Unit 7: Waves and Vibrations — Short Questions

Interference occurs when two or more waves meet. The conditions are:
i. The waves must be coherent (same frequency and constant phase difference)
ii. The waves should have similar amplitudes for noticeable interference
iii. The waves must travel in the same medium and overlap spatially

Constructive Interference Occurs when crests of one wave align with crests of another (or troughs with troughs). This results in increased amplitude (e.g., louder sound or brighter light).
Destructive Interference: Occurs when crests of one wave align with troughs of another. This causes reduced or zero amplitude (e.g., silence in sound or darkness in light).
The path difference for constructive interference of two waves is ΔS = nλ
Where n = 0, ± 1, ± 2 ....
The path difference for destructive interference for two waves is ΔS = (2n + 1)λ/2
Where n = 0, ± 1, ± 2 ....

Coherent waves have the same frequency and a constant phase difference. Coherent sources emit such waves. Examples include two lasers producing light of the same frequency and two speakers connected to the same audio source.

In longitudinal waves, vibrations of particles of medium are parallel to the wave direction, like sound waves in air. In transverse waves, vibrations of particles of medium are perpendicular to the wave direction, like light waves or waves on a string.

No, stationary waves require two identical waves traveling in opposite directions to interfere. If waves move in the same direction, they produce a traveling wave with increased amplitude but not a stationary wave (which has modes and antinodes).

The Doppler effect is used in ultrasound imaging to detect changes in frequency of sound waves reflected from moving blood cells. This helps measure blood flow speed and detect heart valve problems, aiding diagnosis.

Diffraction is the bending of waves around obstacles or through small openings. A ripple tank is used to visually demonstrate wave properties like diffraction, interference, and reflection using water waves.

The waves which don't require any medium for their propagation are known as E.M waves.

The waves which require medium for their propagation are known as mechanical waves.

It is the energy transmitted by the wave per second per unit area. Its S.I unit is wm⁻²

The path difference should be an integral multiple of full wavelength.

The path difference should be an odd integral multiple of half wavelength i.e
Path difference = λ/2 + 3λ/2 + 5λ/2 + (m + 1/2)λ

The points in stationary waves at which amplitude is zero.

The points in stationary waves at which amplitude is maximum.

As f₁ = 4f, so, f₁ = 120/4 = 30Hz

(i) It is used to determine the unknown frequency
(ii) It is used for tuning the musical instruments.
(iii) It is used to produce a variety of tones in music

In open organ pipe, the node is at the center but in closed organ pipe, the node is at closed end and antinode at open end.

Doppler's effect can be used for monitoring blood pressure by directing the beam of ultra sound towards the main arteries and the frequency of scattered beam is detected with the help of receiver. By measuring Doppler shift in the frequency of scattered ultra sound the velocity of the blood can be measured.

Two or more sources of light will behave as coherent sources when they emit light waves of same amplitude, same frequency or wavelength, having the same phase or constant phase difference e.g. laser light and light passing through closely spaced slits (young's double slit experiment).

The most important measurement for determining a wave's intensity is its amplitude. Intensity is directly proportional to the square of the amplitude;
Mathematically: (I ∝ A²)
A larger amplitude means higher intensity. This applies to all types of waves, including sound and light.

Yes, the Doppler effect applies to light waves. When a light source moves toward an observer, its wavelength appears shorter (blue shift). If it moves away, the wavelength appears longer (red shift). This phenomenon is used in astronomy to determine the motion of stars and galaxies.

In a longitudinal wave, compressions are regions where particles are close together, and rarefactions are where they are far apart. In a transverse wave, peaks (crests) are the highest points, and troughs are the lowest points. Both sets represent maximum and minimum values of the wave's disturbance.

The source and observer must have no relative motion. Examples:
i. Both are stationary.
ii. Both move at the same speed and direction. In such cases, the Doppler effect does not occur, so the observed frequency remains unchanged.

When the frequency difference exceeds 10 Hz, the beats occur too rapidly for the human ear to distinguish them as separate pulses. Instead of hearing slow beats, we hear a rough or continuous sound. For example, tuning two guitar strings with a difference of more than 10 Hz produces a harsh sound, not clear beats.

See Q.5 and 6 of theory.

See Q.8 of theory.

See Q.10 of theory.

See Q.12 of theory.

See Q.13 of theory.

See Q.4 and 14 of theory.

See Q.15 of theory.