Enter the peak/maximum velocity into the calculator to determine the root mean square of the velocity.

Root Mean Square Velocity Formula

The following equation is used to calculate the Root Mean Square Velocity.

VelocityRMS = Vp * .7071
  • Where velocity rms is the root mean square velocity (m/s)
  • Vp is the peak velocity (m/s)

To calculate the root mean square velocity, multiply the peak velocity by .7071.

What is Root Mean Square Velocity?

Definition:

A root mean square velocity describes the average velocity of the sine wave of a velocity.

How to Calculate Root Mean Square Velocity?

Example Problem:

The following example outlines the steps and information needed to calculate Root Mean Square Velocity.

First, determine the peak velocity. In this example, the peak velocity is found to be 600 m/s.

Finally, calculate the Root Mean Square Velocity using the formula above:

VelocityRMS = Vp * .7071

VelocityRMS = 600 * .7071

VelocityRMS = 424.26 m/s

FAQ

What is the significance of the .7071 constant in the Root Mean Square Velocity formula?

The constant .7071 is derived from the square root of 1/2. It is used in the formula to convert peak velocity to root mean square velocity for a sine wave, reflecting the fact that the RMS value represents the square root of the average of the squares of all the instantaneous values during one cycle of a sine wave.

Can the Root Mean Square Velocity formula be used for any type of wave motion?

The formula provided, with the constant .7071, is specifically designed for sine waves, which are a common waveform in physics and engineering. For other types of waveforms, such as square or triangular waves, the constant used to calculate the RMS value would be different due to the different distribution of instantaneous values throughout the wave cycle.

How does the Root Mean Square Velocity relate to the average velocity of an object?

Root Mean Square Velocity is a type of average velocity, but it is not the arithmetic mean. Instead, it is a measure that takes into account the square of velocities at different points in time, providing a more accurate representation of the overall energy or power in a system with varying velocity, such as in alternating current (AC) circuits or oscillatory motion. It differs from the simple average velocity, which would just sum up all velocities and divide by the number of measurements, without squaring the values.