Maren presses a guitar string down at a fret and plucks. The note jumps higher. Same string, same tightness; only the vibrating length changed.
The explanation is a chain with three links you have already met: the fundamental, the wave equation, and pitch.
A plucked string vibrates as a standing wave, and its lowest pattern, the fundamental, has one loop between the string's two fixed ends.
Fretting the string shortens the vibrating length.
The fundamental's single loop now spans a shorter length, so the fundamental wavelength is shorter.
The wave's speed along the string is set by the string itself, its material and its tightness, and fretting changes neither. The speed stays fixed.
You met the trade at the wave equation v = fλ: at a fixed speed, a shorter wavelength means a greater frequency.
The string vibrates at a greater frequency, so the sound it makes has that greater frequency too.
Increasing the frequency causes the pitch to rise: the fretted note sounds higher.
A cellist presses a string at a fret position so the vibrating length is shorter. Explain, link by link, why the note sounds higher.
The fundamental's loop spans a shorter length, so the fundamental wavelength is shorter.
The wave speed on the string is unchanged.
At a fixed speed, a shorter wavelength means a greater frequency.
A greater frequency is heard as a higher pitch.
The pressed note sounds higher.
A bass player lifts a fretting finger so the string's full length vibrates. What happens to the pitch, and why?
The vibrating length is longer, so the fundamental wavelength is longer.
At the string's fixed wave speed, a longer wavelength means a smaller frequency.
The pitch falls: the open string sounds lower.
Ottoline frets a banjo string, shortening its vibrating length. Does the note's pitch rise or fall?
A guitar string is fretted to a shorter vibrating length. What happens to its fundamental wavelength?
Noll says: 'A shorter vibrating string has a shorter fundamental wavelength, and at a fixed wave speed that means a greater frequency and a higher pitch.' Is Noll correct?
Fretting a guitar string raises its note. Which option gives the reason?
A harp's strings are alike in material and tightness but differ in length. Which statement is correct?
A double bass string and a violin string are alike in material and tightness, but the bass string's vibrating length is far longer. Which statement is correct?