Explanation of Simulation

What is the Doppler Effect?

The Doppler effect is the change in the frequency of a wave in relation to an observer who is moving relative to the wave's source. This simulation shows the changes in wave propagation based on the movement of the source, which you can control!

What happens above Mach 1?

When the source's speed approaches the wave's speed, the wavefronts in front of the source "bunch up", which creates a high-pressure barrier known as the sound barrier. If the source travels faster than the waves it creates, it breaks through this barrier, generating a V-shaped shockwave known as a "Mach cone".

Fun fact: This cone is the source of the "sonic boom" heard when a supersonic aircraft passes overhead.

Live Statistics

  • Wave Speed (\(v_w\)): 2.00 px/frame
  • Source Speed (\(v_s\)): 0.00 px/frame
  • Mach Number (\(M\)): 0.00
  • Frequency Ahead (\(f'\)): 440 Hz
  • Frequency Behind (\(f'\)): 440 Hz
  • Source Status: STATIONARY

Calculations

The simulation models fundamental principles geometrically. Key real-time calculations include:

Source Velocity (Pythagoras):

\[ v_s = \sqrt{v_{sx}^{2} + v_{sy}^{2}} \]

Mach Number:

\[ M = \frac{v_s}{v_w} \]

Here, \(v_s\) represents source speed, \(v_w\) wave speed, and \(v_{sx}\), \(v_{sy}\) are the horizontal and vertical components of the source velocity.

Instructions

  • Drag the joystick to move the wave generation source
  • Press C to clear the waves
  • Press Space to pause or resume
The blue circle on the joystick is the speed of sound (aka the marking of the exact speed of the waves).

This also represents Mach 1.

Controls