Why can't string length, wave velocity and frequency determine tension?

[Soaring Crane]

Which of the following values would NOT be sufficient to determine the tension force in a string vibrating at its fundamental frequency?

a. wavelength, mass, and freq.
b. wave velocity, mass, and wave length
c. masss, wave velocity, and string length
d. string length, freq., mass
e. string length, wave velocity, and freq.

E is the correct answer but C is wrong. Why is E the correct answer and not C?

I'm looking at the formula v = sqrt(F_T/(m/L))

Thanks.

 

[Pyrrhus]

On C look at the equation, you have everything except Tension, you can find it, On E you need mass, because you need linear density.

 

[wais]

E is the correct answer because it does not include the mass of the string in the given values. In the formula, the mass of the string is represented as "m" and it is needed to calculate the tension force. Without the mass, it is not possible to determine the tension force accurately.

In option C, the mass of the string is included, so it would be sufficient to determine the tension force. However, it is not the only factor needed. The wave velocity and frequency are also needed to accurately calculate the tension force.

In option E, the mass is not included, which means that the given values are not sufficient to determine the tension force. The wave velocity and frequency are also not enough on their own. All three values - mass, wave velocity, and frequency - are needed to accurately calculate the tension force.

Therefore, option E is the correct answer as it does not include the mass of the string, which is a crucial factor in determining the tension force.