# Fundamental frequency of a stretched string

1. Nov 23, 2011

### lykan_004

1. The problem statement, all variables and given/known data

The fundamental frequency of a stretched string is 200Hz. when the length of the string is doubled and Tension of the string made 100times the initial Tension, what is the new fundamental frequency of the string.

(1) 50 Hz (2) 100 Hz (3) 200Hz (4) 400 Hz (5) 800 Hz

2. Relevant equations

F = 1/2L x sqrt(T/ m)

3. The attempt at a solution

The answer I get is 1000Hz.

Last edited: Nov 24, 2011
2. Nov 24, 2011

### grzz

correct attempt

3. Nov 24, 2011

### lykan_004

does that mean the question is wrong? coz there are similar questions, and i dont get the correct answer for any of them.

4. Nov 24, 2011

### Staff: Mentor

I think you'll want to verify this formula. It seems to be missing a factor of L inside the square root. You can verify by checking that the units don't work out to Hz in its present form.

5. Nov 24, 2011

### lykan_004

m - linear density here not mass..that makes the equation dimensionally correct.

6. Nov 24, 2011

### Staff: Mentor

Ah. Perhaps then $\rho$ would have been a better choice of variable name

So it would appear that your answer is correct; The frequency should change by a factor of $\sqrt{100}/2 = 5$. It sometimes happens that the provided answers are not correct.

7. Nov 24, 2011

### lykan_004

u r rite .. i wonder the same thing... :) but i hav no idea why they use m.