Solved Examples of Speed of Sound Calculations: Step-by-Step Solutions

📚 Quick Study Guide

• 🌡️ The speed of sound depends on the medium's properties, primarily temperature, density, and elasticity.
• 💨 In gases, like air, the speed of sound increases with temperature.
• 🌊 The general formula for the speed of sound in a gas is given by $v = \sqrt{\frac{\gamma RT}{M}}$, where $\gamma$ is the adiabatic index, $R$ is the universal gas constant, $T$ is the absolute temperature, and $M$ is the molar mass.
• 🧊 For solids, the speed of sound is generally higher than in liquids or gases due to the stronger intermolecular forces.
• 📏 The speed of sound in a solid rod is given by $v = \sqrt{\frac{E}{\rho}}$, where $E$ is Young's modulus and $\rho$ is the density.

Practice Quiz

1. Question 1: The speed of sound in air at 0°C is approximately 331 m/s. What is the speed of sound in air at 25°C, assuming the speed increases by 0.6 m/s per degree Celsius?
   1. 340 m/s
   2. 346 m/s
   3. 350 m/s
   4. 356 m/s
2. Question 2: If the speed of sound in a metal rod is 5000 m/s and its density is 8000 kg/m³, what is the Young's modulus of the metal?
   1. 2.5 x 10^10 N/m²
   2. 4.0 x 10^10 N/m²
   3. 2.5 x 10^7 N/m²
   4. 4.0 x 10^7 N/m²
3. Question 3: The speed of sound in air is affected by which of the following factors?
   1. Humidity
   2. Temperature
   3. Wind speed
   4. All of the above
4. Question 4: What happens to the speed of sound in water as temperature increases?
   1. Increases
   2. Decreases
   3. Remains constant
   4. Becomes erratic
5. Question 5: A sound wave travels 1715 meters in 5 seconds through water. What is the speed of sound in water?
   1. 343 m/s
   2. 1715 m/s
   3. 8575 m/s
   4. 3430 m/s
6. Question 6: If the adiabatic index ($\gamma$) for a gas is 1.4, the universal gas constant (R) is 8.314 J/(mol·K), the temperature (T) is 300 K, and the molar mass (M) is 0.029 kg/mol, calculate the speed of sound (v) in the gas.
   1. Approximately 347 m/s
   2. Approximately 34.7 m/s
   3. Approximately 3470 m/s
   4. Approximately 3.47 m/s
7. Question 7: In which medium does sound generally travel fastest?
   1. Air
   2. Water
   3. Steel
   4. Vacuum