Question

If a violin and a flute each play 256 Hz tones. Which wave has the longer wavelength?

Answer 1

They should have the same wavelength.

The relationship between these is `v = f lambda`.

where `v` is the speed of sound, `f` is the frequency (in Hz), and `\lambda` is the wavelength.

Since the speed of sound will not change with the instrument being played (it only changes depending on the medium through which it travels), and the frequency is also the same, the wavelength (`lambda`) should also be the same.

What will differ for the two instruments is the harmonic content of the tones. Both produce sounds that contains most of its power at the 256 Hz frequency, but also some power at overtones (multiples) of that frequency. Flutes typically have a closer to pure sinusoidal shape (less overtone content), while violin waveforms are somewhat more sawtooth shaped--which makes sense given the slip-stick physics of bowing. Sawtooth shaped waves have more overtone content. Skilled players of both instruments, however, can vary the overtone content to change the character of the sound.