Math Skills

Speed of Mechanical Waves

One end of a rope is vibrated to produce a wave with a wavelength of 0.25 meters. The frequency of the wave is 3.0 hertz. What is the speed of the wave?

1. Read and Understand

   What information are you given?

   

2. Plan and Solve

   What unknown are you trying to calculate?

   

   What formula contains the given quantities and the unknown?

   $Speed=\genfrac{}{}{0.1ex}{}{Wavelength}{Period}$

   Replace each variable with its known value. ( Hint: $1Hz=\genfrac{}{}{0.1ex}{}{1}{s}$)

   $$\begin{gathered} Speed=0.25m\times 3.0Hz \\ =0.25m\times 3.0\genfrac{}{}{0.1ex}{}{1}{s} \\ Speed=0.75m/s \end{gathered}$$

3. Look Back and Check

   Is your answer reasonable?

   Because the frequency is 3.0 hertz, the wave should travel a distance of 3 wavelengths in 1 second. This distance is 0.75 meters, which agrees with the calculated speed of 0.75 m/s.

For: Links on wave properties

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