You must have heard someone playing a drum or table. The vibrations of a thin membrane produce sound waves. Similarly, in a guitar, the vibration of a stretched string produces sound waves. The origin of every wave is a 'vibration'. Wherever there is a vibration, there will be waves.
In this document, we will study waves in detail.
A wave is a vibratory disturbance in a medium which carries energy from one point to another point in a regular and an organised way without any actual movement of the medium.
A typical Wave
Ripple formation in water
Terms related to waves
There are three types of waves:
Mechanical waves are waves that require a medium in order to transfer energy away from their source. A medium is matter through which waves can travel.
Three familiar examples of mediums that mechanical waves travel through is air, water, and solid earth. For example, earthquake waves travel through layers within the earth. Sound waves are also mechanical waves that travel through the air, water, and solid matter. Water waves are mechanical waves that move wind energy through water.
Transverse waves and longitudinal waves are two main types of mechanical waves, which are disturbances that transfer energy through a medium. The key difference between them lies in the direction of particle displacement and wave propagation.
Here are some differences between Transverse waves and longitudinal waves.
Difference between Transverse and Longitudinal Waves
Sound waves are a type of mechanical wave that propagates through a medium, typically through air, although they can also travel through other materials like liquids and solids. These waves are the result of vibrations or oscillations of particles within the medium.
Here's how sound waves typically work:
Sound waves
Sound waves are mechanical longitudinal waves and require medium for their propagation.
[sound waves cannot propagate through vacuum.
If V_{s}, V_{i} and V_{g} are speed of sound waves in solid, liquid and gases, then
V_{s} > V_{i} > V_{g}
Sound waves (longitudinal waves) can reflect, refract, interfere and diffract but cannot be polarised as only transverse waves can polarised.
The velocity of longitudinal (sound) waves in any medium is given by
where E is the coefficient of elasticity of the medium and ρ is the density of the medium.
Longitudinal waves
According to Newton, the propagation of longitudinal waves in a gas is an isothermal process. Therefore, the velocity of longitudinal (sound) waves in gas should be
where E_{T} is the isothermal coefficient of volume elasticity and it is equal to the pressure of the gas.
According to Laplace, the propagation of longitudinal waves is an adiabatic process. Therefore, the velocity of the longitudinal (sound) wave in gas should be
where, E_{S}, is the adiabatic coefficient of volume elasticity and it is equal to γ p.
(a) Effect of Pressure: The formula for velocity of sound in a gas.
Therefore, (p/ρ) remains constant at a constant temperature.
Hence, there is no effect of pressure on the velocity of the longitudinal wave.
(b) Effect of Temperature: Velocity of longitudinal wave in a gas
The velocity of sound in a gas is directly proportional to the square root of its absolute temperature.
If v_{0} and v_{t} are velocities of sound in air at O°C and t°C, then
(c) Effect of Density: The velocity of sound in the gaseous medium
The velocity of sound in a gas is inversely proportional to the square root of the density of the gas.
(d) Effect of Humidity: The velocity of sound increases with an increase in humidity in the air.
Q.1. If a string wave encounters a completely fixed end, what happens to its phase?
a) Stays the same
b) Changes by π
c) Changes by π/2
d) Waves gets destroyed
Answer: b
Explanation: The reason for the phase to change by π is that the boundary displacement should be zero because it is rigid & by principle of superposition it is only possible if the reflected wave differs by a phase of π.
Q.2. What is the minimum distance between a node & an antinode in a standing wave?
a) λ
b) λ/2
c) 2λ
d) λ/4
Answer: d
Explanation: The amplitude in a standing wave is given by Asin(kx).
Node is a point where amplitude is zero and antinode is a point where amplitude is maximum.
For a node, sin(kx) = 0
kx = 2nπ OR (2π/λ)x = nππ
x = nλ/2.
For an antinode, sin(kx) = 1
kx = (2n+1)π/2
(2π/λ)x = (2n+1)π/2
x = (2n+1) λ/4.
∴ node is at λ/2, λ, 3λ/2 …
& antinode at λ/4, 3λ/4, 5λ/4 …
∴ minimum distance = λ/2 – λ/4 = λ/4.
Q.3. If a standing wave is vibrating in the fourth harmonic and the wavelength is λ, what is the length of the string.
a) 2λ
b) λ
c) 4λ
d) λ/4
Answer: a
Explanation: If the length of string is L, then the wavelength of the standing wave is 2L/n.
Or we can say L = nλ/2, where n corresponds to nth harmonic.
∴ L = 4λ/2
= 2λ.
Q.4. Consider standing waves in an air column with one end closed. What is a pressure node?
a) Pressure variation is maximum
b) Displacement variation is minimum
c) Same as displacement node
d) Least pressure change
Answer: d
Explanation: The point where there is an antinode corresponds to maximum amplitude of displacement. This also implies that here, pressure changes are minimum and it is therefore called a pressure node.
Q.5. A pipe is open at both ends. What should be its length such that it resonates a 10Hz source in the 2nd harmonic? Speed of sound in air = 340m/s.
a) 34m
b) 68m
c) 17m
d) 51m
Answer: a
Explanation: For a pipe open at both ends frequency ‘f’ = nv/2L, where n is speed of sound.
Given: f = 10 & n=2.
∴ 10 = 2*340/2L
∴ L = 680/20
= 34m.
102 videos411 docs121 tests

1. What is a wave? 
2. How does wave propagation occur? 
3. What are some important terms related to wave motion? 
4. What are sound waves? 
5. What factors affect the velocity of sound waves? 

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