How does tension affect a wave's speed on a string?

The speed of a wave on a string increases as the tension in the string increases.

In more detail, the speed of a wave on a string is directly proportional to the square root of the tension in the string. This relationship is described by the equation v = √(T/μ), where v is the wave speed, T is the tension, and μ is the linear mass density of the string (mass per unit length).

When the tension in the string is increased, the string becomes tighter and the particles in the string can move more quickly. This allows the wave to travel faster along the string. Conversely, if the tension is decreased, the string becomes looser and the particles move more slowly, resulting in a slower wave speed.

It's important to note that while increasing the tension increases the wave speed, it does not affect the frequency or wavelength of the wave. This is because the frequency of a wave is determined by the source of the wave, and the wavelength is determined by the speed of the wave and its frequency, according to the equation v = fλ, where v is the wave speed, f is the frequency, and λ is the wavelength.

In practical terms, this principle is applied in musical instruments. For example, when a guitar string is tightened (increasing the tension), the pitch of the note it produces rises. This is because the increased tension causes the wave speed to increase, which in turn increases the frequency of the sound wave, resulting in a higher pitch.

IB Physics Tutor Summary: The speed of a wave on a string gets faster when the string's tension increases, because it makes the string tighter, letting waves move quicker. This is shown by the formula v = √(T/μ), where T is tension and μ is the string's mass per length. This concept is used in musical instruments to change the pitch of notes.