Purpose
Determine the formation of standing waves on a string from the interference of traveling waves traveling in opposite directions.
Determine the tension T in the string required to produce standing waves.
Investigate the relationship between tension T and the wavelength λ of the wave.
Determine an experimental value for the frequency f of the wave and compare it to the known value fo 120Hz.
Theory
Waves are one means by which energy can be transported. Waves on a string are an example of transverse waves. These are waves in which individual particles of the medium (in this case the string) move perpendicular or transverse to energy moving along the string. In Figure 1 a string tied to a vibrator at one end passes over a pulley, and the weight of masses on the other end provides tension T in the string. The vibrator moves up and down at a frequency f, which cases a wave of that same frequency to propagate down the string. In the simulation used a frequency of 60Hz, but because the electromagnet attracts the steel blade twice in each cycle, the vibrator frequency is 120Hz.
The point at which the string passes over the pulley is a fixed point, and the wave is reflected from that point. Thus the string is a medium in which two waves of the same speed, frequency, and wavelength travel in the opposite direction. These two waves will interfere with each other to produce a standing wave when the proper relationship exits between the string length L and the wavelength λ of the wave. When a standing wave is produced, its characteristic features are the existence of nodes and antinodes at points along the string. A node N is a point on the string for which the amplitude of vibration is a maximum at all times. To form a standing wave, a node must occur at each end of the string, and an antinode must occur between each node. The distance between nodes is λ⁄2, or one-half of a wavelength of the wave. In terms of the string length L, a standing wave is possible when
L=n(λ/2),n=1,2,3,4,… (1)