Fundamental frequency of a stretched string

[lykan_004]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

The answer I get is 1000Hz.

 

[grzz]

correct attempt

 

[lykan_004]

does that mean the question is wrong? coz there are similar questions, and i don't get the correct answer for any of them.

 

[gneill]

Homework Equations

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

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.

 

[lykan_004]

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.

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

 

[gneill]

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

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.

 

[lykan_004]

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