Answer:
1 Loudness depends on the square of the amplitude of the wave.
That is, loudness ∝ A
2
Amplitude is the size of the vibration, and this determines how loud the sound is. Larger vibrations make a louder sound.
Hence, wave R produces louder sound because its amplitude is maximum
2 (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.
3Sound of string 'P' will have maximum shrillness as its frequency is maximum. Pitch ∝ frequency.
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The adjacent diagram shows three different modes of vibrations P,Q and R of the same string.
State the ratio of wavelengths of P and R.
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A wavelength is a measure of distance between two identical peaks (crests and troughs) in a wave. Here, we can consider R is having one crest or one trough between the ends of the string. So, its having a wavelength (λ) of
2
λ
. Similarly, P is having two crests and one trough (or one crest and two troughs) which are happening at the same time. Thus its wavelength(λ) is
2
3λ
.
Thus, λ
R
=
2
λ
and λ
P
=
2
3λ
Hence ratio of wavelength of P and R i.e., λ
P
:λ
R
=
2
3λ
:
2
λ
=3:1.
