posted by Tension on .
On a string instrument of the violin family, the effective length of a string is the distance between the bridge and the nut. For a violin, this distance is 29.3 cm, while for a cello it is 37.8 cm.
The string of a violin is placed in a cello with the intention of producing a sound of the same fundamental frequency.
To accomplish this, the string on the cello will be under a larger tension than on the violin.
By how much should the tension in the cello be increased with respect to the tension in the violin?
Express the result as a percentage, and to two significant figures. Only answer in numerical values, without the % sign.
For example, an increase of 11% corresponds to Tcello = (1.11) Tviolin, and should be entered as 11 in the answer box.
You want the answer in a box? Without the % sign?
Do you want fries with that?
If you want to learn the subject and not just fill in the blanks to get some meaningless degree, use the fact that the frequency is proportional to
(wave speed)/(string length)
To keep the frequency the same, the wave speed must increase by a factor 37.8/29.3 = 1.2901
The string lineal density remains the same, since it is the same string. Take a look at the formula for wave speed in a string under tension. If you don't know it, look it up.
It says that you have to increase Tension so than sqrt(tension) is increased by a factor 1.2901
Take it from there