Wave Speed and Types of Waves

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Questions and Answers

The effect of attaining maximum amplitude is called ______.

resonance

Standing waves are only set up at ______ frequency.

resonance

The fundamental frequency is denoted as ______.

f0

If you push the swing at random frequency, the swing bounces around and reaches no great ______.

<p>amplitude</p> Signup and view all the answers

The simplest of the harmonics is called the fundamental or first ______.

<p>harmonic</p> Signup and view all the answers

The relationship between length of the string and wavelength is given by the equation L = n______.

<p>λ/2</p> Signup and view all the answers

When external driving frequency is near natural frequency, the ______ becomes large.

<p>amplitude</p> Signup and view all the answers

These set of all possible standing waves are known as the ______ of a system.

<p>harmonics</p> Signup and view all the answers

The speed of light, denoted as ______, is approximately 3 x 10^8 m/s.

<p>v</p> Signup and view all the answers

Electromagnetic waves consist of travelling electric and magnetic fields that are at right angles to each other and to the direction of ______.

<p>travel</p> Signup and view all the answers

The range of all types of electromagnetic radiation is known as the electromagnetic ______.

<p>spectrum</p> Signup and view all the answers

Waves with a very short wavelength have ______ frequency and high energy.

<p>high</p> Signup and view all the answers

Electromagnetic waves are ______ in nature since oscillating electric and magnetic fields are perpendicular to the direction of propagation.

<p>transverse</p> Signup and view all the answers

The equation v = fλ relates the speed of light, frequency, and ______.

<p>wavelength</p> Signup and view all the answers

Electromagnetic waves travel through a vacuum (space) at the speed of ______.

<p>light</p> Signup and view all the answers

The phrase 'Roman Men Invented Very Unusual X-ray Guns' helps to remember the order of the electromagnetic ______.

<p>spectrum</p> Signup and view all the answers

The speed of a transverse wave in a string is given by v = √[𝜇 / 𝛽], where 𝛽 is the ______.

<p>Bulk Modulus</p> Signup and view all the answers

The speed of a longitudinal wave in a medium (e.g., liquid/air) is given by v = √[𝜌 / 𝜎], where 𝜌 is the ______.

<p>Density</p> Signup and view all the answers

The speed of a longitudinal wave in a medium (e.g., solid bar) is given by v = √[𝐸 / 𝜌], where 𝐸 is the ______.

<p>Elastic Modulus</p> Signup and view all the answers

There are three types of progressive waves: Mechanical Waves, ______ Waves, and Matter Waves.

<p>Electromagnetic</p> Signup and view all the answers

Mechanical waves require a material medium (e.g., air, liquid, solid) for their ______.

<p>propagation</p> Signup and view all the answers

The wave function of a travelling wave in a positive direction can be expressed as y(x, t) = A sin(kx - ______t).

<p>ω</p> Signup and view all the answers

Sine function repeats itself when the angle is ______ radians.

<p>2π</p> Signup and view all the answers

The relationship 𝑣 = 𝜔 / 𝑘 shows how the speed of a wave is related to its angular frequency (𝜔) and ______ (k).

<p>wave number</p> Signup and view all the answers

The relationship between wavelength, frequency and speed of light shows that as wavelength decreases, frequency ______ .

<p>increases</p> Signup and view all the answers

Energy is carried in ______ and is given by the equation E = fh.

<p>photons</p> Signup and view all the answers

Plank's constant is valued at approximately ______ in Joules second.

<p>6.6 × 10−34</p> Signup and view all the answers

In space, infrared light helps to map the interstellar ______.

<p>dust</p> Signup and view all the answers

Infrared is used by electrical heaters and cookers for cooking ______.

<p>food</p> Signup and view all the answers

Infrared radiation (IR) can be detected by our bodies through its ______ effect on the skin.

<p>heating</p> Signup and view all the answers

Radio waves are mainly used for ______ communication and television broadcasting.

<p>TV/mobile</p> Signup and view all the answers

Microwaves are used for cooking because they are easily ______ by molecules in food.

<p>absorbed</p> Signup and view all the answers

X-rays are used in hospitals to take an image of ______ or teeth.

<p>bone</p> Signup and view all the answers

Night vision goggles are designed to capture ______ light emitted by warm objects.

<p>infrared</p> Signup and view all the answers

Gamma rays are used in the treatment and detection of ______.

<p>cancer</p> Signup and view all the answers

Infrared sensors are used for various applications including weather forecasting and ______ alarms.

<p>intruder</p> Signup and view all the answers

The sun is the main source of ultraviolet ______.

<p>radiation</p> Signup and view all the answers

Ultraviolet light can cause the skin to ______ or burn.

<p>tan</p> Signup and view all the answers

Fluorescent substances are used in energy-efficient lamps to absorb ultraviolet light and re-emit the energy as ______ light.

<p>visible</p> Signup and view all the answers

Visible light can be detected by our ______.

<p>eyes</p> Signup and view all the answers

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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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