Speed of Sound - Newtons Formula and Laplace Correction - UNSOLVED PRACTICE SET
Chapter: Waves | Topic: Speed of Sound Newtons Formula and Laplace Correction
SPEED OF SOUND - NEWTONS FORMULA AND LAPLACE CORRECTION - UNSOLVED PRACTICE SET
Topic: Speed of Sound Newtons Formula and Laplace Correction
Multiple Choice Questions
Q1. According to Newton's formula, the speed of sound in a gas is:
- v = √(P/ρ)
- v = P/ρ
- v = √(ρ/P)
- v = Pρ
Q2. Newton assumed that the propagation of sound in a gas is:
- An isothermal process
- An adiabatic process
- An isobaric process
- An isochoric process
Q3. Laplace corrected Newton's formula by assuming that sound propagation is:
- Isothermal
- Adiabatic
- Isobaric
- Isothermal but with heat loss
Q4. The Laplace correction introduces the factor:
- γ
- 1/γ
- √γ
- γ²
Q5. The speed of sound in a gas increases with temperature because:
- Density increases
- Pressure increases
- The ratio P/ρ increases
- The gas becomes lighter
Q6. On a hot summer day in Jaipur, a student notices that sound from a distant temple bell reaches her faster than on a cold winter morning. This is because:
- The air is denser in summer
- The speed of sound increases with temperature
- The bell rings louder in summer
- The wind carries sound faster
Short Answer Questions
Q7. State Newton's formula for the speed of sound in a gas. Why did Newton's theoretical value not agree with experimental observations?
Q8. What is Laplace's correction? Explain why the propagation of sound in a gas should be considered adiabatic rather than isothermal.
Q9. Show that the speed of sound in a gas is independent of pressure but depends on temperature.
Q10. Calculate the speed of sound in air at 0°C using Laplace's correction. (γ = 1.4, ρ = 1.29 kg/m³, P = 1.01 × 10⁵ Pa)
Q11. The speed of sound in air at 0°C is 331 m/s. Calculate the speed at 27°C.
Q12. Explain why the speed of sound in hydrogen is much greater than in oxygen at the same temperature.
Long Answer Questions
Q13. Derive Newton's formula for the speed of sound in a gas: v = √(P/ρ). Explain the assumptions made by Newton and why the calculated value was about 16% lower than the experimental value. Then derive Laplace's corrected formula v = √(γP/ρ) and explain the physical reasoning behind the adiabatic assumption.
Q14. Discuss the factors affecting the speed of sound in a gas. Show mathematically that:
(i) The speed is independent of pressure (at constant temperature)
(ii) The speed is directly proportional to the square root of absolute temperature
(iii) The speed depends on the molecular mass of the gas
(iv) The speed depends on γ (ratio of specific heats)
Calculate the speed of sound in hydrogen at 0°C and compare it with that in oxygen.
Q15. A student performs an experiment to measure the speed of sound using resonance in an air column.
(i) Describe the experimental setup.
(ii) Explain how the first and second resonance positions are determined.
(iii) How is the speed of sound calculated from the data?
(iv) Why does the calculated value differ slightly from the theoretical value? Discuss possible sources of error.
Numerical / Application-Based Problems
Q16. For air at STP:
Density ρ = 1.29 kg/m³
Pressure P = 1.013 × 10⁵ Pa
γ = 1.4
Calculate:
(i) The speed of sound using Newton's formula
(ii) The speed of sound using Laplace's corrected formula
(iii) The percentage error in Newton's value
(iv) The speed of sound at 40°C
(v) The temperature at which the speed of sound would be 350 m/s
Q17. The speed of sound in a diatomic gas at 0°C is measured to be 1260 m/s.
(i) Identify the gas. (Hint: calculate γ and compare)
(ii) Calculate the molecular mass of the gas.
(iii) Calculate the speed of sound in this gas at 100°C.
(iv) If this gas is mixed with an equal volume of oxygen at the same temperature, how does the speed of sound in the mixture compare with pure oxygen?
(Given: R = 8.31 J mol⁻¹ K⁻¹)
Q18. In a school physics lab, students measure the speed of sound using a resonance tube. A tuning fork of frequency 480 Hz is used, and the first resonance is observed when the air column length is 16.5 cm. The second resonance is at 50.5 cm. The room temperature is 25°C.
(i) Calculate the wavelength of sound from the resonance data.
(ii) Calculate the experimental speed of sound.
(iii) Calculate the theoretical speed of sound at 25°C and compare with the experimental value.
(iv) Calculate the end correction of the tube.
(v) The students repeat the experiment on a day when the temperature is 35°C. Without doing the experiment, predict how the resonance positions would change.
(Given: Speed of sound at 0°C = 331 m/s)