Reflection Of Waves

Shortcut methods and tricks:

• The reflection coefficient for a wave reflecting from a rigid boundary is always 1. This means that the wave is completely reflected and there is no transmission.
• The reflection coefficient for a wave reflecting from a free boundary is always -1. This means that the wave is completely reflected and its phase is shifted by 180°.
• The phase change for a wave reflecting from a rigid boundary is always 0°. This means that the wave does not change its phase when it is reflected.
• The phase change for a wave reflecting from a free boundary is always 180°. This means that the wave changes its phase by 180° when it is reflected.

Superposition Of Waves

Shortcut methods and tricks:

• The principle of superposition states that the resultant displacement at any point due to two or more waves is the algebraic sum of the individual displacements at that point. This means that the waves simply add together at each point.
• Interference is the phenomenon of superposition of two or more waves with different frequencies and amplitudes resulting in a new wave pattern. The pattern of the resulting wave depends on the frequencies and amplitudes of the individual waves.
• Constructive interference occurs when two waves with the same frequency and phase superpose. The resultant wave has an amplitude that is the sum of the amplitudes of the individual waves.
• Destructive interference occurs when two waves with the same frequency and opposite phase superpose. The resultant wave has an amplitude that is the difference between the amplitudes of the individual waves.

Standing Waves On A String And Their Frequencies

Shortcut methods and tricks:

• Standing waves are formed by the superposition of two waves of equal frequency and opposite direction traveling on a string. The waves must have the same wavelength and amplitude.
• Nodes are points on a standing wave where the displacement is zero. Antinodes are points on a standing wave where the displacement is maximum.
• The fundamental frequency is the lowest frequency at which a standing wave can be formed on a string. The fundamental frequency is equal to the frequency of the wave that is reflected from the fixed end of the string.
• Harmonics are frequencies that are multiples of the fundamental frequency. The harmonics are equal to the frequencies of the waves that are reflected from the free end of the string.
• The frequency of a standing wave on a string is given by:

$$f = \frac{v}{2L}$$

where:

• f is the frequency in Hz
• v is the speed of the wave in m/s
• L is the length of the string in m