Transverse and longitudinal waves MCQ Quiz - Objective Question with Answer for Transverse and longitudinal waves - Download Free PDF

Concept:

The speed of a wave on a string is given by the formula:

v = √(T / μ), where v is the wave speed, T is the tension in the string, and μ is the linear mass density of the string.

The speed of the wave is proportional to the square root of the tension, i.e., v ∝ √T.

Calculation:

Given, v₁ = 150 m/s, T₁ = 120 N, and the new wave speed v₂ = 1.2 × 150 = 180 m/s.

Using the proportionality relation: v₂ / v₁ = √(T₂ / T₁),

1.2 = √(T₂ / 120)

Squaring both sides: 1.44 = T₂ / 120

T₂ = 1.44 × 120 = 172.8 N

The percentage increase in tension is:

% Increase = ((T₂ - T₁) / T₁) × 100 = ((172.8 - 120) / 120) × 100 = 44%

∴ The percentage increase in the tension is 44%. Option 1) is correct.

The correct answer is Option 3.

Key Points

• P-waves (Primary waves): These are a type of body wave that travels through the Earth's interior. They are compressional waves and are the fastest seismic waves.
• S-waves (Secondary waves): These are another type of body wave that travels through the Earth's interior. They are shear waves and are slower than P-waves.
• Surface waves: These are seismic waves that travel along the Earth's surface, not through its interior, making them different from body waves.

The Correct answer is 10 Hz to 1 MHz.

Key Points

• Radio waves are a type of electromagnetic radiation with wavelengths in the electromagnetic spectrum longer than infrared light.
• The frequency range of radio waves is typically from about 10 Hz to 1 MHz.
• Radio waves are used for various forms of wireless communication, including AM and FM radio broadcasting, television, cell phones, and satellite communications.
• Lower frequency radio waves (<10 Hz) are typically used for communication with submarines because they can penetrate seawater.
• Higher frequency radio waves (up to 1 MHz) are used in applications such as medium-wave (MW) broadcasting and long-wave (LW) broadcasting.

 Additional Information

• 30 MHz to 40 MHz
  • This range is typically used for VHF (Very High Frequency) applications such as television broadcasting and FM radio.
• 20 MHz to 30 MHz
  • This frequency range falls into the HF (High Frequency) band, often used for shortwave radio broadcasting and amateur radio.
• 2 MHz to 10 MHz
  • This range is part of the HF (High Frequency) band, used for marine and aviation communications as well as international shortwave broadcasts.

Calculation:

Fundamental frequency:

f = (1 / 2l) × √(T / μ)

= (1 / 2l) × √(T / Aρ)

= (1 / 2l) × √(stress / ρ)

= (1 / (2 × 1.5)) × √[(22 × 10¹¹ × 10^-2) / (77 × 10³)]

= 10³ × 0.17817 = 178.2 Hz

Answer : 1

Solution :

Let the initial length and tension be l and T respectively.

After shortening,

The new length l_new = \(l-\frac{40}{100} l=\frac{3}{5} l\)

After increase in tension,

the new tension T_new = \(\mathrm{T}+\frac{44}{100} \mathrm{~T}=\frac{144 \mathrm{~T}}{100}\)

Fundamental frequency of a vibrating string is given by

\(\mathrm{n}=\frac{1}{2 l} \sqrt{\frac{\mathrm{~T}}{\mathrm{~m}}}\)

∴ \(\mathrm{n}_{1}=\frac{1}{2 l} \sqrt{\frac{\mathrm{~T}}{\mathrm{~m}}}\)

\(\mathrm{n}_{2}=\frac{1}{2 l} \sqrt{\frac{\mathrm{~T}_{\mathrm{new}}}{\mathrm{~m}}}\)

∴ \(\frac{\mathrm{n}_{1}}{\mathrm{n}_{2}}=\frac{l_{\mathrm{new}}}{l} \times \frac{\sqrt{\mathrm{T}}}{\sqrt{\mathrm{~T}_{\mathrm{new}}}}\)

= \(\frac{\frac{3}{5} l}{l} \times \sqrt{\frac{100 \mathrm{~T}}{144 \mathrm{~T}}}\)

= \(\frac{3}{5} \times \frac{10}{12}=\frac{1}{2}\)

∴ \(\frac{\mathrm{n}_{2}}{\mathrm{n}_{1}}=\frac{2}{1}\)

The correct answer is the Transverse wave.

• Light is a Transverse wave.

Key Points

• Light is a form of energy that is propagated as electromagnetic waves.
• Electromagnetic waves are transverse, hence light is a transverse wave.
• The wave nature of light explains rectilinear propagation, reflection, refraction, interference, diffraction, and polarization of light.
• In quantum theory, light is regarded as a packet or bundle of energy called the photon.
• Light behaves as wave and particle both. Thus light has dual nature.
• Speed of light is maximum in vacuum and air (3 × 10⁸ m/s).

• Longitudinal Wave:
  • If the particles of the medium vibrate in the direction of propagation of the wave, the wave is called a longitudinal wave.
  • Waves on springs or sound waves in the air are examples of longitudinal waves.
• Transverse Wave:
  • If the particles of the medium vibrate perpendicular to the direction of propagation of a wave, the wave is called a transverse wave.
  • Wave on strings under tension, light wave, waves on the surface of the water are examples of transverse waves.

The correct answer is the Transverse wave.

• Light is a Transverse wave.

Key Points

• Light is a form of energy that is propagated as electromagnetic waves.
• Electromagnetic waves are transverse, hence light is a transverse wave.
• The wave nature of light explains rectilinear propagation, reflection, refraction, interference, diffraction, and polarization of light.
• In quantum theory, light is regarded as a packet or bundle of energy called the photon.
• Light behaves as wave and particle both. Thus light has dual nature.
• Speed of light is maximum in vacuum and air (3 × 10⁸ m/s).

• Longitudinal Wave:
  • If the particles of the medium vibrate in the direction of propagation of the wave, the wave is called a longitudinal wave.
  • Waves on springs or sound waves in the air are examples of longitudinal waves.
• Transverse Wave:
  • If the particles of the medium vibrate perpendicular to the direction of propagation of a wave, the wave is called a transverse wave.
  • Wave on strings under tension, waves on the surface of the water are examples of transverse waves.

The correct answer is option 3) i.e. stationary waves.

CONCEPT:

EXPLANATION:

• A stationary wave is a standing wave and does not move.
• Therefore, they cannot propagate any disturbance or energy through them.
• The energy associated with these waves is contained within themselves.

Hence, stationary waves do not propagate energy.

CONCEPT:

Sound: 

• A sound is a form of energy that produces a sensation of hearing in our ears.
• It is a kind of disturbance that travels through a medium due to repeated vibrations of the particles of the medium about their mean positions.
• The disturbance being handed over from one particle to the next.

Light:

• Light is a form of electromagnetic radiation that can be detected by the human eye.
• When light falls on an object, some part of the light is reflected on our eyes and we are able to see.

EXPLANATION:

• Sound waves are longitudinal waves and light waves are transverse waves. 

• Light can travel in a vacuum because light waves are electromagnetic in nature, which sound waves are not.
• Sound waves require a medium to travel. The speed of sound is faster in solid materials, slower in liquids, and slowest in gases.
• The speed of light in a vacuum is commonly given the symbol c. It is a universal constant that has the value c = 3 x 10⁸ m/second.

CONCEPT:

• Wave motion: The type of disturbance that travels through a medium due to repeated vibrations of the particles of the medium about their mean positions is called wave motion.

There are two types of wave motion:

• Longitudinal wave motion: It is that wave motion in which individual particles of the medium execute simple harmonic motion about their mean position along the same direction, in which the wave is propagated.
  • For example: Sound waves
• Transverse wave motion: Vibration of particles in a medium and the propagation of waves are perpendicular to each other.
  • Example: Waves in the surface of the water, waves in a string.

EXPLANATION:

• Sound waves produced in the gas are longitudinal. So option 1 is correct.

Explanation:

Wave motion: The type of disturbance that travels through a medium due to repeated vibrations of the particles of the medium about their mean positions is called wave motion.

There are two types of wave motion:

Longitudinal wave motion: It is that wave motion in which individual particles of the medium execute simple harmonic motion about their mean position along the same direction, in which the wave is propagated.

• For example: Sound waves

Transverse wave motion: Vibration of particles in a medium and the propagation of wave are perpendicular to each other.

• Example: Waves in the surface of the water, waves in a string, light waves, etc.

CONCEPT:

• The electromagnetic wave is those wave which doesn't require any medium to propagate.
  • Electromagnetic waves are transverse in nature.

EXPLANATION:

• A sound wave needs a medium to travel.
• Light is an example of Electromagnetic waves. It doesn't need any medium to travel. Hence option 2 is correct.
• Sound waves travel due to compression and rarefaction. 
• Sound waves, water waves, and waves in a string are mechanical waves that require the medium to travel.

• Electromagnetic waves are produced by an oscillating charged particle.

CONCEPT:

• Sound wave: The longitudinal wave in an elastic medium that produces an audible sensation is called a sound wave.
  • As sound waves are longitudinal waves, the air particles vibrate to and fro in the direction of propagation of sound.
  • It is a wave of compression and rarefaction.
  • Compressions and rarefactions are part of a sound wave.

• Compression: A region in a longitudinal wave where the particles are closest together is called compression. Compression has high density and high pressure

  Rarefaction: A region in a longitudinal wave where the particles are furthest apart is called rarefaction. The rarefaction has a low density and low pressure

EXPLANATION:

• The speed of sound is in dry air, which is like 343 m/s whereas the speed of light is 3 × 10⁸ m/s. Therefore, sound travels at a speed slower than the speed of light. Hence option 1 is correct.
• As sound waves are longitudinal waves, the air particles vibrate to and fro in the direction of propagation of sound. Therefore option 2 is incorrect and option 3 is correct.

Effect of density: 

• The velocity of sound decreases, as density increases.

\(v = \sqrt {\frac{{\gamma P}}{\rho }} \Rightarrow v \propto \frac{1}{{\sqrt \rho }}\)

• From the above equation, it is clear that the velocity of sound in a gas is inversely proportional to the square root of its density, and as we know the density of moist air is less than that of dry air, therefore, the velocity of sound in moist air is greater than that in dry air. Hence option 4 is correct.

CONCEPT:

• Wave motion: The type of disturbance that travels through a medium due to repeated vibrations of the particles of the medium about their mean positions is called wave motion.

There are two types of wave motion:

• Longitudinal wave motion: It is that wave motion in which individual particles of the medium execute simple harmonic motion about their mean position along the same direction, in which the wave is propagated.
  • For example: Sound waves
• Transverse wave motion: Vibration of particles in a medium and the propagation of wave are perpendicular to each other.
  • Example: Waves in the surface of the water, waves in a string, light waves, etc.

EXPLANATION:

• Light wave is a transverse wave. 
• The radio wave is also a type of light. So it is a transverse wave.
• Sound is a longitudinal wave and ultrasound is also a type of sound wave. So ultrasound is the longitudinal wave. Hence option 3 is correct.
• Surface water waves is a transverse wave.

CONCEPT:

On the basis of the direction of propagation, waves are classified into two types:

• Longitudinal Waves: Those waves whose direction of propagation and direction of disturbance is always parallel.
  • These waves produced in a medium that can sustain compressive strain. 
  • Example Sound Wave
• Transverse Waves: Those waves whose direction of propagation and direction of disturbance is always perpendicular. 
  • These waves produced in a medium that can sustain shearing strain.
  • Example: Electromagnetic Waves.

​EXPLANATION:

• The direction of disturbance and direction of propagation is always perpendicular to each other in a transverse wave.
• The direction of disturbance and direction of propagation is always parallel to each other in a longitudinal wave.
• The Sound waves are longitudinal in nature.
• Longitudinal wave generally forms in a medium that can sustain compressive strain.
• Since the statement of option 1 is wrong. Hence option 1 is correct.

Additional Information

• Electromagnetic waves are produced by an oscillating charged particle.