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Question
The adjacent diagram shows three different modes of vibrations P, Q and R of the same string.
(i) Which vibration will produce a louder sound and why?
(ii) The sound of which string will have maximum shrillness?
(iii) State the ratio of wavelengths of P and R.
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Solution 1
(i) The loudness or softness of a sound is determined by the amplitude (or intensity) of the wave. In this case the amplitude of R is greater than the amplitude of other vibration modes. Hence, the vibration R will produce more sound than the other two. Louder sound corresponds to the wave of larger amplitude.
(ii) Shrillness or Pitch of a note depends on the wavelength or frequency of wave and here the vibration P has m ore frequency than others. If f is the principle frequency, then
Frequency (P) = 3 f
Frequency (Q) = 2 f
Frequency (R) = f
Hence P has more shrillness than others.
(iii) If the frequency of vibration of R = f, frequency of vibration of Q = 2f, and that of P =3 f.
`Ratio f_P/f_R=3/1`
`f_P:f_R=3:1`
As `fprop1/lambda` hence `lambda_P/lambda_R=1:3`
OR (Another method)
From figure we can say that 3 vibration of P corresponds to 1 vibration of R
i.e `3lambda_P=1lambdaR`
`thereforelambda_P/lambda_R=1/3=1:3`
Therefore, ratio of wavelength of P and R is 1:3.
Solution 2
(i) Vibration R as its amplitude is high as loudness ∝ A2
(ii) Sound of string ‘P’ will have maximum shrillness as its frequency is maximum.
Pitch ∝ frequency.
(iii) λP : λR = 3 : 1
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