Longitudinal Waves Questions

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Very Short Answers Questions [1 Mark Questions]

Ques. Which of the following is not a longitudinal wave?

1. Sound
2. Seismic P-wave
3. Ultrasound
4. Light

Ans. The correct answer is d. Light

Explanation: The waveform for light changes perpendicular to the relative motion. The medium vibrates perpendicular to the wave energy, making it clear that it is a particular form of transverse wave.

Ques. Identify the longitudinal waves from the following

1. Ultrasonic waves
2. Light waves
3. Radio waves
4. Surface water waves

Ans. The correct answer is a. Ultrasonic waves

Explanation: Longitudinal waves with a frequency greater than 20,000 Hz are considered ultrasonic waves. This indicates the upper limit of detectable sound, or the human hearing range, is 20,000 hertz (Hz).

Ques. A longitudinal wave is a wave that consists of oscillations that are

1. Radial to the direction of wave propagation
2. Perpendicular to the direction of wave propagation
3. Parallel to the direction of wave propagation
4. None of the above

Ans. The correct answer is c. Parallel to the direction of wave propagation

Explanation: When the oscillations of the particles of the medium are parallel to the direction of propagation, longitudinal waves are produced.

Ques. How longitudinal waves are different from other waves?

1. Particles of the medium move in a direction below the direction of energy transport
2. Particles of the medium move in a direction parallel to the direction of energy transport
3. Particles of the medium move in a direction perpendicular to the direction of energy transport
4. None of the above

Ans. The correct answer is b. Particles of the medium move in a direction parallel to the direction of energy transport

Explanation: Because medium particles in longitudinal waves move parallel to the direction of energy transmission for longitudinal waves, longitudinal waves differ from other waves.

Ques. Longitudinal waves move faster through

1. Solids
2. Liquids
3. Gases
4. None of the above

Ans. The correct answer is a. Solids

Explanation: Because solid particles are less mobile than those in liquids or gases, more densely packed together, and have higher molecular cohesion, longitudinal waves move more quickly through solids.

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Short Answers Questions [2 Marks Questions]

Ques. What is meant by a longitudinal wave?

Ans. Longitudinal waves are waves in which the particles of the medium oscillate in the direction of the propagation of the wave. Because longitudinal waves produce rarefaction and compression as they move through a material, they are often referred to as compression or compressional waves. They are also known as pressure waves because they create changes in pressure.

Ques. What is the longitudinal wave formula?

Ans. The displacement y of the element of the medium located at a distance x in time t, while a longitudinal wave is traveling in the +x direction, is given by

y = A sin (kx – ωt + Φ)

The displacement y of the element of the medium located at a distance x in time t, while a longitudinal wave is traveling in the -x direction, is given by

y = A sin (kx + ωt + Φ)

Where

• x = position of the particle from the wave’s source
• A = Maximum amplitude
• k = Propagation constant or angular wave number
• y = Displacement of the particle of the medium in time t
• t = Time elapsed
• Φ = initial phase
• ω = Angular frequency of the wave

Ques. What is a sound wave?

Ans. An important example of a longitudinal wave is a sound wave. The fast oscillation of particles moving through an elastic material causes it to be produced. A tuning fork's sound acts as a perfect example of sound waves that travel longitudinally. The amplitude of a sound wave is the difference in pressure between the medium that is being disturbed and the wave's maximum pressure. The type, composition, and temperature of the medium used for the transmission of sound all affect how fast sound travels.

Ques. What is meant by transverse waves?

Ans. A transverse wave is one whose vibrations are parallel to the wave's direction of motion. Compared to longitudinal waves, which propagate along the direction of their vibrations, this is completely different. Transverse waves include electromagnetic waves such as microwaves, light waves, and radio waves.

Ques. What is meant by pressure waves?

Ans. A change in pressure in a medium consisting of physical materials causes pressure waves, which are waves like sound waves.

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Long Answers Questions [3 Marks Questions]

Ques. What are the properties of longitudinal waves?

Ans. The following are the properties of longitudinal waves

• Longitudinal waves are considered mechanical waves since they need a medium for their propagation.
• The two components of longitudinal waves that have been observed whenever they travel through a medium are, in fact, compressions and rarefactions.
• Rarefaction occurs if molecules or elements are spaced further apart.
• Particles compress whenever they are close to one another.

Ques. What is a wave? Give some examples of a wave. What are the two types of waves?

Ans. A wave is a dynamic disturbance of one or more variables that propagates through time. When waves oscillate repeatedly around an equilibrium value at a certain frequency, they are said to be periodic.

Examples of waves are

• Electromagnetic waves (microwaves, light waves, radio waves).
• Waves on the surface of water bodies.
• Seismic S-wave.
• Synchronized crowd wave in a football field.
• Oscillations in a guitar string.

The two types of waves are

• Longitudinal wave: The displacement of the particles of the medium in a longitudinal wave is parallel to the direction of wave propagation.
• Transverse wave: The displacement of the particles of the medium in a transverse wave is perpendicular to the direction of wave propagation.

Ques. What is a plane wave?

Ans. Plane waves are waves with wave fronts that are infinitely parallel to each other and parallel to their propagation directions.

• These waves have an increasing radius and are planar rather than spherical.
• Disturbances in plane waves spread in one direction, much as string waves.
• A plane wave that travels in the direction indicated by k and k = ω/c
• Plane waves are referred to as free-space modes because they satisfy wave equations in homogeneous mediums.

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Very Long Answers Questions [5 Marks Questions]

Ques. What is the main difference between longitudinal waves and transverse waves?

Ans. The differences between longitudinal and transverse waves are

Ques. What are the main characteristics of a longitudinal wave?

Ans. The following are the main characteristics of a longitudinal wave

• Compression: A region in a longitudinal wave where the wave particles are closest to one another is referred to as compression.
• Rarefaction: A region in a longitudinal wave where the wave particles are spaced apart from one another is referred to as rarefaction.
• Wavelength: The separation between two consecutive points on a wave is referred to as its wavelength. Between two rarefactions or two compressions, these two points can be located. Therefore, a wave's wavelength is the distance that it travels in a single cycle of disturbance in a medium. Sometimes the wavelength can be represented by the length of the repeating patterns since a wave repeats the pattern once every cycle.
• Amplitude: The maximum displacement of the wave particle from its position of rest is known as amplitude. The distance between the medium's equilibrium position and the region of rarefaction or compression is known as the amplitude in a longitudinal wave. 
• Period: The period is the interval of time it takes a wave to cover one wavelength.
• Frequency: The frequency of a longitudinal wave is measured as the number of wavelengths per second.

Ques. If the speed of the longitudinal mechanical wave in water is 1400 m/s, then calculate the bulk modulus of elasticity of water.

Ans. The formula for the speed of the longitudinal wave is given by

\(v = \sqrt{\frac{B}{\rho}}\)

Where

• B is the bulk modulus of elasticity of the medium
• ρ is the density of the medium

From the above formula, we can write

B = v² x ρ

Given, the speed of the longitudinal mechanical wave in water, v = 1400 m/s

And we know, the density of water is, ρ = 1000 kg/m³

On substituting the values, we get

B = 1400² x 1000

⇒ B = 1.96 x 10⁹ N/m²

Hence the bulk modulus of elasticity of water is 1.96 x 10⁹ N/m²

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