Standing Waves on Strings Physics 121 Lab - UW-Milwaukee Introduction Several important properties of waves can be shown by means of standing waves in a string. This type of wave is important because most of the vibrations of extended bodies, such as the prongs of a tuning fork or the strings of a piano, are standing waves. The purpose of this experiment is to examine how the tension required to produce a standing wave in a vibrating string of fixed length and mass density is affected by the wavelength and the frequency of the wave. This is a hands-on experiment where the student gets to feel the force required to change the number of vibrating segments. Theory Standing waves (stationary waves) are produced by the addition of two traveling waves, both of which have the same wavelength and speed, but travel in opposite directions through the same medium. Figure 1 shows such a system, where a mechanical vibrator produces a wave on a string which moves to the right and reflection from a fixed end produces a left moving wave. Where the two waves are always 1800 out of phase, very little motion occurs (none of the amplitudes are the same). Such places where destructive interference between the traveling wave pulses leads to very little (sometimes zero) displacement of the medium are called nodes (see Figure 1). Figure 1: Standing Wave Photo Where the two waves are in phase, the motion is maximum. These positions where constructive interference between the traveling wave pulses leads to a maximum displacement of the medium are call anti-nodes. Figure 2 shows a representation of a standing wave on a string that has three anti-nodes and four nodes. Figure 2: Standing Wave Representation This matches well what the eye or camera sees since the string speed is minimum at the extremes. However, don't forget that the string goes through all of the positions in between the extremes as shown by the blur in Figure 1. Note that as shown in Figure 2, the node-to-node distance is one-half of the wavelength. The necessary conditions for the