4.2 Travelling waves
There are many forms of waves available to be studied. A common characteristic of all travelling waves is that they carry energy, but generally the medium
through which they travel will not be permanently disturbed.
- Travelling waves
- Wavelength, frequency, period and wave speed
- Transverse and longitudinal waves
- The nature of electromagnetic waves
- The nature of sound waves
Applications and Skills:
- Explaining the motion of particles of a medium when a wave passes through it for both transverse and longitudinal cases
- Sketching and interpreting displacement–distance graphs and displacement– time graphs for transverse and longitudinal waves
- Solving problems involving wave speed, frequency and wavelength
- Investigating the speed of sound experimentally
Data booklet reference:
- Mechanical waves : These waves require material medium for their propagation. For example : sound waves, waves in stretched string etc.
- Non-mechanical waves or electromagnetic waves : These waves do not require any material medium for their propagation. For example : light waves, x-rays etc.
- Transverse waves : In the transverse wave, the particles of medium oscillate in a direction perpendicular to the direction of wave propagation. Waves in stretched string, waves on the water surface are transverse in nature.
- Longitudinal waves : In longitudinal waves particles of medium oscillate about their mean position along the direction of wave propagation.
EQUATION OF A HARMONIC WAVE
- Phase difference of 2π radian is equivalent to a path difference λ and a time difference of period T.
- Phase difference = × path difference
- Phase difference = × time difference
- Time difference = × path difference
SPEED OF TRANSVERSE WAVES
- The speed of transverse waves in solid is given by
- The speed of transverse waves on stretched string is given by
SPEED OF LONGITUDINAL WAVES
SPEED OF SOUND IN A GAS
POWER AND INTENSITY OF WAVE MOTION
PRINCIPLE OF SUPERPOSITION OF WAVES
INTERFERENCE OF WAVES
- The ratio of maximum and minimum intensities in any interference wave form.
- Average intensity of interference in wave form :
Put the value of Imax and Imin
- Condition of maximum contrast in interference wave form
- For a wave, v = f λ
- The wave velocity of sound in air
- Particle velocity is given by. It changes with time. The wave velocity is the velocity with which disturbances travel in the medium and is given by .
- When a wave reflects from denser medium the phase change is π and when the wave reflects from rarer medium, the phase change is zero.
- In a tuning fork, the waves produced in the prongs is transverse whereas in the stem is longitudinal.
- A medium in which the speed of wave is independent of the frequency of the waves is called non-dispersive. For example air is a non-dispersive medium for the sound waves.
- Transverse waves can propagate in medium with shear modulus of elasticity e.g., solid whereas longitudinal waves need bulk modulus of elasticity hence can propagate in all media solid, liquid and gas.
ENERGY TRANSPORTED BY A HARMONIC WAVE ALONG A STRING
- Abeat = 2A cos 2πnAt, amplitude of resultant wave varies periodically as frequency
- Since intensity is proportional to amplitude i.e.,
FILING/LOADING A TUNING FORK
- When a tuning fork of frequency ν produces Δν beats per second with a standard tuning fork of frequency ν0, then
- If the beat frequency decreases or reduces to zero or remains the same on loading the unknown fork with a little wax, then
- When source is in motion and observer at rest
- when source moving towards observer
- when source moving away from observer
- When source is at rest and observer in motion
- when observer moving towards source
- when observer moving away from source and
V0 = velocity of observer.
- When source and observer both are in motion
- If source and observer both move away from each other.
- If source and observer both move towards each other.
- When the wind blows in the direction of sound, then in all above formulae V is replaced by (V + W) where W is the velocity of wind. If the wind blows in the opposite direction to sound then V is replaced by (V – W).
- The motion of the listener causes change in number of waves received by the listener and this produces an apparent change in frequency.
- The motion of the source of sound causes change in wavelength of the sound waves, which produces apparent change in frequency.
- If a star goes away from the earth with velocity v, then the frequency of the light emitted from it changes from ν to ν’.
If wavelength of the observed waves decreases then the object from which the waves are coming is moving towards the listener and vice versa.
STATIONARY OR STANDING WAVES
- As = 0, when cos kx = 0 i.e., kx = π/2, 3π/2…………
i.e., x = λ/4, 3λ/4……………….[as k = 2π/λ]
- As is maximum, when cos kx is max
- The distance between node and antinode is λ/4 (see figure)
- When a string vibrates in one segment, the sound produced is called fundamental note. The string is said to vibrate in fundamental mode.
- The fundamental note is called first harmonic, and is given by, where v = speed of wave.
- If the fundamental frequency be then , , … are respectively called second third, fourth … harmonics respectively.
- If an instrument produces notes of frequencies …. where ….., then is called first overtone, is called second overtone, is called third overtone … so on.
- Harmonics are the integral multiples of the fundamental frequency. If ν0 be the fundamental frequency, then nν0 is the frequency of nth harmonic.
- Overtones are the notes of frequency higher than the fundamental frequency actually produced by the instrument.
- In the strings all harmonics are produced.
STATIONARY WAVES IN AN ORGAN PIPE
- For closed organ pipe : l is replaced by l + e where e = 0.3D, D is the diameter of the tube.
- For open organ pipe : l is replaced by l + 2e where e = 0.3D
COMPARISON OF PROGRESSIVE (OR TRAVELLING) AND STATIONARY (OR STANDING) WAVE
COMPARATIVE STUDY OF INTERFERENCE, BEATS AND STATIONARY WAVE
CHARACTERISTICS OF SOUND
- Pitch depends on frequency
- loudness depends on intensity
- quality depends on the number and intensity of overtones
- Electro acoustics. This branch deals with electrical sound production with music.
- Musical acoustics. This branch deals with the relationship of sound with music.
- Architectural acoustics. This branch deals with the design and construction of buildings.
α1 , α2 …. are their respective absorption coefficient.
INTENSITY OF SOUND
- ratio of frequencies or time periods of two waves
- ratio of amplitude of two waves
- phase difference between two waves.