If Tom were so foolish as to play his keyboard instrument under water, where the speed of sound is 1500 m/s , what would be the wavelength of the B note in water ? Explain why the B tone has a longer wavelength in water than in air. (frequency of middle B tone is 494 Hz )
At any traveling wave, there exists a fixed relationship between speed, wavelength and frequency, as follows:
[tex]v = \lambda* f (1)[/tex]
We know the value of speed of sound in water (1500 m/s), and the frequency of middle B tone (494 Hz) , so we can find the wavelength λ (in meters) as follows:
[tex]\lambda_{w} = \frac{v_{sw}}{f} = \frac{1500m/s}{4941/s} = 3.04 m (2)[/tex]
Since the frequency is the same at any medium, and the speed of sound in air is lower than in water (334 m/s) this means that the wavelength in water must be longer than in air.
