Increasing wave speed on a tring

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To increase wave speed on a string, one must consider both tension and mass per unit length. The wave velocity is determined by the formula v = (T0/ρ)½, where T0 is the tension and ρ is the mass per unit length. Decreasing the string thickness increases wave speed if tension remains constant, as it reduces the mass per unit length. Therefore, string thickness does impact wave velocity. Understanding these relationships is crucial for manipulating wave speed effectively.
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To increase wave speed on a string i would have to decrease the frequency and the string thickness correct? the string thickness would not make an impact correct?
 
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The wave velocity v along a string is equal to

v = (T0/ρ)½ meters per second

where T0 is string tension in Newtons, and ρ is string mass per unit length (Kg/m). (Note that the units are correct). If you decrease the string thickness without changing tension, the velocity increases. The string thickness (i.e., mass per unit length) is important.

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