posted by Bruce .
A particular steel guitar string has mass per unit length of 1.79 g/m. and tension of 61.9 N. For the wave speed to be increased by 1.9%, how much should the tension be changed?
I tried increasing the wave speed (186 m/s) by 1.9%, plug that into v=sqrt(T/linear mass density), solve for T, and then take the ratio of it and the initial tension, but it is still not correct. It is probably something simple that i am over looking, but im stuck on it. Thank you!
Wave speed is proportional to the square root of tension. To increase it by a factor of 1.019, the tension must increase by a factor 1.019^2. That makes the new tension 61.9* 1.0384 = 64.3 N
You don't need to use the string mass per unit length. It does not change. You also don't need to compute the wave speed. Adding extra steps just increases the chances of making an error.