Palm Pipe Lab

Music is Math?! How could this be???

First some key vocabulary:

• standing wave: stationary wave that remains in a constant with no net transport of energy
• frequency: shakes per second; measured in Hertz (Hz)
• harmonics: certain frequencies at which standing waves occur
• wavelength: length of wave; measured in meters (m)
• velocity: speed of sound; measured in meters per second (m/s)

Well it turns out that music is a blend of harmonics with whole number ratios in between. The difference between sound and music is that sound produces all different types of frequencies that aren't harmonics and not mathematically proportional; whereas music produces all harmonics at once which we perceive as one because we only hear the peak frequency.


BIG Questions:
1. How can we tell something (like sound) is a wave if it is invisible or too small for us to see?
2. How do musical instruments work?
3. What's the difference between woodwind and a stringed instrument?

Task: figure out what musical note my palm pipe generates.

In order to find the frequency, I measured the length and diameter of my palm pipe and plugged my information into the equation Length = 1/4 (wavelength) - 1/4 (diameter inside)

• length: 14 cm —> .14 m
• diameter: 1.3 cm —> .013 m
• .14 = 1/4 (w) - 1/4 (.013)
• .143 = .25w
• wavelength = .573 m

Then we used the fundamental wave equation to find the frequency:

** speed of sound traveling in air is 343 m/s **

       

    V = f (w)

    343 = f (.573)

    f = 598.604 Hz

We used Wolfram Alpha to figure out what musical note is played by typing in the peak frequency. This musical note plays a D5. We also checked our answer using our Labquest2 that electronically calculated the peak frequency which gave us the same note. THEN we created a palm pipe symphony in the classroom! We played "Twinkle Twinkle Little Star" and it actually sounded like the song!