## Now if you are watching

Characteristics of Waves : Speed
Now if you are watching a wave go by you will notice which they move at a constant velocity. Thinking back to rectilinear motion you will be able to remember which we know how to work out how fast something moves. The speed is the distance you travel divided by the time you take to travel which distance. This is excellent because we know which the waves travel a distance {\displaystyle \lambda } \lambda in a time T. This means which we cone determine the speed.

{\displaystyle v={\frac {\lambda }{T}}} {\displaystyle v={\frac {\lambda }{T}}}

v : speed (m.s−1)
{\displaystyle \lambda } \lambda : wavelength (m)
T : period (s)
There are a number of relationships involving the various characteristic quantities of waves. A simple example of how this would be useful is how to determine the velocity when you have the frequency and the wavelength. We cone take the above equation and substitute the relationship between frequency and period to produce one equation for speed of the form

{\displaystyle v=f\lambda } v=f\lambda

v : speed (m.s−1)
{\displaystyle \lambda } \lambda : wavelength (m)
f : frequency (Hz or s−1)
Is this correct? Remember a simple first check is to check the units! On the right hand side we have speed which has units ms−1. On the left hand side we have frequency which is measured in s−1 multiplied by wavelength which is measure in m. On the left hand side we have ms−1 which is exactly what we want.

Speed of a wave through strings
The speed of a wave traveling along a vibrating string (v) is directly proportional to the square root of the tension (T) over the linear density (μ):

{\displaystyle v={\sqrt {\frac {T}{\mu }}}\,} {\displaystyle v={\sqrt {\frac {T}{\mu }}}\,}
μ is equal to the mass of the string divided by the length of the string.
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{\displaystyle \mu ={\frac {M}{L}}} {\displaystyle \mu ={\frac {M}{L}}}

The Free High School Science Texts: A Textbook for High School Students Studying Physics.
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Waves and Wavelike Motion
Definition – Types of Waves – Properties of Waves – Practical Applications: Sound Waves – Practical Applications: Electromagnetic Waves – Equations and Quantities