A very large container consists of an ideal gas. The speed of sound in the gas is x. When the pressure of the gas is doubled while keeping the temperature constant, the speed of sound now becomes y. What is the ratio of x to y?
- A.1
- B.√2
- C.2
- D.4
Correct answer
Explanation
The correct answer is A, 1. At a fixed temperature, changing the pressure of an ideal gas does not change the speed of sound in it, so x and y are equal.
By Laplace's formula the speed of sound in a gas is v = √(γP/ρ), where P is the pressure and ρ the density. For an ideal gas P/ρ = RT/M, which depends only on the temperature and the molar mass. When the pressure is doubled at constant temperature, the gas is squeezed and its density also doubles, so the ratio P/ρ stays the same and the speed does not change. The speed does change with temperature: it varies as the square root of the absolute temperature.
B is wrong: √2 would follow only if the density stayed fixed while the pressure doubled.
C is wrong: speed does not grow in direct proportion to pressure.
D is wrong: 4 has no basis in the formula at all.
Exam tip: speed of sound in a gas depends on temperature, not on pressure, as long as temperature is held constant.
Practice Questions
View allThe speed of the wind is measured by
- A.wind vane
- B.wind rose
- C.barometer
- D.anemometer
Show answer
An anemometer measures how fast the wind is blowing; its name comes from the Greek word anemos, meaning wind.
Read the full explanation →Brilliance of diamond is due to
- A.interference of light
- B.diffraction of light
- C.polarization of light
- D.total internal reflection of light
Show answer
Light that enters a cut diamond is reflected again and again inside it before it escapes, which makes the stone sparkle.
Read the full explanation →Which one of the following is NOT an electromagnetic wave ?
- A.Light wave
- B.Radio wave
- C.Sound wave
- D.Micro wave
Show answer
Sound is a mechanical wave that needs a medium to travel, while the other three are electromagnetic waves. Sound travels as a longitudinal wave of compressions and rarefactions in air, water or solids, which is why it cannot pass through a vacuum.
Read the full explanation →Which one of the following is NOT true for an electromagnetic wave ?
- A.Electromagnetic wave transports energy and momentum
- B.Electromagnetic wave can be polarized and reflected
- C.Electromagnetic wave is longitudinal
- D.Electromagnetic wave propagation is described by the varying electric and magnetic fields
Show answer
Electromagnetic waves are transverse, not longitudinal, so this statement is false. In an electromagnetic wave the electric field and the magnetic field oscillate at right angles to each other and both at right angles to the direction in which the wave travels.
Read the full explanation →Which one of the following frequency ranges is sensitive to human ears ?
- A.0-200 Hz
- B.20-20,000 Hz
- C.200-20,000 Hz only
- D.2,000-20,000 Hz only
Show answer
The normal human ear hears sound from about 20 hertz to 20,000 hertz, the audible range. Frequency, measured in hertz, is the number of vibrations per second, and it decides the pitch of a sound: the higher the frequency, the shriller the note.
Read the full explanation →