michaelraymen said:Homework Statement
using a wire of length L= 1 M with both ends fixed, can you produce a standing wave with the following wavelengths? Explain why or why no.
a. 30 cm:
b. 1m :
c. 75 cm :
d. 2 m :
Homework Equations
L=n. (λn/2)
The Attempt at a Solution
1m= n. 30 cm/2 ?
HallsofIvy said:A standing wave must fit a full "wave" inside the given length. In other words the length must be an integer multiple of the wavelength.
michaelraymen said:So would all of the wave lengths work except for the 2 meter one?And How can I explain it with the formula?
Thank you for your help.
A standing wave is a type of wave that appears to stand still and does not move forward or backward. It is created when two waves with the same frequency and amplitude travel in opposite directions and interfere with each other. This results in certain points along the wave remaining stationary, while other points experience maximum displacement.
To produce a standing wave, you will need a medium, such as a string or air, and a source of vibration. The medium must be fixed at both ends and the source of vibration must have a constant frequency. As the waves travel in opposite directions and interfere with each other, a standing wave will be created.
The equation for a standing wave is y = 2Asin(kx)cos(ωt), where y is the displacement of the wave at a certain point, A is the amplitude, k is the wave number, x is the position along the wave, ω is the angular frequency, and t is the time. This equation describes the motion of the wave and can be used to calculate various properties of the standing wave.
Nodes are points along a standing wave where the displacement is always zero. These points remain stationary as the wave oscillates. Antinodes, on the other hand, are points where the displacement is at its maximum. These points move back and forth as the wave oscillates.
The wavelength of a standing wave can be determined by measuring the distance between two consecutive nodes or two consecutive antinodes. The frequency of a standing wave can be determined by counting the number of oscillations that occur in a certain amount of time, or by using the formula f = nω/2π, where n is the number of nodes or antinodes and ω is the angular frequency.