First slide

Standing waves

Question

A piano wire having a diameter of 0 .90 mm is replaced by another wire of the same material but with a diameter0 .93mm. If the tension of the wire is kept the same, then the percentage change in the frequency of the fundamental tone is

Easy

A

+3%
B

+3.2%
C

-3.2%
D

-3%

Solution

kt D be the diameter of the wire. Then
$n â (\frac{1}{D}) or d n â (\frac{d D}{D^{2}}) \frac{d n}{n} = \frac{d D}{D} = â \frac{0 â 03}{0 â 90} o r \frac{d n}{n} Ã 100 = â \frac{0 â 03}{0 â 90} Ã 100 = â 3 â 2 %$

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