The ratio of wavelengths of three different sounds in the same medium is the inverse of the ratio of their frequencies. Therefore, if the ratio of frequencies is 1:2:3, the ratio of wavelengths would be 1/1:1/2:1/3, which simplifies to 1:1/2:1/3. To simplify further, we can convert the fractions to a common denominator:
1:1/2:1/3 = 6/6:3/6:2/6 = 6:3:2
Therefore, the ratio of wavelengths would be 6:3:2.