If a vibrating string is shortened to half its length, the pitch becomes what?

If a vibrating string is shortened to half its length, the pitch becomes what?

• A. Twice as high
• B. Half as high
• C. Unchanged
• D. Four times higher

Answer: (A)

Pitch comes from how fast the string vibrates. For a string fixed at both ends with the same tension and mass per length, the fundamental vibration frequency is inversely related to the length. If you shorten the string to half its length, the fundamental wavelength becomes shorter, and with the same wave speed, the frequency doubles. Doubling the frequency raises the pitch by an octave, so the note sounds twice as high.

Pitch comes from how fast the string vibrates. For a string fixed at both ends with the same tension and mass per length, the fundamental vibration frequency is inversely related to the length. If you shorten the string to half its length, the fundamental wavelength becomes shorter, and with the same wave speed, the frequency doubles. Doubling the frequency raises the pitch by an octave, so the note sounds twice as high.