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The string of a violin has a frequency of 440 cps. If the viol

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The string of a violin has a frequency of $440 c p s$ . If the violin string is shortend by one fifth, its frequency will be changed to

440 c p s

880 c p s

550 c p s

2200 c p s

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The string of a violin has a frequency of

440 c p s

. If the violin string is shortend by one fifth, its frequency will be changed to

13 mins ago

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13 mins ago

Text solutionVerified

F = frequency of wave

n = order of harmonic

c = speed of wave

l = length of string

f = 440

l_{2} = \frac{1}{5} l_{1}

f = \frac{n c}{2 l}

∴ f \propto \frac{1}{l}

∴ \frac{f _{1}}{f _{2}} = \frac{l _{2}}{l _{1}}

\frac{f _{1}}{f _{2}} = \frac{l _{2}}{l _{1}} \Rightarrow \frac{440}{f _{2}} = \frac{\frac{1}{5} l _{1}}{l _{1}}

\frac{440}{f _{2}} = \frac{1}{5} \Rightarrow f_{2} = 5 \times 440

= 2200

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Question Text	The string of a violin has a frequency of $440 c p s$ . If the violin string is shortend by one fifth, its frequency will be changed to
Answer Type	Text solution:1
Upvotes	153