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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.

  • Physics -

    You want the answer in a box? Without the % sign?

    Do you want fries with that?

  • Physics -

    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

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