[What Was Supposed To Be...The Eighth Blog] Sound.

Wow, it’s been a while... So here’s the response on sound from December that I just never got around to posting:

Values/Calculations

Instrument

Violin

Properties

Chosen string: D

- Frequency: 294 Hz

- Vibrating length: 0.32 m

- Mass density: 9.375 x 10^-4 kg/m [mass = 0.30 g]

- Tension: 33.191 N

      

Frequencies Of Next Highest Harmonics

- Second harmonic: 588.00 Hz

- Third harmonic: 882.00 Hz

    

Analysis

Fingering Positions

The fingering positions correspond to where the frequencies for the next notes can be found.  When you press the string down with your finger, it decreases the vibrating length of the string.  This shorter length results in a higher frequency.  When placed in the correct position, the new frequency is that of a new note.  For example, in first position, placing your first finger on the D-string gives the note E while your second finger can give either the F♮or F#, depending on where it is placed.

To play an E on the D-string, the vibrating length is reduced by about 0.03 m, making the new length 0.29 m.  So when the new frequency is calculated, it comes out to 324.412 Hz (which is fairly close to the established 329.63 Hz...).

Plucking/Bowing Location

The plucking/bowing location is close to the bottom (by the bridge) node of the string.  At this location...all (or most of...many of...) the harmonics are likely to be heard! :]

Plucking Versus Bowing

When a string is plucked, energy is only applied for an instant so the sound diminishes quickly.  When it is bowed, energy is constantly applied so the note can be heard for a longer period.  After the initial sound of a plucked note is heard (with all of its frequencies), some of the higher frequencies are lost so only lower and fundamental frequencies can be heard until the sound is stopped altogether.  However, when a note is bowed, all frequencies are being heard together continuously, giving it greater depth.  

[The Seventh Blog] Fluids.

     Well it's been a while since we've done a blog and I honestly forgot about it till not too long ago, but that's okay because I still have ample time to finish it.  And luckily I found something to write about while scavenging through old trip photos, otherwise who knows what I'd be doing right now (maybe shooting my brother with a water gun or something...).  So anyway, here is the lovely picture that I came across of a pirate-y looking boat (in Japan, which just makes it all the better. :]).  

     
     Why is it that an object that seems so heavy can float on water?  I can understand rubber duckies floating in a bathtub, but gigantic ships floating on the ocean? I think not. But it's possible (anything is possible if you just believe. ^_^) and the explanation lies in PHYSICS, of course!  Contrary to what seems logical, it is really not the weight of an object that determines whether it will sink or float; it is the object's density as compared to the fluid's density that matters.  If an object's density is less than the fluid's density, it will float, and if it is greater than the fluid's density, the object sinks.  This must mean that the ship's average density is lower than the density of sea water. 
     Also, all objects placed in liquids have this thing called buoyant force acting on them.  This force counteracts the object's weight, pushing up on it from below.  Buoyant force is equal to ρVg (density of the liquid x volume submerged x gravity), also stated as the density of the liquid multiplied by the weight of the fluid displaced.  When buoyant force is greater than or equal to an object's weight, the object floats, and when it is less than the object's weight, the poor object sinks to the bottom.  And good thing there is physics to explain why the boat floats instead of sinking to the bottom of the ocean as would be expected if we didn't know any better, because I don't think the people on it would appreciate if it sank - who knows what creepy things are hidden far far below the ocean's surface...

[The Sixth Blog] Circular Motion.

Circular motion can be observed in many instances of everyday life, such as in the blades of a ceiling fan as they spin or as a car makes a rounded turn.  However, today I will be discussing circular motion regarding something that generally can't be as commonly observed - a ferris wheel (this one was in Japan ^_^).  

There are several forces at work as the ferris wheel moves.  There is mg, which is always directed downward, F_N, which is perpendicular to the surface in contact (directed upward since people in the individual carts are sitting down...), and there is F_C, which is directed toward the center of the ferris wheel.  

Even though velocity (instantaneous velocity, tangent to circle) is unchanging, there is acceleration because the direction of motion is constantly changing.  Centripetal acceleration is equal to v²/r.

Since there is acceleration, we know that there must be some sort of unbalanced net force causing it, and that special force is known as centripetal force, which points toward the circle's center, as I have mentioned above.  At the top, F_C is equal to (mg - F_N), whereas at the bottom, it's equal to (F_N - mg).  We can also derive the equation for F_C because we know that 

F_net = ma and therefore F_C = m(v²/r).

We can even find angular values by knowing linear ones, 

ω = v/r (velocity) or α = a_T/r (acceleration). There is so much to learn from just a few values (plus all of these lovely physics equations, of course)! :]

[The Fifth Blog] Momentum.

       Yesterday I attended the UH versus New Mexico State football game – my first live UH football game, might I add, and only my second time sitting in Aloha Stadium.  Honestly, the (unnecessarily) loud, screaming fans and blinding bright lights don’t do much for me, but that’s okay because at least I got to experience some physics while I was there. 

I didn’t take any pictures of my own, but this one will do:

       I will refer to the UH player as A, the other as B, and assume that they were running toward each other from opposite directions prior to the collision.  The collision that these two players experienced was a perfectly inelastic collision, so momentum was conserved but kinetic energy was not, and the two players ended up “stuck together” (Hmm, what if it had been an ordinary inelastic collision and they had bounced off of each other instead... o_O). Anyway...if we give the two players random masses and initial velocities... (A has a mass of 110 kg and was moving at a velocity of 5 m/s and B has a mass of 90 kg and was moving at a velocity of -5 m/s) we can solve for the common final velocity of the two players upon impact because we know that momentum is conserved. 

                                                                            

                                                                             

[The Fourth Blog] Work, Energy, & Power.

When we hear the word work, we usually think of that place where our parents go while we're in school or, much more likely (being that we are such studious 'Iolani students), homework. To a physicist, though, work can be defined as displacement times force in the direction of displacement (W = FcosθΔx) or as a change in energy (W = E_f - E_i).

     I normally don't think much about walking up the stairs at home because it's something I do every day, but I thought twice about it today since such an action can be related to physics.  When I am standing at the bottom of the stairs, kinetic and potential energy are both zero (no velocity and no h). When I reach the top, though, both my kinetic and potential energy have changed and thus I have done work - little as it may be. To calculate my work, I find my total energy at the bottom (0 J) and subtract it from my total energy at the top (612 J), resulting in 612 J of work. Not much work, but work nonetheless...  (And probably a greater value than that representing the amount of homework I have accomplished thus far. Not good.) From this I can calculate my power (P = W/t), which comes out to be 266 W (or 0.357 hp).  Physics has redefined the meaning of work for me and has taught me about the relationship between work, energy, and power.   

         

I made it to the top. :]