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A piano tuner needs to double the frequency of note that a particularstring is playing. Should he/she tighten or loosen the string, and bywhat factor?(A) Tighten, 4(B) Tighten, 2(C) Loosen, 2(D) Loosen, 4

A

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Chapter 1

Practice Test 1

Section 1

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Yeah, So we have to double the frequency of a string and we have to find out the factor by which the tension must be increased or decreased frequency for any time on it. For a string fixed at both ends is given by n which is ant harmonic T by mu Distention mu is mass per unit length divided by two l l is the length of the string. So this is the initial frequency and initial tension for the same note and will remain same. So new frequency a prime is equal to end. Tension is new. Deep prime mass parent length will remain the same because it is the same string and length will also remain the same. So from this F death, sorry prime by F is equal to we put the values and this gives us equal to route under deep prime by t. Now, if crime is twice the initial frequency so we can let it do it by f is equal to d prime by d. This gives us to equal to t prime by t square, both sides for equal to keep prime by d. This gives us deep prime new frequency attention is called to four t. So clearly the tension must be increased by a factor of four. Hence, the correct option is a titan by a factor of four. This completes the solution. Thank you.

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