You are creating a transverse wave in a rope by shaking your hand from side to side. Without changing the distance that your hand moves, you begin to shake it slower and slower. What happens to the wavelength?
it decreases
Doesn't the wave equation...
Frequency*wavelength=velocity of waves?
frequency decreases, and velocity stays the same....
To find the wavelength you divide velocity over frequency
ok i understand what you said but we've estanblished that the frequency decreases. i don't understand what velocity has to do with anything b/c wavelength = v/f. I'm just confused on this one. my first answer was it stays the same but them I changed it but I don't fully understand why
The speed of waves in the rope depends upon the mass per unit length of the rope and the tension in the rope. That is probably not something they have taught you at this point. The mass per length is constant and the tension probably is also, but that depends upon how the experiment is done. It's not a very good question.
It the tension applied to the rope is constant, then the wave speed is constant.
To understand what happens to the wavelength when you shake your hand slower and slower to create a transverse wave in a rope, let's break down the concepts involved.
A transverse wave is a type of wave where the particles of the medium(vibrating rope) move perpendicular to the direction of the wave. In this case, when you shake your hand from side to side, the wave travels along the length of the rope.
The wavelength refers to the distance between two consecutive points on the wave that are in the same phase. In simpler terms, it is the distance between two peaks or two troughs of the wave.
When you shake your hand slower while maintaining the same distance, it implies that it takes a longer time for the wave to complete one full cycle. As a result, the wave's frequency decreases.
Since the speed of the wave remains constant, the equation v = fλ (where v represents the speed of the wave, f represents the frequency, and λ represents the wavelength) indicates that if the frequency decreases, the wavelength must also decrease.
Therefore, as you shake your hand slower and slower, the wavelength of the transverse wave in the rope decreases.