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???

1 answer

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