Factors Affecting the Speed of Sound
The speed of sound in a medium depends primarily on two factors:
- Elasticity (or Bulk Modulus): This measures the medium's resistance to compression. The stiffer or more elastic the medium, the faster sound travels. It's represented by B.
- Density: This is the mass per unit volume of the medium. Denser mediums tend to slow down sound waves. It's represented by \(\rho\).
The relationship is generally given by the formula:
\( v = \sqrt{B / \rho} \)
Where \(v\) is the speed of sound.
As a general rule, sound travels fastest in solids, then liquids, and slowest in gases because solids are typically much more elastic (stiffer) than liquids, and liquids are more elastic than gases, even though gases might be less dense.
Comparing Sound Speed in Aqueous and Methanol Media
The question asks in which of the given mediums the speed of sound would be maximum. The options provided are different types of liquids:
- Distilled water
- Sea water
- Drinking water
- Methanol
All these are liquids. Within liquids, the speed of sound is influenced by their bulk modulus and density.
Water Variations
Distilled water, drinking water, and sea water are all variations of water. The main difference affecting sound speed is the presence of dissolved salts and minerals:
- Distilled water is pure water with minimal impurities.
- Drinking water contains minerals and possibly dissolved gases, slightly altering its properties compared to distilled water.
- Sea water has a significant concentration of dissolved salts. These salts increase both the density (\(\rho\)) and, more importantly, the bulk modulus (\(B\)) of the water. The increase in bulk modulus typically has a greater effect than the increase in density, leading to a higher speed of sound.
Methanol Comparison
Methanol (\(\text{CH}_3\text{OH}\)) is an organic compound, a type of alcohol. It has different physical properties (density and bulk modulus) compared to water.
- The speed of sound in methanol at room temperature is approximately 1100 m/s to 1140 m/s.
- The speed of sound in fresh water (like distilled or drinking water) at 20°C is around 1482 m/s.
- The speed of sound in sea water at 20°C (with average salinity) is around 1522 m/s.
Comparing these values, the speed of sound is highest in sea water among the given options.
Conclusion
Due to the dissolved salts increasing its bulk modulus more significantly than its density, sea water provides a medium where the speed of sound is generally maximum compared to distilled water, drinking water, and methanol.
Similar Questions
Which of the following statements for persons suffering from presbyopia is/are correct?
1. They cannot distinguish colours.
2. It usually develops with ageing.
3. They wear either bi-focal lenses consisting of both concave and convex lenses or progressive lenses.
Select the answer using the code given below :- A sound wave travelling at a speed of 330 m/s produces 20 crests and 20 troughs in 0.1 second. The wavelength of the sound wave is:
Important Questions from Sound
Which one among the following components is used as an amplifying device?
- What is required for the generation of a sound wave?
How long will a sound wave take to travel 1.5km, which has a frequency of 5 kHz and wavelength of 6 cm?
Which phenomenon is responsible for the echo of sound wave?
We hear an echo due to
