The speed of sound will be fastest in ________.
(a) Iron bar
Understanding the Speed of Sound in Different Media
The speed at which sound travels depends heavily on the medium through which it passes. Sound waves are mechanical waves, meaning they require particles of a medium to vibrate and transmit the energy. Without a medium, such as in a vacuum, sound cannot travel at all.
The speed of sound is primarily determined by the elasticity and density of the medium. Generally:
- Elasticity: A more elastic medium allows particles to return to their original positions quickly after being disturbed, leading to faster sound propagation. Solids are generally more elastic than liquids, which are more elastic than gases.
- Density: Denser materials have more mass per unit volume. While higher density might seem like it would slow sound down, in solids and liquids, the effect of elasticity is usually more significant than density. However, within the same state of matter (like comparing different gases), lower density often means higher speed (if temperature is constant).
Comparing the states of matter, the speed of sound is typically fastest in solids, slower in liquids, and slowest in gases. This is because the particles in solids are much closer together and strongly bonded, allowing vibrations to be transmitted very efficiently and quickly.
Analyzing the Options for Speed of Sound
Let's examine each option provided and determine the state of matter and likely speed of sound:
- (a) Iron bar: Iron is a solid. Solids generally have high elasticity and particle proximity, making them excellent conductors of sound. The speed of sound in iron is quite high.
- (b) Water: Water is a liquid. Sound travels faster in liquids than in gases, but typically slower than in solids.
- (c) Hill top: This implies air at a higher altitude. Air is a gas. The speed of sound in air is relatively slow compared to liquids and solids. On a hill top, the air pressure and temperature might be lower than at sea level, which could further slightly reduce the speed of sound in air compared to sea level conditions.
- (d) Vacuum: A vacuum is a space with no matter. Since sound requires a medium (particles) to propagate, sound cannot travel through a vacuum at all. The speed of sound in a vacuum is zero.
Comparing Speeds: Solid vs. Liquid vs. Gas vs. Vacuum
Based on the general principles, we can compare the approximate speeds:
| Medium Type | Example (from options) | Typical State of Matter | Approximate Speed of Sound (m/s) |
|---|---|---|---|
| Solid | Iron bar | Solid | ~5100 m/s (Iron) |
| Liquid | Water | Liquid | ~1480 m/s (Water at 20°C) |
| Gas | Air (Hill top) | Gas | ~343 m/s (Air at 20°C, sea level) |
| Vacuum | Vacuum | None | 0 m/s |
Comparing the approximate speeds, it is clear that sound travels significantly faster in the iron bar (a solid) than in water (a liquid) or air (a gas). In a vacuum, sound does not travel at all.
Conclusion on Fastest Speed of Sound
The speed of sound is highest in the medium where particles are closest together and interactions are strongest, allowing vibrations to transmit quickly. This is characteristic of solids. Among the given options, the iron bar is the only solid.
Therefore, the speed of sound will be fastest in the iron bar.
Revision Table: Speed of Sound Concepts
| Concept | Explanation |
|---|---|
| Mechanical Wave | Requires a medium to propagate (e.g., sound). |
| Speed of Sound Factors | Elasticity and density of the medium. Temperature also affects speed, especially in gases. |
| Speed in Solids | Generally fastest due to high elasticity and close particle packing. |
| Speed in Liquids | Faster than gases, slower than most solids. |
| Speed in Gases | Generally slowest among states of matter. |
| Speed in Vacuum | Zero, as there is no medium. |
Additional Information on Speed of Sound
The exact formula for the speed of sound varies depending on the medium. For instance, in an ideal gas, the speed of sound (\(v\)) is given by:
\(v = \sqrt{\frac{\gamma P}{\rho}}\)
where \(\gamma\) is the adiabatic index, \(P\) is the pressure, and \(\rho\) is the density of the gas. This can also be expressed in terms of temperature:
\(v = \sqrt{\frac{\gamma R T}{M}}\)
where \(R\) is the ideal gas constant, \(T\) is the absolute temperature, and \(M\) is the molar mass of the gas. This shows that for a given gas, the speed of sound depends on temperature.
For solids and liquids, the speed of sound depends on the bulk modulus (\(B\)) or Young's modulus (\(Y\)) and the density (\(\rho\)):
- For a fluid (liquid or gas): \(v = \sqrt{\frac{B}{\rho}}\)
- For a long solid bar: \(v = \sqrt{\frac{Y}{\rho}}\)
These formulas quantitatively show how elasticity (represented by \(B\) or \(Y\)) and density (\(\rho\)) influence the speed of sound in different materials. High elasticity and low density contribute to higher speeds, but the effect of elasticity is often dominant when comparing different states of matter.
Important Questions from Blood Relations
Shyam said Deepak’s Mother is the mother of my father’s wife. How is Deepak related to Shyam?
Pointing to a woman in a picture, Raju said, "Her mother-in-law has only one grandchild whose mother is my wife." How is the woman in the picture related to Raju?
Pankaj is younger than Sonali and Rupali is older than Tinu. Who among them is oldest?
Statements:
A. Rupali is older than Pankaj.
B. Sonali is older than Rupali.
C. Tinu is youngest among all.
Choose the correct answer from the options given below:
Pointing to a man A lady said "His mother is the only daughter of my mother." How is the man related to the lady?
Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).
