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Acoustics: the following topics are covered in this page:
Vibrations, Oscillations, Simple harmonic motions; Free and Forced vibrations, Damped, undamped and overdamped vibrations; Progressive waves, Longitudinal and Transverse waves; Superposition of waves, Interference, beats; Velocity of sound.
Click on a question to see the answer:
1. The velocity of sound is greater in solids than in gases at N.T.P. – Why?
The velocity of sound in a solid, according to Newton’s formula, is
![\[ V = {\sqrt\frac{Young's\, modulus\, of\, the\, solid}{Density\, of\, the\, solid}}.\]](https://physicscare.com/wp-content/ql-cache/quicklatex.com-c0127f17dbc913a71ec3e98f96265269_l3.png "Rendered by QuickLaTeX.com")
The velocity of sound in a gas, following Laplace’s correction on Newton’s formula, becomes
![\[ V=\sqrt{\frac{\gamma P}{\rho}}.\]](https://physicscare.com/wp-content/ql-cache/quicklatex.com-2d2ff0cd0ebdcb869dcfb6fb70cc475f_l3.png "Rendered by QuickLaTeX.com")
Here, 
is the ratio of two specific heats for the gas, 
is the pressure, and 
is the density.
Now, although the density of solids is much greater than that of the gases, the value of the elasticity of solids is much larger than the value of the pressure of the gases. Hence the velocity of sound in solids is generally greater than that of the gases.
2. Sound from an open organ pipe is more musical than that from an organ pipe closed at one end. Why?
In an open organ pipe all harmonics (odd and even) of the fundamental frequency are present. But a closed organ pipe produces only the odd harmonics. Consequently, the presence of bigger number of harmonics makes the sound from an open organ pipe more musical.
3. Determine the precentage change in the velocity of sound when the temperature changes from 
to 
.
The relation between the velocity of sound and temperature is,
![\[ V = \sqrt{T} \]](https://physicscare.com/wp-content/ql-cache/quicklatex.com-86ba92cbf952d8ebc4cb2d91a4803c23_l3.png "Rendered by QuickLaTeX.com")
Therefore,
![\[ \frac{V_{20}}{V_{10}}=\sqrt{\frac{T_{20}}{T_{10}}}=\sqrt{\frac{273+20}{273+10}}=\sqrt{\frac{293}{283}}\]](https://physicscare.com/wp-content/ql-cache/quicklatex.com-c70f4295ca49d9d9644f015455e412a1_l3.png "Rendered by QuickLaTeX.com")
As a result, the percentage change in velocity is
![\[=\frac{V_{20}-V_{10}}{V_{10}}\times 100 = \frac{\sqrt{293}-\sqrt{283}}{\sqrt{283}}\times 100 = 1.75\%.\]](https://physicscare.com/wp-content/ql-cache/quicklatex.com-ebb6209fdaa6b281cdaeb632c22563f3_l3.png "Rendered by QuickLaTeX.com")
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