# Beat Frequency Problem

nietzsche

## Homework Statement

Two strings with otherwise identical properties differ in tension by 0.25 N. If both strings are struck at the same time, what is the resulting beat frequency?

## Homework Equations

frequency is proportional to the root of tension?

## The Attempt at a Solution

I tried setting T2 = T1 - 0.25 N and substituting this into an equation with f1/f2 proportional to sqrt{T1/T2}.

But I can't seem to figure anything out from this.

willem2
I can't make anything of it either.

If I put $f_1 = k \sqrt {T}$ and

$$f_2 = k \sqrt {T + 0.25}$$

I get

$$f_2 - f_1 = k \sqrt {T+0.25} - k \sqrt {T}$$

wich I can't simplify further.

0.25 N is probably quite small compared to the tension in the string, so we can apply

$$\sqrt {T+0.25} \approx \sqrt {T} + 0.25 \frac {1} {2 \sqrt {T}}$$

this results in

$$f_2 - f_1 \approx \frac {0.125 k} {\sqrt{T}}$$

so the answer does depend on the tension, and the other properties of the string as well.

nietzsche
I can't make anything of it either.

If I put $f_1 = k \sqrt {T}$ and

$$f_2 = k \sqrt {T + 0.25}$$

I get

$$f_2 - f_1 = k \sqrt {T+0.25} - k \sqrt {T}$$

wich I can't simplify further.

0.25 N is probably quite small compared to the tension in the string, so we can apply

$$\sqrt {T+0.25} \approx \sqrt {T} + 0.25 \frac {1} {2 \sqrt {T}}$$

this results in

$$f_2 - f_1 \approx \frac {0.125 k} {\sqrt{T}}$$

so the answer does depend on the tension, and the other properties of the string as well.

thank you so much willem. i don't think my prof worded the question properly, so i'm going to ask him tomorrow. thanks again!