In musical acoustics, when a vibrating string is shortened to half its length, what happens to the pitch?

In musical acoustics, when a vibrating string is shortened to half its length, what happens to the pitch?

• A. The pitch remains the same
• B. It vibrates twice as fast, producing a pitch twice as high
• C. It vibrates slower, producing a lower pitch
• D. It vibrates irregularly, with no clear pitch

Answer: (B)

Shortening a vibrating string while keeping its tension and material the same raises its fundamental frequency, because the standing-wave pattern must fit into a shorter length. For a string fixed at both ends, the fundamental wavelength is twice the length (λ1 = 2L). Since the wave speed v on the string depends on tension and linear density (v = sqrt(T/μ)) and frequency f = v/λ, halving the length halves the wavelength and doubles the frequency. That higher frequency corresponds to a pitch one octave higher (twice as high).

Shortening a vibrating string while keeping its tension and material the same raises its fundamental frequency, because the standing-wave pattern must fit into a shorter length. For a string fixed at both ends, the fundamental wavelength is twice the length (λ1 = 2L). Since the wave speed v on the string depends on tension and linear density (v = sqrt(T/μ)) and frequency f = v/λ, halving the length halves the wavelength and doubles the frequency. That higher frequency corresponds to a pitch one octave higher (twice as high).