Question

Under constant tension and constant mass per unit length, the note produced by a plucked string is 500 Hz when the length of the string is 0.90 m. At what length is the frequency 150 Hz?

Answer 1

Frequency of the string is inversly ploportional to its length

$$f =\dfrac{k}{L}$$

where $k$ is some constant. From the given values, let's find this constant:

$$k = fL = 500Hz\times 0.9m = 450m/s$$

Then for $f = 150Hz$, the length will be:

$$L = \dfrac{k}{f} = \dfrac{450m/s}{150Hz} = 3m$$

Answer. 3m.