question: When filling a water bottle from a tap, why does the pitch of the tap increase as the bottle fills up?
comment: Because the pitch comes not from the tap but from the bottle. It's the frequency the column of air between the water level and the top of the bottle resonates at. Therefore, the pitch rises as the bottle fills and the column of air gets shorter. Incidentally, The pitch depends (almost) *only* on how much air is left in the bottle. Knowing this and remembering the pitch, you can fill bottles almost without looking. No matter the bottle and no matter the tap, the pitch is always the same at a given amount of space left with air at the top, so you can stop filling the bottle in time.
passages: Section::::Free surface effect.
  
  In tanks or spaces that are partially filled with a fluid or semi-fluid (fish, ice, or grain for example) as the tank is inclined the surface of the liquid, or semi-fluid, stays level. This results in a displacement of the centre of gravity of the tank or space relative to the overall centre of gravity. The effect is similar to that of carrying a large flat tray of water. When an edge is tipped, the water rushes to that side, which exacerbates the tip even further.
   Outside and far from the tube, the liquid reaches a ground level in contact with the atmosphere. Liquids in communicating vessels have the same pressures at the same heights, so a point formula_15, inside the tube, at the same liquid level as outside, would have the same pressure formula_16. Yet the pressure at this point follows a vertical pressure variation as
   Hydraulic jumps occur commonly in everyday situations such as during the use of any household sink. The jump can be seen in the form of a circular, stationary wave surrounding the inflow of water. The hydraulic jump occurs at the point where the seemingly still water becomes turbulent. As water hits the sink, it disperses, increasing in depth to a critical radius where the flow (supercritical with low depth, high velocity, and a Froude number greater than 1) must suddenly jump to a greater, subcritical depth (high depth, low velocity, and a Froude number less than 1) that is known to conserve momentum.
   Figure 7. Effect of increasing q on depth up- and down-stream of hydraulic jump
   This type of water meter is most often used in residential and small commercial applications and homes. Displacement meters are commonly referred to as Positive Displacement, or "PD" meters. Two common types are oscillating piston meters and nutating disk meters. Either method relies on the water to physically displace the moving measuring element in direct proportion to the amount of water that passes through the meter. The piston or disk moves a magnet that drives the register.
   Temporal Theory posits that the cause is from looking at the phase locking to tell what the pitch is. This theory has a hard time explaining diplacusis. There are some examples of pitch which don’t have an "edge" on the basilar membrane, which this would account for—i.e. white noise, clicks, etc. (need a reference)
   If made with constant pitch (wire thickness), conical springs have a variable rate. However, a conical spring can be made to have a constant rate by creating the spring with a variable pitch. A larger pitch in the larger-diameter coils and a smaller pitch in the smaller-diameter coils forces the spring to collapse or extend all the coils at the same rate when deformed.
  
  Section::::Physics.:Simple harmonic motion.
  
  Since force is equal to mass, "m", times acceleration, "a", the force equation for a spring obeying Hooke's law looks like:
   Figure 2 above illustrates an example of a hydraulic jump, often seen in a kitchen sink. Around the place where the tap water hits the sink, a smooth-looking flow pattern will occur. A little further away, a sudden "jump" in the water level will be present. This is a hydraulic jump.
  
  Section::::Hydraulic jump variations.:Internal wave hydraulic jumps.
  
  Section::::Hydraulic jump variations.:Internal wave hydraulic jumps.:Hydraulic jumps in abyssal fan formation.
   When the slotted line is terminated with a precision matching load there is no variation in the detected power along the line, other than a very small decrease due to losses in the line. However, when this is replaced by a device under test (DUT) which is not perfectly matched to the line there will be a reflection back towards the source. This causes a standing wave to be set up on the line with periodic maxima and minima (collectively, "extrema") due to alternating constructive and destructive interference. These extrema are found by moving the probe back and forth along the line and the level at that point can then be measured on the meter.
   Section::::Relationship of conjugate depths on M-y diagram.:Example 1: Conjugate depths and the M-y diagram.
  
  Given: br
  
  Find: br
  
  Solution: br
   Just as the primary loads have their origin in some force, secondary loads are caused by displacement of some kind. For example, the pipe connected to a storage tank may be under load if the tank nozzle to which it is connected moves down due to tank settlement. Similarly, pipe connected to a vessel is pulled upwards because the vessel nozzle moves up due to vessel expansion. Also, a pipe may vibrate due to vibrations in the rotating equipment it is attached to.
  
  Displacement Loads:
  
  BULLET::::- Load due to Thermal Expansion of pipe
   In more detail, one can look at how the hydrostatic pressure varies through a static siphon, considering in turn the vertical tube from the top reservoir, the vertical tube from the bottom reservoir, and the horizontal tube connecting them (assuming a U-shape). At liquid level in the top reservoir, the liquid is under atmospheric pressure, and as one goes up the siphon, the hydrostatic pressure decreases (under vertical pressure variation), since the weight of atmospheric pressure pushing the water up is counterbalanced by the column of water in the siphon pushing down (until one reaches the maximal height of a barometer/siphon, at which point the liquid cannot be pushed higher) – the hydrostatic pressure at the top of the tube is then lower than atmospheric pressure by an amount proportional to the height of the tube. Doing the same analysis on the tube rising from the lower reservoir yields the pressure at the top of that (vertical) tube; this pressure is lower because the tube is longer (there is more water pushing down), and requires that the lower reservoir is lower than the upper reservoir, or more generally that the discharge outlet simply be lower than the surface of the upper reservoir. Considering now the horizontal tube connecting them, one sees that the pressure at the top of the tube from the top reservoir is higher (since less water is being lifted), while the pressure at the top of the tube from the bottom reservoir is lower (since more water is being lifted), and since liquids move from high pressure to low pressure, the liquid flows across the horizontal tube from the top basin to the bottom basin. Note that the liquid is under positive pressure (compression) throughout the tube, not tension.
   There are a few key locations on the M-y diagram which are labeled in Figure 6 above developed based on the information in Example 1. The first location of interest is the critical point labeled with y and M in Figure 6. The critical point represents the minimum value of the momentum function available for that particular flow per unit width, "q". An increase in q would cause the M function to move to the right and slightly up, giving the flow access to more momentum at its critical point. It follows that a decrease in the q value would move the M function down and to the left, decreasing the momentum available to the flow at its critical value. This is shown graphically Figure 7 below.
   The bell is deployed over the side of the vessel or platform using a gantry or A-frame or through a moon pool. Deployment usually starts by lowering the clump weight, which is a large ballast weight suspended from a cable which runs down one side from the gantry, through a set of sheaves on the weight, and up the other side back to the gantry, where it is fastened. The weight hangs freely between the two parts of the cable, and due to its weight, hangs horizontally and keeps the cable under tension. The bell hangs between the parts of the cable, and has a fairlead on each side which slides along the cable as it is lowered or lifted. The bell hangs from a cable attached to the top. As the bell is lowered, the fairleads guide it down the clump weight cables to the workplace.
   When looking at the critical points on the M-y diagram and what their locations tell us about the nature of the hydraulic jump, we mentioned that an increase in q would affect the energy lost in the jump. From Figure 7 we see that increasing the flow rate decreases the difference in the upstream and downstream depth of the jump ("y" – "y"). From this we can infer that if the momentum is held to be constant, there will be a decrease in the energy lost in the jump if the flow rate is increased.
   In beating, or striking, reed wind instruments such as the saxophone, clarinet, and oboe, the transition from lower to higher register is aided by a "register key" which encourages a vibration node at a particular point in the pipe such that a higher harmonic is produced.
  
  Another type of overblowing is that used on instruments such as the flute, where the "direction" of the airstream is altered in order to sound higher notes. This technique can also be demonstrated when blowing across the top of a glass bottle (beer bottle, wine bottle, etc.) to produce a pitch.
   The second biggest factor that affects drum sound is head tension against the shell. When the hoop is placed around the drum head and shell and tightened down with tension rods, the tension of the head can be adjusted. When the tension is increased, the amplitude of the sound is reduced and the frequency is increased, making the pitch higher and the volume lower.
   Section::::Levelling.
  
  Leveling of an instrument is done to make it vertical axis with respect to the apparent force of gravity at the station.
  
  For two spirit vials at right angles;
  
  BULLET::::1. Bring one of the level tubes parallel to any two of the foot screws, by rotating the upper part of the instrument.
  
  BULLET::::2. The bubble is brought to the centre of the level tube by rotating both the foot screws either inward or outward. The bubble moves in the same direction as the left thumb.
   Any liquid-producing reservoir will have a 'reservoir pressure': some level of energy or potential that will force fluid (liquid, gas or both) to areas of lower energy or potential. The concept is similar to that of water pressure in a municipal water system. As soon as the pressure inside a production well is decreased below the reservoir pressure, the reservoir will act to fill the well back up, just like opening a valve on a water system. Depending on the depth of the reservoir and density of the fluid, the reservoir may or may not have enough potential to push the fluid to the surface - a deeper well or a heavier mixture results in a higher pressure requirement.
   The heart of the instrument is a tunable LC circuit whose exposed external coil will loosely couple to the measured resonant circuit when held "moderately" close-by. The measuring distance must be skillfully adjusted to be close enough to provide sufficient coupling for the dip to show clearly, but far enough that the meter and the tested circuit oscillate independently, so neither device’s frequency is significantly distorted by the other, and so that power lost to the external circuit does not swamp the dip meter’s oscillator.
   The design of the displacer units, and the way in which they are mounted means that as the suspension is compressed, the (roughly spherical) displacer deforms, and hence presents a larger area to the mounting plates. The pressure in the system is thus acting over a larger area, and hence applying additional force. This gives the suspension a sharply rising rate even in pitch, so that there is a strong tendency to return to equilibrium. Without this rising rate there would be no effective pitch resistance at all.
   where "m" is the mass of the bottle and "g" the gravitational acceleration at the location at which the measurements are being made. "ρ" is the density of the air at the ambient pressure and "ρ" is the density of the material of which the bottle is made (usually glass) so that the second term is the mass of air displaced by the glass of the bottle whose weight, by Archimedes Principle must be subtracted. The bottle is, of course, filled with air but as that air displaces an equal amount of air the weight of that air is canceled by the weight of the air displaced. Now we fill the bottle with the reference fluid e.g. pure water. The force exerted on the pan of the balance becomes:
   BULLET::::- For a "sine wave", the wave height "H" is twice the amplitude:
  
  BULLET::::- For a "periodic wave" it is simply the difference between the maximum and minimum of the surface elevation "z" = "η"("x" – "c" "t"):
   Some pipe organs makes use of this phenomenon as a resultant tone, which allows relatively smaller bass pipes to produce very low-pitched sounds.
  
  Section::::Audio processing applications.
   Imagine putting a marble in a ladle. It will settle itself into the lowest point of the ladle and, unless disturbed, will stay there. Now imagine giving the ball a push, which is an approximation to a Dirac delta impulse. The marble will roll back and forth but eventually resettle in the bottom of the ladle. Drawing the horizontal position of the marble over time would give a gradually diminishing sinusoid rather like the blue curve in the image above.
  