The speed of a transverse wave on a string is 450m/s, while the wavelength is 0.18m. The amplitude is 2.0mm.
What is the total up and down distance moved by the wave particle for each cycle of the wave?
How many cycles of the wave would have to pass by a given point so that the particle on the string moves a total distance of 1.0km
How much time is required for a particle to move through a total distance of 1.0km?
Where do I even start to find the answers to these questions???
The longitudinal speed is 450 m /s
How long to go 0.18 meters?
T = 0.18 / 450 = 0.0004 seconds
f = 1/T = 2500 Hz
transverse:
A = 2 * 10^-3 meters
y = A sin(2 pi f t) = 2*10^-3 sin (15700 t)
In one cycle a particle moves:
from 0 to A
then from A to -A
then from -A to zero
So
Moves 4 A = 8* 10^-3 meters = 8 mm
Move 1 km = 1000 meters up and down?
well that would take 1000 meters / 8*10^-3 meters/cycle = 125,000 cycles
T = 0.18 / 450 = 0.0004 seconds
125,000 cycles* 0.0004 seconds/cycle = 50 cycles
To find the answers to these questions, we can use the formulas and concepts related to waves and their properties. Let's break down each question step by step:
1. The total up and down distance moved by the wave particle for each cycle of the wave can be found using the formula:
Total distance = 2 * amplitude
Given that the amplitude is 2.0 mm, we can convert it to meters by dividing by 1000:
Total distance = 2 * (2.0 mm / 1000) = 0.004 m
Therefore, the total up and down distance moved by the wave particle for each cycle is 0.004 meters.
2. To determine the number of cycles required for the particle to move a total distance of 1.0 km, we need to use the formula:
Total distance = wavelength * number of cycles
Rearranging the formula, we have:
Number of cycles = Total distance / wavelength
Given that the total distance is 1.0 km and the wavelength is 0.18 m, we need to convert the total distance to meters by multiplying it by 1000:
Number of cycles = (1.0 km * 1000) / 0.18 = 5555.56 cycles
Since we cannot have a fraction of a cycle, we round it to the nearest whole number.
Therefore, the number of cycles required for the particle to move a total distance of 1.0 km is approximately 5556 cycles.
3. To find the time required for a particle to move through a total distance of 1.0 km, we need to use the formula:
Time = Total distance / Speed
Given that the total distance is 1.0 km, we need to convert it to meters by multiplying it by 1000:
Time = (1.0 km * 1000) / 450 = 2222.22 seconds
Therefore, the time required for a particle to move through a total distance of 1.0 km is approximately 2222.22 seconds.
Now you have the step-by-step explanation of how to find the answers to these questions.