Strings & Waves 🎸

• Strings can generate standing waves.
• Cool Fact: A flexible wire can also create a standing wave, but it needs to be supported at a nodal point. So, imagine your guitar strings wiggling to the tune of your favorite song!

Nodes & Antinodes 📍

• Node: A point on a standing wave that doesn't move (zero amplitude).
• Antinode: A point on a standing wave with max amplitude.
• Fun Fact: When both ends of a string are free, we get an antinode at each end! Just like doing a double jump on a trampoline!

Harmonics 🎶

• Harmonics are the different modes of vibration a string can have.
• Sequence: first harmonic, second harmonic, and so on...
• Note: The second harmonic can't show up if the wire is clamped in the center. (Just like a stubborn child who refuses to come out and play if it's raining outside).

• Scenario: A 0.80m metal rod, clamped in the middle, rocking in the first harmonic mode. a. Frequency: λ = 1.6m (because the rod length is half the wavelength). Using f = \(\frac vλ\)​, we get \(f = \frac {3200}{1.6} = 2kHz.\)b. Other Harmonics: Only the first harmonic has a frequency < 5kHz here. The third harmonic is the next possible mode at 6kHz. (So, only the first one passes the 5kHz party invitation).

• Scenario: 66cm guitar string, first harmonic mode, 380Hz. a. Wave Speed \(v = f × λ. Given λ = 2 × 66cm = 1.32m,v = 380 × 1.32 = 501.6ms^-1.\) 1. b. Fretboard Press: A guitarist tweaks the string against the fretboard, producing 480Hz. (It's like when you play with a ruler on the edge of a table, adjusting the length changes the sound).