Debye-Sears Effect

The Debye-Sears effect , named after the physicists Peter Debye and Francis Sears , enables a very precise determination of the speed of sound in media on the basis of wave optics .

Measurement of the speed of sound using the Debye-Sears effect

The medium to be examined, for example, a ultrasonic -Schwinger (usually a piezoelectric crystal placed) to vibrate. Parallel light is sent through the body or the liquid in a cuvette . The sound waves lead to density differences and these in turn lead to a changed refractive index at the corresponding point in the medium, which thus acts as a phase grating . This phase grating can now be measured using different methods:

Measurement via the diffraction pattern

Diffraction pattern

If, after passing through the medium, the parallel light is bundled again by means of a lens, diffraction phenomena can be shown. By measuring the diffraction pattern, it is possible to determine the speed of sound in the examined medium. The diffraction pattern can be better measured if the light is sent through a filter beforehand.

Measurement with lens:

${\displaystyle c_{\mathrm {s} }={\frac {fN\lambda }{d}}\nu _{\mathrm {s} }}$

Measurement without lens:

${\displaystyle c_{\mathrm {s} }={\frac {Nx\lambda \nu _{\mathrm {s} }}{d}}}$

${\displaystyle c_{\rm {s}}}$ = Phase velocity ultrasound

${\displaystyle f}$= Focal length

${\displaystyle N}$= Diffraction order

${\displaystyle \lambda }$= Wavelength of light

${\displaystyle d}$= Distance of the N th diffraction order from the 0 th

${\displaystyle \nu _{\rm {s}}}$ = Frequency of the ultrasound

${\displaystyle x}$ = Distance between ultrasound and screen

Measure the diffraction phenomenon

Photometer

The diffraction image can be projected onto a screen to make it visible. If you put a camera in the focal point of the lens behind the medium, you can photograph the diffraction image directly and then use a photometer to measure the distances on the negative.

Measurement over the corrugated grid image

Corrugated grid image

If the sound waves are reflected in a liquid by a reflector (metal plate), a standing wave is formed. The diffraction pattern produced here can be observed directly using a microscope.

${\displaystyle c_{\rm {US}}=2d\,\nu _{\rm {US}}}$

If one compares the wave lattice and the diffraction pattern method, there is much to be said for the wave lattice method. Here it is possible to average distances over 15–20 maxima, with the diffraction image you can hardly get to the third order. This minimizes the error enormously, since this is the place where there is the greatest margin for the person carrying out the experiment. The tolerance is therefore three to five times with the diffraction image method.

Quartz winch

Quartz winds in the liquid cuvette occur when the oscillating piezo crystal strongly pushes the liquid away from itself when it expands and then contracts faster than the liquid can flow back again. The result is liquid particles flowing in from the side, which then go through the same cycle. The result is a flow in the cuvette, which brings about a density gradient and thus undesirable refraction effects. These can be proven by projecting onto a screen after the cuvette in the silent state. If you now switch on the ultrasonic oscillator, a possible shadow cast by refraction effects proves quartz winds.

Individual evidence

1. ↑ gampt.de: Debye-Sears-Effect