The gap between seeing lightning and hearing thunder is one of the most familiar real-world examples of this chapter, and NEB exams lean on it often, along with echo-timing problems using the same underlying idea: sound takes measurable time to travel, and that speed depends heavily on the medium and temperature it’s moving through. This chapter is almost entirely about why sound travels faster in solids than gases, and how Newton’s original formula for the speed of sound in air turned out to be wrong until Laplace corrected it — a derivation that shows up as a long-answer question nearly every year in some phrasing.
Numerically, this chapter revolves around one relationship: how the speed of sound in air changes with temperature (roughly 0.6 m/s increase per °C rise), combined with the basic wave relation v = fλ. Most problems either ask you to find speed/wavelength at a new temperature given values at a reference temperature, or work backward from a timed echo or thunder-delay to calculate distance.
The complete set of past NEB and HISSAN questions for this chapter is below. Step-by-step numerical solutions are available on the Solutions page for this chapter.
MCQs
Which factor primarily determines the speed of mechanical wave in a medium?
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In which of the following medium, the velocity of sound is highest?
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If the speed of sound in air at 20oC is 344 m/s, the change in speed for 1oC change in air temperature is
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Theoretical questions
Obtain Laplace’s formula for velocity of sound in air starting from Newton’s formula. [2]
Why and how Laplace corrected Newton’s formula for the velocity of sound in air? Explain. [3]
Discuss the effect of temperature and pressure on velocity of sound in a gas. [2]
Explain the effect of temperature and humidity on the velocity of sound in air. [2]
What correction was made by Laplace over the Newton’s formula for velocity of sound in a gas? Obtain the corrected formula. [3]
Write down the Newton’s formula for the velocity of sound in a gas medium with its discrepancy. [1+1]
Velocity of sound in solids is more than that in liquids. Why?
OR The velocity of sound in solid is generally greater than that in gas at STP, why? Give reason.
When sound waves travel through a medium, does the temperature at various point remain constant? Explain.
Explain why sound travels faster in metals than in air. Discuss the effect of temperature, pressure and density of a gaseous medium on velocity of sound.
Discuss Newton’s formula for the velocity of sound in air and explain why and how this formula was modified by Laplace.
Does the propagation of sound wave cause change in thermodynamic condition of medium? Derive Laplace formula of velocity of sound in air.
Describe Newton’s formula for the velocity of sound in air. Explain why and how this formula is modified by Laplace.
What correction was made in Newton’s expression for the velocity of sound? Also explain, how change of temperature and pressure affect the velocity of sound.
OR Write the Newton’s formula for the velocity of sound in air. Explain why and how this formula is modified by Laplace.
OR Write down the Newton’s formula for the velocity of sound in air. Explain why this formula has to be modified. Discuss Laplace’s correction on it.
Numerical problems
Calculate the ratio of wavelengths of wave in a gas medium at [latex]0^oC[/latex] and [latex]27^oC[/latex] if the velocity of sound in gas at [latex]20^oC[/latex] is [latex]345ms^{-1}[/latex]. [Given the frequency of wave = 256Hz] Ans: 0.953
Calculate the wavelength of wave in air at 25oC if the frequency of sound wave is 256 Hz and velocity of sound at 0oC is 330 [latex]ms^{-1}[/latex]. [2] Ans: 1.35 m
At what temperature, the velocity of sound in air is increased by 60% to that at 27oC? Ans: 495oC
In a stormy day, a person observes a lightning flash which is followed by a thunder 3 s later. How would you estimate the distance of the lightning flash from the person. (Velocity of sound = 340 m/s, velocity of light = 3 x 108 m/s) Ans: 1020 m
A source of sound of frequency 550 Hz emits waves of wavelength 60 cm in air at 20oC. What would be the wavelength of sound from the source in air at 0oC? Ans: 0.579 m
What is the difference between the speed of longitudinal waves in air at 27oC and at – 13oC? What is the speed at 0oC? Ans: 23.94 m/s, 330.693 m/s
At what temperature, the velocity of sound in air is increased by 50% to that at 27oC? Ans: 402oC
Calculate the bulk modulus of a liquid in which longitudinal waves with frequency of 250 Hz have the wavelength of 8 m if the density of liquid is 900 kgm-3. Ans: 3.6 x 109 N/m2
A source of sound produces a note of 512 Hz in air at 17oC with wavelength 66.5 cm. Find the ratio of molar heat capacities at constant pressure to constant volume at NTP. (Densities of air and mercury at NTP are 1.293 kg/m3 and 13600 kg/m3 respectively). Ans: 1.4
A source of sound of frequency 512 Hz emits waves of wavelength 64.5 cm in air at 20oC. What would be the velocity of sound at 0oC? Ans: 318.77 m/s
In a stormy day, a boy observes a lightning flash which is followed by a thunder 3 sec later. How would you estimate the distance of the lightning strike from the boy? (Given velocity of sound on that day = 332 m/s, velocity of light c = [latex]3\times 10^8[/latex] m/s). Ans: 996 m
When a detonator is exploded on a railway line, an observer standing on the rail 2 km away hears two sounds. What is the time interval between them? (Young’s modulus of steel = [latex]2\times 10^{11}\ Nm^{-2}[/latex], density of steel = [latex]8\times 10^3\ kgm^{-2}[/latex], density of air = 1.4 [latex]kgm^{-3}[/latex], [latex]\gamma[/latex] – for air = 1.4, atmospheric pressure = [latex]10^5\ Nm^{-2})[/latex]. Ans: 5.92 s
A source of sound of frequency 512 Hz emits waves of wavelength 670 mm in air at 20oC. What is the velocity of sound in air at this temperature? What would be the wavelength of sound from the source in air at 0oC? Ans: 343.04 [latex]ms^{-1}[/latex], 0.646 m
A man standing at one end of a closed corridor 57 m long blow a short blast on a whistle. He found that the time from the blast to the sixth echo was 2 seconds. If the temperature was 17oC, what was the velocity of sound at 0oC? Ans: 331.8 [latex]ms^{-1}[/latex]
The interval between the flash of lighting and the sound of thunder is 2 seconds, when temperature is 10oC. How far is the storm if the velocity of sound in air at 0oC is 330 [latex]ms^{-1}[/latex]? Ans: 672 m