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Questions and Answers
The effect of attaining maximum amplitude is called ______.
The effect of attaining maximum amplitude is called ______.
resonance
Standing waves are only set up at ______ frequency.
Standing waves are only set up at ______ frequency.
resonance
The fundamental frequency is denoted as ______.
The fundamental frequency is denoted as ______.
f0
If you push the swing at random frequency, the swing bounces around and reaches no great ______.
If you push the swing at random frequency, the swing bounces around and reaches no great ______.
The simplest of the harmonics is called the fundamental or first ______.
The simplest of the harmonics is called the fundamental or first ______.
The relationship between length of the string and wavelength is given by the equation L = n______.
The relationship between length of the string and wavelength is given by the equation L = n______.
When external driving frequency is near natural frequency, the ______ becomes large.
When external driving frequency is near natural frequency, the ______ becomes large.
These set of all possible standing waves are known as the ______ of a system.
These set of all possible standing waves are known as the ______ of a system.
The speed of light, denoted as ______, is approximately 3 x 10^8 m/s.
The speed of light, denoted as ______, is approximately 3 x 10^8 m/s.
Electromagnetic waves consist of travelling electric and magnetic fields that are at right angles to each other and to the direction of ______.
Electromagnetic waves consist of travelling electric and magnetic fields that are at right angles to each other and to the direction of ______.
The range of all types of electromagnetic radiation is known as the electromagnetic ______.
The range of all types of electromagnetic radiation is known as the electromagnetic ______.
Waves with a very short wavelength have ______ frequency and high energy.
Waves with a very short wavelength have ______ frequency and high energy.
Electromagnetic waves are ______ in nature since oscillating electric and magnetic fields are perpendicular to the direction of propagation.
Electromagnetic waves are ______ in nature since oscillating electric and magnetic fields are perpendicular to the direction of propagation.
The equation v = fλ relates the speed of light, frequency, and ______.
The equation v = fλ relates the speed of light, frequency, and ______.
Electromagnetic waves travel through a vacuum (space) at the speed of ______.
Electromagnetic waves travel through a vacuum (space) at the speed of ______.
The phrase 'Roman Men Invented Very Unusual X-ray Guns' helps to remember the order of the electromagnetic ______.
The phrase 'Roman Men Invented Very Unusual X-ray Guns' helps to remember the order of the electromagnetic ______.
The speed of a transverse wave in a string is given by v = √[𝜇 / 𝛽], where 𝛽 is the ______.
The speed of a transverse wave in a string is given by v = √[𝜇 / 𝛽], where 𝛽 is the ______.
The speed of a longitudinal wave in a medium (e.g., liquid/air) is given by v = √[𝜌 / 𝜎], where 𝜌 is the ______.
The speed of a longitudinal wave in a medium (e.g., liquid/air) is given by v = √[𝜌 / 𝜎], where 𝜌 is the ______.
The speed of a longitudinal wave in a medium (e.g., solid bar) is given by v = √[𝐸 / 𝜌], where 𝐸 is the ______.
The speed of a longitudinal wave in a medium (e.g., solid bar) is given by v = √[𝐸 / 𝜌], where 𝐸 is the ______.
There are three types of progressive waves: Mechanical Waves, ______ Waves, and Matter Waves.
There are three types of progressive waves: Mechanical Waves, ______ Waves, and Matter Waves.
Mechanical waves require a material medium (e.g., air, liquid, solid) for their ______.
Mechanical waves require a material medium (e.g., air, liquid, solid) for their ______.
The wave function of a travelling wave in a positive direction can be expressed as y(x, t) = A sin(kx - ______t).
The wave function of a travelling wave in a positive direction can be expressed as y(x, t) = A sin(kx - ______t).
Sine function repeats itself when the angle is ______ radians.
Sine function repeats itself when the angle is ______ radians.
The relationship 𝑣 = 𝜔 / 𝑘 shows how the speed of a wave is related to its angular frequency (𝜔) and ______ (k).
The relationship 𝑣 = 𝜔 / 𝑘 shows how the speed of a wave is related to its angular frequency (𝜔) and ______ (k).
The relationship between wavelength, frequency and speed of light shows that as wavelength decreases, frequency ______ .
The relationship between wavelength, frequency and speed of light shows that as wavelength decreases, frequency ______ .
Energy is carried in ______ and is given by the equation E = fh.
Energy is carried in ______ and is given by the equation E = fh.
Plank's constant is valued at approximately ______ in Joules second.
Plank's constant is valued at approximately ______ in Joules second.
In space, infrared light helps to map the interstellar ______.
In space, infrared light helps to map the interstellar ______.
Infrared is used by electrical heaters and cookers for cooking ______.
Infrared is used by electrical heaters and cookers for cooking ______.
Infrared radiation (IR) can be detected by our bodies through its ______ effect on the skin.
Infrared radiation (IR) can be detected by our bodies through its ______ effect on the skin.
Radio waves are mainly used for ______ communication and television broadcasting.
Radio waves are mainly used for ______ communication and television broadcasting.
Microwaves are used for cooking because they are easily ______ by molecules in food.
Microwaves are used for cooking because they are easily ______ by molecules in food.
X-rays are used in hospitals to take an image of ______ or teeth.
X-rays are used in hospitals to take an image of ______ or teeth.
Night vision goggles are designed to capture ______ light emitted by warm objects.
Night vision goggles are designed to capture ______ light emitted by warm objects.
Gamma rays are used in the treatment and detection of ______.
Gamma rays are used in the treatment and detection of ______.
Infrared sensors are used for various applications including weather forecasting and ______ alarms.
Infrared sensors are used for various applications including weather forecasting and ______ alarms.
The sun is the main source of ultraviolet ______.
The sun is the main source of ultraviolet ______.
Ultraviolet light can cause the skin to ______ or burn.
Ultraviolet light can cause the skin to ______ or burn.
Fluorescent substances are used in energy-efficient lamps to absorb ultraviolet light and re-emit the energy as ______ light.
Fluorescent substances are used in energy-efficient lamps to absorb ultraviolet light and re-emit the energy as ______ light.
Visible light can be detected by our ______.
Visible light can be detected by our ______.
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Study Notes
Wave Speed
- The speed of a transverse wave in a string is determined by the tension (T) and the linear mass density (μ) of the string: 𝑣 = √(T/μ)
- The speed of a longitudinal wave in a medium (e.g., liquid or air) is determined by the bulk modulus (β) and the density (ρ) of the medium: 𝑣 = √(β/ρ)
- The speed of a longitudinal wave in a solid bar is determined by the elastic modulus (E) and the density (ρ) of the solid: 𝑣 = √(E/ρ)
Types of Waves
- There are three main types of progressive waves: mechanical, electromagnetic, and matter waves.
- Mechanical waves require a material medium (e.g., air, liquid, solid) for propagation.
- Electromagnetic waves can travel through both a medium and a vacuum.
- Matter waves are associated with particles like electrons, protons, and even atoms or molecules.
Mathematical Description of Travelling Waves
- The equation for a travelling wave in the positive direction is given by the wave function 𝑦(𝑥, 𝑡) = 𝐴𝑠𝑖𝑛(𝑘𝑥 − 𝜔𝑡)
- A represents the amplitude, k represents the wave number, and 𝜔 represents the angular velocity.
- The displacement, y, is the same after every wavelength, λ.
- The wave number (k) and angular velocity (ω) are related to wavelength (λ) and period (T) by: 𝑘 = 2𝜋/λ and 𝜔 = 2𝜋/T =2𝜋𝑓 (where f is frequency).
Electromagnetic Waves
- Electromagnetic waves are transverse waves consisting of oscillating electric and magnetic fields perpendicular to each other and to the direction of wave travel.
- The electromagnetic spectrum is a range of frequencies, wavelengths, and photon energies.
- Waves with shorter wavelengths have higher frequencies and higher energies.
- Waves with longer wavelengths have lower frequencies and lower energies.
- Electromagnetic waves travel through a vacuum at the speed of light (3 x 10^8 m/s).
- They exhibit interference, diffraction, and polarization, which further suggests their transverse wave nature.
- Electromagnetic waves carry energy from one place to another and can be absorbed by matter to cause heating and other effects.
Uses of Electromagnetic Waves
- Radio waves: Primarily used for television, mobile communication, and satellite communication.
- Microwaves: Used for cooking, satellite communications, and understanding the structure of galaxies and stars.
- Infrared (IR): Used for night vision goggles, thermal imaging cameras, weather forecasting, monitoring land use, assessing heat loss, intruder alarms, detecting victims of earthquakes, electrical heaters, cookers, short-range communications (like remote controls), optical fibers, and security systems.
- Visible light: Detected by our eyes and used for photography, illumination, and various other applications.
- Ultraviolet (UV): Mainly from the sun, causes tanning and burns, has bactericidal properties used for water disinfection, and serves as the energy source in fluorescent lamps.
- X-rays: Hospital imaging (bones and teeth), airport security screening.
- Gamma rays: Medicine (diagnostic imaging and cancer treatment), food and medical equipment sterilization.
Standing Waves and Resonance
- A standing wave is formed when two waves of the same frequency and amplitude travel in opposite directions and interfere.
- Resonance occurs when the external driving frequency is close to the natural frequency of a system, resulting in a large amplitude oscillation.
- The natural frequency is the frequency at which a system naturally oscillates in the absence of any driving force.
- Standing waves are only set up at resonance frequency.
- The relationship between the length of a string (L) and the wavelength (λ) for standing wave patterns is: L = nλn/2, where n = 1, 2, 3...
- The fundamental frequency (f0) is the simplest harmonic with one antinode and two nodes.
- Subsequent harmonics are the second harmonic (n=2), third harmonic (n=3), etc.
Key Relationships & Formulas
- v = fλ (wave equation)
- E = hf (energy of a photon)
- 𝑓𝑛 = 𝑛𝑓0 (harmonics)
- v = √(T/μ) (transverse wave in a string)
- v = √(β/ρ) (longitudinal wave in a medium)
- v = √(E/ρ) (longitudinal wave in a solid bar)
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