For both waves on strings and sound waves in tubes, For both waves on strings and sound waves in tubes,

A. The mode number is independent of the wavelength.

B. A higher mode number means a shorter wavelength.

C. A higher mode number means a longer wavelength.

option (B) is correct.

Explanation:

frequency is directly proportional to the speed of wave and inversely proportional to the wavelength.

For string

frequency, f = v/λ

for tube

frequency ∝ 1 / λ

So, we can say that the frequency is inversely proportional to the wavelength.

thus, the higher the mode means shorter the wavelength.