Can you please provide suggestions on how I can improve this EEI Introduction and whether my ideas are right? Please also correct any grammatical errors if noted?  Introduction – Wine Glasses...

Can you please provide suggestions on how I can improve this EEI Introduction and whether my ideas are right? Please also correct any grammatical errors if noted? 

Introduction – Wine Glasses

The purpose of this investigation was to examine how frequency changes with different sized wine glasses and when additional water is added to each wine glass. It was hypothesised that if water was added to the wineglass, its frequency decreases. The higher the water volume, the smaller the frequency. It was also hypothesised that small wineglasses produce the highest pitch.

The singing wine glass, also known as glass harp or the Harmonica, is a glass instrument invented in 1714 by Richard Pockrich (Yang). Every material, including wineglasses, have their own natural frequency (resonate frequency) at which they vibrate. When energy is applied to the glass, the physical properties of the glass will be forced to resonate (resonance is a forced vibration). This applied energy’s source is the rubbing of a wet finger on the rim of the glass, called the slip-and-stick effect. The rubbing passes on energy onto the glass molecules, causing them to resonate. The motion of the hand builds up a wave of vibration travelling through the glass. The vibrating glass causes air molecules to vibrate the same frequency where the vibrating air molecules are the sound heard (frequency or pitch of the sound wave is the same as the resonant frequency of the glass) (Howstuffworks, 2015).

The glass resists distortions and has some restoring force that depends linearly on how much it is distorted. It also has normal modes of oscillation, a set of characteristic frequencies at which the glass will respond to perturbations. Those frequencies are dependent on the glass’s material (its ‘springiness’), on its mass and effectively, but not (at least, not much), on how rapidly or strongly the system is perturbed. That is the reason why the wineglass’s pitch cannot be greatly altered by the speed of a person’s finger running over the rim of a wineglass (Thomas D. Rossing, 2014) (Team Of Germany).

When water is added to the wine glass, the resonant wave moves around the glass and drags the water molecules with it, producing a wave of water visible close to the edge of the glass. When those waves a produced repeatedly, a standing wave builds up and a sound is produced. The dragging water molecules effectively increase the mass (both the water and the glass molecules) and decrease the energy of the wave traveling through the glass. When the energy decreases, the frequency of the wave in the glass also decreases, which is reflected in the lower pitch that is heard. Therefore, to produce the same initial frequency, greater energy must be applied  (Howstuffworks, 2015).

The basic theory behind standing waves is superposition where when there is more than one wave travelling in the same medium, the sum of the wave functions is the algebraic sum of the values of the wave function. Therefore, when waves trace towards each other, instead of breaking the rhythm completely, they travel through one another. The two types of superposition are constructive (net sum of waves gives a positive displacement) and destructive (net sum of waves gives a negative displacement) (The Physics Classroom, 2015 ).

A typical wineglass has a strong, rigid supporting stem, and a bowl that is thick at the base and progressively thins out toward the upper rim. This system’s vibrations most easily occur under conditions that leave the circumferential length of the rim unchanged, because glass is highly resistant to extension or compression. Such condition to a high approximation is only achieved if the rim deforms from a circle into an ellipse and back again through the circle into another ellipse with its major axis at right angles to the first ( Dr. A. Loeliger, 2003). 

The slip and stick effect (the applied energy to the wine glass) is a friction effect where two surfaces are dragged along each other to stick together and slip with very short intervals of time. The ‘stick’ is due to the friction between two surfaces that want to hold them together. The ‘slip’ on the other hand is from the external forces acting from one surface on the other, continuously trying to pull the two surfaces away.  Then the kinetic friction coefficient becomes larger than the static coefficient, and vice versa when the two surfaces are “sticked” together. Thus the name stick-and-slip effect. For this reason a clean finger improves the stick and slide action. This motion is not a simple harmonic motion. Wine glass however also uses this technique to produce the sounds. The stick-and-slip effect creates vibrations within the glass wall due to the frictional jerking. Due to the stick-and-slip motion, the rim of the glass begins to deform into an elliptical shape since glass is quite elastic.

A.P French has also written a journal paper about this specific type of resonance use on wineglasses and derived a general formula for how the frequency could vary with different volumes of water. His formula shows that frequency is also dependent on many variables.

A.P French’s formula was intended to describe an ideal cylindrical glass, however he later discovered that his formula works approximately for any type of glass.

If a wineglass is ideal and cylindrical, the best fit line for plotting (f0/f)^2 against (1-d/H*) ^4, should give a straight and linear line  (Yang).