a Substitute the given values into the equation and solve for T.
B
b Write a ratio relating the tension applied to the string and its mass per unit length.
A
a About 71.5 newtons
B
b More tension, see solution.
Practice makes perfect
a Consider the given equation for the frecuency f (in cycles per second) of a guitar string with length l (in meters), tension T (in newtons), and mass per unit length m (in kilograms per meter).
f=1/2lsqrt(T/m)
We are told that the string is 0.64 meters long and has a mass per unit length of 0.000401 kilograms per meter. To find how much tension would be needed to produce a frequency of 330 cycles per second, we will substitute these given values into the equation and solve for T. Let's do it!
Therefore, to produce a frequency of 330 cycles per second we would require a tension of about 71.5 newtons.
b Suppose now that we want to produce the same frequency f in a string with the same length l but greater mass m_2 than our original string with mass m_1.
f=1/2lsqrt(T_1/m_1) f=1/2lsqrt(T_2/m_2)Since we are looking to produce the same frequency, we can set the right hand side of both expressions equal to each other.
1/2lsqrt(T_1/m_1)=1/2lsqrt(T_2/m_2)
Let's work this equation a little more.
Since m_2 is greater than m_1, we would be required to increase T_2 in order to keep the same ratio. Therefore, we would need more tension on a string with greater mass per unit length.
