Which of the following statements is correct?
The minimum distance between two points in a wave having the same phase at a particular instant of time is called the wave length.
Understanding Wave Characteristics and Properties
Waves are disturbances that transfer energy through a medium or space. They have specific properties like wavelength, frequency, and amplitude, and can be classified based on how the particles of the medium oscillate relative to the direction of wave propagation. Let's examine each statement to identify the correct one.
Analyzing the Statements on Wave Definitions
Statement 1: Transverse Wave Definition
The statement says: "If the constituents of the medium oscillate along the direction of wave propagation, we call the wave a transverse wave".
Let's define a transverse wave correctly. In a transverse wave, the particles of the medium oscillate perpendicular to the direction of wave propagation. A common example is waves on the surface of water or light waves.
Therefore, this statement is incorrect as it describes longitudinal wave behavior but calls it a transverse wave.
Statement 2: Frequency Definition
The statement says: "Frequency of a wave is the number of oscillations of each constituent particle in the vibrating medium per minute".
Frequency ($f$) is defined as the number of complete oscillations or cycles performed by a particle of the medium in one second. The standard unit for frequency is Hertz (Hz), which is equivalent to one oscillation per second ($s^{-1}$). Oscillations per minute would be $\frac{\text{Frequency in Hz}}{60}$.
Therefore, this statement is incorrect because frequency is measured per second, not per minute.
Statement 3: Longitudinal Wave Definition
The statement says: "If the constituents of the medium oscillate perpendicular to the direction of wave propagation, we call the wave a longitudinal wave."
Let's define a longitudinal wave correctly. In a longitudinal wave, the particles of the medium oscillate parallel to the direction of wave propagation. Sound waves are a prime example of longitudinal waves, where air particles compress and expand in the same direction the sound travels.
Therefore, this statement is incorrect as it describes transverse wave behavior but calls it a longitudinal wave.
Statement 4: Wavelength Definition
The statement says: "The minimum distance between two points in a wave having the same phase at a particular instant of time is called the wave length."
Wavelength ($\lambda$) is indeed defined as the distance between two consecutive points on a wave that are in the same phase. Points in the same phase could be two consecutive crests, two consecutive troughs, or any other two corresponding points on consecutive cycles of the wave that are moving in the same direction. This definition captures the minimum repeating unit of the wave's spatial pattern.
Therefore, this statement is correct.
Identifying the Correct Statement about Waves
Based on the analysis of each statement:
- Statement 1 incorrectly defines transverse waves.
- Statement 2 incorrectly states the time unit for frequency.
- Statement 3 incorrectly defines longitudinal waves.
- Statement 4 correctly defines wavelength.
Thus, the correct statement is the one defining wavelength.
| Wave Property | Correct Definition | Statement Analysis |
|---|---|---|
| Transverse Wave | Oscillation is perpendicular to wave direction. | Statement 1 is incorrect. |
| Frequency | Number of oscillations per second (Hz). | Statement 2 is incorrect (uses per minute). |
| Longitudinal Wave | Oscillation is parallel to wave direction. | Statement 3 is incorrect (uses perpendicular). |
| Wavelength ($\lambda$) | Minimum distance between points in the same phase. | Statement 4 is correct. |
Revision Table: Key Wave Definitions
| Term | Definition | Direction of Oscillation relative to Wave Propagation | Example |
|---|---|---|---|
| Transverse Wave | A wave where particles oscillate perpendicular to the direction of energy transfer. | Perpendicular | Light waves, waves on a string |
| Longitudinal Wave | A wave where particles oscillate parallel to the direction of energy transfer. | Parallel | Sound waves |
| Frequency ($f$) | Number of cycles/oscillations per second. Unit is Hertz (Hz). | N/A | Higher frequency means more oscillations per second. |
| Wavelength ($\lambda$) | The spatial period of the wave; the minimum distance between two points in phase. | N/A | Distance between consecutive crests or troughs. |
Additional Information on Wave Concepts
Beyond wavelength, frequency, transverse, and longitudinal types, waves have other important properties:
- Amplitude: The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position. It indicates the intensity or energy of the wave.
- Period (T): The time taken for one complete oscillation or cycle. It is the reciprocal of frequency ($T = 1/f$).
- Wave Speed (v): The distance a wave crest (or any point of constant phase) travels per unit time. It is related to wavelength and frequency by the equation $v = f\lambda$.
- Phase: Describes the position and direction of motion of a point on a wave. Points in the same phase are at the same relative position within their cycle and are moving in the same direction.
Understanding these basic properties is crucial for studying wave phenomena like superposition, interference, and diffraction.
Important Questions from Wave
Which one of the following statements is true for sound waves propa- gating in air?
Which one of the following optical phenomena supports that the light is a transverse wave?
Which of the following is the horizontal distance between two successive crests?
What is the correct order of radiations in descending order of frequencies?
In which year was the Doppler effect discovered by Austrian scientist Christian Doppler, that describes the change in frequency of any kind of sound or light wave produced by a moving source with respect to an observer?
