Question

You can decrease the frequency of a standing wave on a string by __________.

Answer 1

making the string longer, using a thicker string, decreasing the tension

Answer 2

The n-th harmonic frequency of the standing wave is given by

`f_n=(v)/((2L)/(n)) =(nv)/(2L)`.

Here
`v=\sqrt{(T)/(m/L)}`,
`T` is tension in the string,
`m` is mass of the string and
`L` is the length of the string. Thus,

`f_n=(v)/((2L)/(n)) =\frac{n\sqrt{(T)/(m/L)} }{2L}=(n)/(2) \sqrt{(T)/(mL)}`.

From the above equation, the frequency can be decreased by decreasing tension or increasing mass and length of the string.