Wave and SoundS
Wave
→ A wave allows energy to be transmitted from one point to another some distance away without any
particles of the medium travelling between the two points.
→ On the basis of the medium required for the transmission of wave, it is classified into two types-
mechanical wave and electromagnetic wave.
1. Electromagnetic Wave
i. It does not require any physical medium.
ii. It travels at speed of light (3 x 108 m/s).
iii. They are transverse in nature.
iv. Examples of electromagnetic wave are radio,
microwave, infrared, visible light, ultraviolet, x-
rays, etc.
2. Mechanical wave
i. A mechanical wave can be propagated only in a material medium.
ii. The energy is passed by the molecules.
iii. Mechanical waves may be longitudinal or transverse in nature.
A. Longitudinal Wave
i. A wave in which the vibrations occurs in the same direction as the
direction of travel of wave.
ii. The displacements of the particle causes region of high density
(compressions C) and of low density (rarefactions R).
iii. The distance between two successive compression or rarefaction
is called wavelength.
iv. In longitudinal wave motion, density of medium changes.
v. These types of wave are possible in solid, liquid and gases.
B. Transverse Wave
i. A wave which is propagated by vibrations perpendicular to
direction of travel of wave is called transverse wave.
ii. Examples of transverse wave are waves plucked on string,
waves on water, electromagnetic wave such as light, waves on
surface of solids.
Some terms related to waves
a. Amplitude (a)
→ Maximum displacement of particle from their mean position.
→ The maximum displacement in upward direction from mean position is called crest.
→ The maximum displacement in downward direction from mean position is called trough.
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b. Wavelength (λ)
→ The length between two consecutive crest or consecutive trough is called wavelength.
→ It is measured in meter.
c. Frequency (f)
→ The number of vibration of oscillation completed in one second.
→ It is denoted in s-1 and its unit is Herz.
d. Time period (T)
→ Time taken by particle to complete one oscillation or one vibration.
→ It is measured in seconds.
❖ Speed of transverse wave on stretched string
𝑻
𝒗=√ 𝑤ℎ𝑒𝑟𝑒 𝑇 𝑖𝑠 𝑡ℎ𝑒 𝑡𝑒𝑛𝑠𝑖𝑜𝑛 𝑖𝑛 𝑠𝑡𝑟𝑖𝑛𝑔 𝑎𝑛𝑑 𝒎 𝑖𝑠 𝑚𝑎𝑠𝑠 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑙𝑒𝑛𝑔𝑡ℎ
𝒎
❖ Velocity of sound
The speed of sound in a medium is given by
𝑬
𝒗=√
𝝆
Where E = modulus of elasticity of the medium and ρ is density of medium
It does not depend upon amplitude, frequency, intensity and shape of a wave.
1. Speed of sound in solid
𝒀
𝒗=√
𝝆
Where Y is Young’s modulus and 𝜌 is density of solid
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2. Speed of sound in a liquid
𝑩
𝒗=√
𝝆
Where B is Bulk’s modulus
3. Speed of sound in a gas
A. Newtons Formula (for isothermal elasticity)
𝑷
𝒗 = √𝝆 Where P is pressure of gas and 𝜌 is density of gas
B. Laplace Formula (for adiabatic elasticity)
𝜸𝑷
𝒗=√
𝝆
Where 𝛾 is ratio of molar heat capacity ( = 1.40 for air at STP)
Factors affecting velocity of sound in gas
1. Effects of temperature
→ 𝑣 ∝ √𝑇
𝑣2 𝑇
→ = √𝑇2
𝑣1 1
→ Velocity of sound in gases increases by 0.61 m/s for every 10C rise in temperature.
2. Effects of pressure
𝑃
→ For a given mass of gas, 𝜌 is a constant so v is also constant.
3. Effects of density of medium
→ Velocity of sound in air or gas is inversely proportional to square root of the density of the
medium if pressure is constant.
𝑣1 𝜌
→ = √𝜌2
𝑣2 1
4. Effects of humidity
1
→ The density of moist air is less than density of dry air and we know 𝑣 = .
√𝜌
→ Thus velocity of sound increases with increase in humidity in air.
5. Effects of wind
→ If wind moves in the direction of wave then v1 = v + w
→ If wind moves against the direction of wave then v1 = v + w
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