The question describes a phenomenon where two sound waves of slightly different frequencies combine, leading to a periodic variation in the loudness of the resulting sound. We need to identify the correct term for this phenomenon from the given options.
Correct Option: C) Beats is the phenomenon where two sound waves of slightly different frequencies superpose to produce a periodic variation in the loudness of the combined sound. This occurs due to constructive and destructive interference happening alternately as the phase relationship between the two waves changes over time.
This question tests the fundamental properties of waves as they propagate through different media. When a wave transitions from one medium to another, some of its characteristics change due to the change in the medium's properties, while one crucial characteristic remains constant. We need to identify this invariant characteristic.
Understand Wave Propagation: A wave is a disturbance that transfers energy without transferring matter. When a wave moves from one medium to another (e.g., light from air to water, or sound from air to a solid), the properties of the medium change, which affects how the wave propagates.
Relationship between Speed, Frequency, and Wavelength: The speed of a wave (\(v\)), its frequency (\(f\)), and its wavelength (\(\lambda\)) are related by the formula:
\[ v = f \lambda \]Analyze the Change in Medium: When a wave enters a new medium, the speed of the wave (\(v\)) generally changes because the speed of a wave is determined by the properties of the medium (e.g., density, elasticity for sound; refractive index for light).
Consequence of Speed Change: Since \(v = f \lambda\), if \(v\) changes, then either \(f\) or \(\lambda\) or both must change. However, the frequency of the wave is determined by the source that generates the wave, not by the medium through which it travels. The source dictates how many oscillations per second it produces, and this rate of oscillation remains constant as the wave passes into a new medium.
Wavelength Adjustment: Because the frequency (\(f\)) remains constant and the speed (\(v\)) changes, the wavelength (\(\lambda\)) must adjust according to the formula \(\lambda = v/f\). If the speed decreases, the wavelength decreases, and vice-versa.
B) Frequency — The frequency of a wave is determined by its source and represents the number of wave cycles passing a point per unit time. When a wave passes from one medium to another, the source continues to oscillate at the same rate, thus the frequency of the wave remains unchanged. This is a fundamental principle of wave mechanics.
The energy carried by a mechanical wave is related to its physical properties. We need to recall the formula for the energy of a wave, particularly how it depends on amplitude, frequency, and wavelength, to determine the correct proportionality.
Correct Option: C) The energy carried by a mechanical wave is directly proportional to the square of its amplitude. This is a fundamental property of wave motion, where energy is proportional to the square of the displacement (amplitude).
The question asks for the definition of the Doppler effect. We need to identify the option that accurately describes this physical phenomenon.
D) The apparent change in the observed frequency of a wave due to relative motion between the source and the observer
This option perfectly defines the Doppler effect. When a source of waves (like sound or light) moves towards an observer, the waves are compressed, leading to a higher observed frequency. Conversely, when the source moves away, the waves are stretched, resulting in a lower observed frequency. This change is only apparent to the observer; the actual frequency emitted by the source remains constant.
A) A permanent change in the actual frequency emitted by a stationary source — This is incorrect. The Doppler effect deals with an *apparent* change in frequency due to relative motion, not a *permanent* change in the actual frequency emitted by the source. The source itself emits waves at a constant frequency.
B) The splitting of white light into its constituent colours — This phenomenon is known as dispersion, typically observed when white light passes through a prism or water droplets (forming a rainbow). It is unrelated to the Doppler effect.
C) The bending of waves as they pass around an obstacle — This phenomenon is called diffraction. It describes how waves spread out when they encounter an obstacle or aperture. This is also distinct from the Doppler effect.
The question asks to identify the scientist who first explained the Doppler effect for sound waves. This is a direct knowledge-based question about the history of science.
D) Christian Doppler. Christian Doppler published his most famous work, "Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels" (On the coloured light of the binary stars and some other stars of the heavens), in 1842, where he first theoretically explained the phenomenon that now bears his name. His initial explanation was primarily for sound waves, and later extended to light waves.
This question relates to the Doppler Effect, which describes the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. When a sound source moves towards a stationary observer, the sound waves are compressed, leading to an increase in the perceived frequency.
A) Increases, so the sound appears to have a higher pitch. As explained by the Doppler Effect, when a sound source moves towards a stationary observer, the sound waves are compressed, leading to a higher apparent frequency and thus a higher perceived pitch.