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Question
The diagram below shows three different modes of vibration P, Q and R of the same string of a given length.
 |
 |
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| P | Q | R |
- Which vibration will produce a louder sound and why?
- Which vibration will produce sound of maximum shrillness (or pitch) and why?
- What is the ratio of wavelength of vibrations P and R?
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Solution
(a) R will produce maximum sound because it has maximum amplitude.
(b) P will produce maximum shrillness because it has a maximum frequency.
(c) Let's suppose the string has length l
Then wavelength of P = `"2 l"/3`
Wavelength of R = 2 l
∴ `lambda_"P"/lambda_"R" = ("2 l"/3)/"2 l" = 1/3`
∴ λp : λR = 1 : 3
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