If the frequency of a sound wave is multiplied by 10, the wavelength becomes 1/10 of its original value. This is because the speed of sound remains constant, and the wavelength is inversely proportional to the frequency.

Mathematically, the relationship between wavelength (λ), frequency (f), and the speed of sound (v) is given by the formula:

λ = v / f

If we increase the frequency by a factor of 10 (f' = 10f), the new wavelength (λ') becomes:

λ' = v / f'

λ' = v / (10f)

λ' = (1/10) * (v / f)

Therefore, the new wavelength is 1/10 of the original wavelength.

This inverse relationship between frequency and wavelength is a fundamental property of waves, including sound waves. It means that as the frequency increases, the wavelength decreases, and vice versa.