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Laws Of Motion

Question
CBSEENPH11020667

Two identical piano wires kept under the same tension T have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to occurrence of 6 beats/s when both the wires oscillate together would be

  • 0.02

  • 0.03

  • 0.04

  • 0.01

Solution

A.

0.02

According to law of tension, the frequency of the string varies directly as the square root of its tension

straight n space proportional to space square root of straight T

fraction numerator increment straight n over denominator straight n end fraction space equals space 1 half. fraction numerator increment straight T over denominator straight T end fraction
or
fraction numerator increment straight T over denominator straight T end fraction space equals space 2 space straight x space fraction numerator increment straight n over denominator straight n end fraction
fraction numerator increment straight T over denominator straight T end fraction space equals space 2 space straight x space 6 over 600

equals space 0.02