Rearranging the equation: wavelength = total distance travelled / 2 = 18.4 m / 2 = 9.2 m.
3. The amplitude of a wave is half the wavelength. Therefore, the amplitude can be calculated as:
Amplitude = wavelength / 2 = 9.2 m / 2 = 4.6 m.
Thus, the amplitude of the wave is 4.6 meters.