### A ripple tank shows the Doppler Effect and shock waves.

Watch Video:

Teachable Topics:
• Speed of Sound
• Doppler Effect
• Mach Numbers

Theory:

The Doppler Effect is what causes a change in pitch when a wave source is moving. The theory behind it is explained in more detail on the page for the Doppler shift, but can be simplified here.

In front of the wave source, the waves are compressed together causing a higher frequency noise to be heard, while behind the wave source the waves are more spread out, causing a lower frequency to be heard. This can be seen in the video. The important fact about the Doppler Effect however, is that the wave source is never moving faster than the waves being emitted from it. But what would happen if the wave source was moving faster than the speed of sound?

By moving faster than the speed of sound, the wave source creates a shock wave. This is also known as a sonic boom. The wave source is now moving so fast that the waves in front of it are compressed into a single wavefront extending outwards at an angle from the wave source, as seen in the video. The angle between the wavefront and the direction of travel of the the wave source is α, and is related to the speed of the wave source, u, and the speed of sound, v, like so:

#### sin(α) = v/u

The value of v / u is the Mach number, and α is the Mach angle. For a Mach number of less than 1, the Doppler Effect occurs. For a Mach number greater than 1, a shock wave is formed.

Apparatus:

• Ripple Tank with movable wave source

Procedure:

• Set up the ripple tank. Have it so the wave source can be moved from one end to the other as seen in the video.
• Place the wave source at one edge and slowly move it to the opposite side. The space between the waves in front of the wave source should compress, while the space between the waves behind the wave source should spread out. This is the Doppler Effect.
• Bring the wave source back to the starting point, and move it towards the opposite side. This time move the wave source faster so that a solid wavefront heading out at an angle from the wave source forms. This wavefront is a shock wave.