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Wave speed on a string
Intermediate
Depends on tension and mass per unit length.
v = √(T/μ)v = √(T/μ), where T is tension and μ mass per unit length. Tighter and lighter strings carry waves faster.
T = 100 N, μ = 0.01 kg/m: v = 100 m/s.
Frequency doesn't change the speed.
In more detail
The speed of a transverse wave on a string is v = sqrt(T/μ), where T is the tension and μ is the mass per unit length. Tighter, lighter strings carry waves faster.
Real-world uses
- Guitar and piano strings are tuned by adjusting tension.
- Engineers calculate wave speeds in cables and ropes.
- Guitar makers choose strings of a given tension and mass per length so that the waves travel at the speed needed for the right pitch.
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Frequently asked questions
Does amplitude change the speed?
No, only tension and linear density set the speed.
Why do thicker strings sound lower?
Because they have a higher mass per unit length, which lowers the wave speed and the frequency.
Why does a tighter string make a higher note?
The wave speed increases with tension, so for a fixed length the frequency of the harmonics rises.
Related topics in Waves & Sound
Amplitude and intensity · Wave equation (travelling) · Wave number · Wave speed in a medium · Speed of sound · Speed of sound in gases