I've a problem that I can't solve, could someone please help me?

The problem says:

Two strings of a bass vibrate in a normal oscillation mode with the same period of 8.0 milliseconds. If the tension in one of the strings is decreased by 7 N a beat frequency of 6 Hz is heard.

Determine: - The period of oscillation of the string with the reduced tension. - The initial tension in both strings.

My attempt to solve this exercise:

I used the period to calculate the frequency: $T_1 = 8ms = 0.008s$ so the frequency is $$f_1 = 1/T = 125Hz$$

The beat frequency heard is $6Hz$ so the new frequency (the one in the string with the lower tension) is $$f_2 = 125-6 = 119Hz$$. Therefore the new period is $T_2= 1/119Hz = 8.4 ms$.

Now I've tried to solve the second part but i couldn't.

My difficulty is that I can't calculate the tension because in order to do that I should have more information about the string which I don't.

Is my reasoning right?


Edit: The formula that relates frequency to tension, mass and length for each string is $$f_1 =\frac{n}{2L}\sqrt{\frac{T_1}{\frac{m}{L}}}$$ and $$f_2 =\frac{n}{2L}\sqrt{\frac{T_2}{\frac{m}{L}}}$$ where $T_2 = T_1 - 7$

$$\frac{f_1}{f_2} = \sqrt{\frac{T_1}{T_2}}$$ $$\frac{f_1^2}{f_2^2} = \frac{T_1}{T_2} $$ $$(f_1^2 - f_2^2)*T_1 = f_1^2 * (7) $$ And finally $$ T_1 = \frac{7f_1^2}{f_1^2 - f_2^2} \approx 74.7 N $$

Is this right?


closed as off-topic by Diracology, David Z Jul 21 '16 at 13:37

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  • 1
    $\begingroup$ You mean "tension" not "voltage" - I am afraid your translation software let you down. Do you know the relationship between mass per unit length, tension, length, and frequency of the fundamental mode of a string? That's where you have to start. And note - we don't "do your homework for you" - you have to do most of the work, we will help with concepts. But you have to clarify what concept you are struggling with. $\endgroup$ – Floris Jul 21 '16 at 13:42
  • $\begingroup$ Hi , i've edited the question with all my reasoning, I speak another language so it is hard for me trying to explain this kind of concepts. $\endgroup$ – Luigi Cerone Jul 21 '16 at 13:46
  • $\begingroup$ As Floris says, try writing down the formula which relates period to tension, mass and length for each string. Then decide if you have enough information to find the initial tension. $\endgroup$ – sammy gerbil Jul 21 '16 at 14:26
  • $\begingroup$ I've edited the post , is that formula correct? Thanks $\endgroup$ – Luigi Cerone Jul 21 '16 at 14:42
  • $\begingroup$ You are getting close. You have the ratio of tensions from the ratio of frequencies squared; and you have their difference. Two equations, two unknowns. Solve. $\endgroup$ – Floris Jul 21 '16 at 16:11