Plant Responses

Summary

Summary
 
Key terms
Wave: A disturbance or oscillation that moves through a medium.
Wave Motion: The movement of a disturbance produced in one part of a medium to another involving the transfer of energy but not the transfer of matter is called wave motion.
Wavelength: For a transverse wave it is the distance between consecutive crests or troughs. In case of a longitudinal wave, wavelength is defined as the distance between centers of consecutive compressions or consecutive re-fractions.
Frequency: It is the number of vibrations a particle undergoes per second. It is denoted by f or n. Its unit is inverse of time or s−1 (or Hertz). Frequency gives the number of oscillations per second.
Interference: It is a phenomenon in which two waves superimpose to form a resultant wave of greater or lower amplitude.
Time period: It is the time taken by a particle of the medium through which the wave is passing to do one cycle of vibration and return to its original position.
Amplitude: It is the maximum displacement of the particles in the medium when the wave passes, about their mean undisturbed positions.
Phase: It is used to describe the relative positions of the crests and troughs. When the crests and troughs are aligned, for constructive interference, the two waves are said to be in phase.
Standing waves: A Condition where two waves of equal frequency traveling in opposite directions meet and form stationary regions of maximum displacement due to constructive interference and stationary regions of zero displacement due to destructive interference.
Wave velocity: It is the velocity of the wave or it is the distance traveled by the wave in one second. It has units of velocity m/s.
Key concepts
  • Wave Motion: The process by which a disturbance at one point in space is propagated to another point more remotely from the source with no net transport of the material of the medium itself. As a wave propagates, it carries energy.

    There are two types of waves:
    • Mechanical Waves and
    • Electromagnetic waves.
    • Mechanical Waves: These are the waves in which a disturbance requires some material or substance to travel. Such material (or) substance is called the medium of propagation for the waves. Clearly, these waves cannot travel through vacuum. The motion is being transferred from particle to particle. Accordingly, there are two types of mechanical waves, depending on the nature of the wave Transverse waves and Longitudinal waves.

      • Transverse waves
      • Longitudinal waves.

        Transverse wave Longitudinal wave
        When a transverse wave is propagating in a medium, particles in the medium vibrate at right angles to the direction of wave motion. When a longitudinal wave is propagating in a medium, particles the medium vibrate anti-parallel or parallel to the direction of wave motion.
        Transverse waves consist of crests and troughs. Longitudinal waves consist of compressions and refractions.
        Transverse waves are propagated through solids and surface of liquids. Light waves, which are a special case of transverse waves, do not need any medium for propagation. Longitudinal waves need a medium for propagation.
      • Electromagnetic waves: These are the waves in which a disturbance does not require a material medium for its transmission. These waves can travel through vacuum also. The light waves, X-rays etc are called electromagnetic waves. The transfer of energy by electromagnetic waves is due to the motion of electromagnetic fields.
    • Wave Characteristics: A wave has a periodic cycle of a certain fixed pattern. A wave can be described by its wavelength, frequency, amplitude, time period, phase and wave velocity. A wavelength of a transverse wave is the distance between consecutive crests or troughs. In case of a longitudinal wave, wavelength is defined as the distance between centres of consecutive compressions or consecutive rarefactions.

      Frequency of a wave is the number of vibrations a particle undergoes per second. It is denoted by f or n . Its unit is inverse of time or s-1 (or Hertz). Frequency gives the number of oscillations per second. Time period is the time taken by a particle of the medium through which the wave is passing to do one cycle of vibration and return to its original position. Amplitude of a wave is the maximum displacement of the particles in the medium when the wave passes, about their mean undisturbed positions.

      Wave velocity is the velocity of the wave or it is the distance traveled by the wave in one second. It has units of wave velocity m/s. We know that,   Velocity = Distance traveled/Time taken.   In other words: Velocity of a wave = Frequency × Wavelength. Phase of a wave is nothing but all points on a wave, which have the same state of vibration, are said to be in phase with each other.
    • Energy and Intensity of a wave: Every wave motion has energy associated with it. As waves travel through a medium, the energy is transferred as vibrational energy from particle to particle of the medium. For a sinusoidal wave of frequency of frequency f, the particles in the medium move in simple harmonic motion as a wave passes. So each particle has an Energy E = ½ k A2 , Where, A is the amplitude of the motion, either transversely or longitudinally and k is the force constant of the medium.

      The intensity I of a wave is defined as the power (energy per unit time) transported across unit area perpendicular to the direction of energy flow.   I = (Energy) / (Time* Area) = Power/Area.   Since the energy is proportional to the square of the wave amplitude , so too is the wave intensity.
    • Transmission and Reflection of a wave: The transmission of a wave can occur in two different conditions between two different media:
      (a) Transmission of a wave Across a Boundary from Less to More Denser medium (b) Transmission of a wave Across a Boundary from More to Less Denser medium.

      • Transmission of a wave Across a Boundary from Less to More Denser medium: At the boundary, A portion of the energy carried by the incident wave is reflected and returns towards the left end of the thin string. The wave that returns to the left after bouncing off the boundary is known as the reflected wave . A portion of the energy carried by the incident wave is transmitted into the thick string. The disturbance that continues moving to the right is known as the transmitted wave. The reflected wave will be found to be inverted in this kind of case.
      • Transmission of a wave Across a Boundary from More to Less Denser medium: The reflected wave in this situation will not be inverted. Similarly, the transmitted wave is not inverted (as is always the case). Since the incident wave is in a heavier medium, when it reaches the boundary, the first particle of the less dense medium does not have sufficient mass to overpower the last particle of the more dense medium. The result is that an upward displaced wave incident towards the boundary will reflect as an upward displaced wave. In this case, The transmitted wave (in the less dense medium) travels faster than the reflected wave (in the more dense medium) and has a larger wavelength than the reflected wave. The speed and the wavelength of the reflected wave are the same as the speed and the wavelength of the incident wave.
    • Interference: It is a phenomenon in which two waves superimpose to form a resultant wave of greater or lower amplitude. Interference usually refers to the interaction of waves that are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency. Interference effects can be observed with all types of waves.

      There are two types of Interference:

      (a) Constructive Interference.
      (b) Destructive Interference.


      (a) Constructive Interference: If a crest of a wave meets a crest of another wave of the same frequency at the same point, then the magnitude of the displacement is the sum of the individual magnitudes - this is constructive interference.
      (b) Destructive Interference: If a crest of one wave meets a trough of another wave then the magnitude of the displacements is equal to the difference in the individual magnitudes - this is known as destructive interference.
    • Phase is used to describe the relative positions of the crests and troughs. When the crests and troughs are aligned , for constructive interference, the two waves are said to be in phase. At points where destructive interference occurs, the waves are said to be completely out of phase.
    • Standing Waves: It is a wave that remains in a constant position. Two opposing waves combine to form a standing wave. This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions. There is no propagation of disturbance. The crests and troughs, or compressions and rarefactions, appear and disappear at the same place. All particles of the medium perform simple harmonic motion with the same period. The amplitude, of each individual particle is constant, varying from zero at the node to the maximum at the antinode.
key formulae
  • Speed of EM waves in air/vacuum = 3 × 108 m/s
  • Time period (T) of a wave is related to its frequency (f) by
    T = 1/f
  • The velocity of a wave,
    ν = f λ = λ/T
    where 'λ' is the wavelength.
  • For most mechanical waves,
    where
    F = restoring force of the string
    μ = mass per unit length
  • Intensity of a spherical wave,
  • Relation between energy carried by a wave, its amplitude (A) and frequency (f)
    I = 2 π 2 ρ V f 2 A2
    where
    ρ = density
    V = volume of slice of medium (S.l)
  • The frequency of a harmonic

    where
    l = length of the string
    λ = wavelength
    p = segments of the string
    ν = velocity
  • The fundamental frequency (or first harmonic) is given by

    where
    T = Tension in the string
    m = Linear density
    l = Length of the string
  • Laws of vibrating strings :
    • First law : f l = constant
    • Second law : f /√T = constant
    • Third law : f /√m = constant