Q1.
What if … the speed of sound in air depended on its frequency? Would music still sound pleasant when a singer performs with instruments? Why or why not?
Answer
No — music would fall apart as it travelled, and the further you sat from the stage the worse it would sound.
A sung note or an instrument's note is never a single frequency: it is a fundamental together with several overtones. All of them leave the stage at the same instant.
Suppose the fundamental (200 Hz) travelled at 340 m s⁻¹ and an overtone (400 Hz) at 350 m s⁻¹.
Time for the fundamental to cross a 34 m hall = 34 m ÷ 340 m s⁻¹ = 0.100 s
Time for the overtone = 34 m ÷ 350 m s⁻¹ = 0.097 s
Gap on arrival = 0.100 s − 0.097 s = 0.003 s, and it grows with distance
Time for the fundamental to cross a 34 m hall = 34 m ÷ 340 m s⁻¹ = 0.100 s
Time for the overtone = 34 m ÷ 350 m s⁻¹ = 0.097 s
Gap on arrival = 0.100 s − 0.097 s = 0.003 s, and it grows with distance
- The overtones of a single note would arrive before or after the fundamental, so the note would smear out and its timbre would change with distance — a tabla would not sound like a tabla at the back of the hall.
- The singer's high notes and the accompanying instrument's low notes would arrive at different times, so the two would drift out of rhythm even though they were played together.
- Different listeners at different distances would hear different rhythms and different tone colours from the same performance.
Why the real world is kind to music: in air, the speed of sound depends only on the medium — on temperature and humidity — and not on the source or its frequency. So every frequency in a chord travels at the same 344 m s⁻¹ and arrives together, keeping the note whole. If the frequency changes, it is the wavelength that adjusts (λ = v/ν), never the speed.
Did you know? Some engineered materials, such as porous foams and specially designed structures, do make sound speed depend on frequency. Acoustic engineers use them precisely because of that unusual behaviour.