Question

If the wavelength of a wave on a string is increased, will you see more nodes or fewer nodes? Explain.

Answer 1

In the middle of the string, the oscillation amplitude is largest; such a position is defined as an antinode. We assign a wavelength to the fundamental (and each higher harmonic discussed below) standing wave. At a fixed moment in time, all we observe is either a crest or a trough, but we never observe both at the same time for the lowest frequency standing wave. From this, we determine that half a standing wave length fits along the length of the string for the fundamental. Alternatively, we say that the wavelength of the fundamental is twice the length of the string, or

As we'll discuss later, the oscillation frequencies of stretched strings effect the tone of the sounds we hear from instruments such as guitars, violins and cellos. Higher frequency oscillations result in higher-pitched tones; lower frequency oscillations produce lower-pitched tones. So how can we change the oscillation frequency of a stretched string? The above equation tells us. If we either increase the wave speed along the string or decrease the string length, we get higher frequency oscillations for the first (and higher) harmonic. Conversely, reducing the wave speed or increasing the string length lowers the oscillation frequency. How do we change the wave speed? Keep in mind, it is a property of the wave medium, so we have to do something to the string to alter the wave speed. From earlier discussions, we know that tightening the string increases the wave speed. We also know that more massive strings have smaller wave speeds.