29 Questions
Which type of waves require a material medium to exist?
Mechanical waves
What is the speed of all electromagnetic waves when traveling through a vacuum?
$3 \times 10^8$ m/s
Which type of waves are commonly used in modern technology and probably unfamiliar to most people?
Matter waves
Which type of waves do not require a material medium to exist?
Electromagnetic waves
Which waves are governed by Newton's laws?
Mechanical waves
What is a common example of a matter wave according to the text?
Light wave
What type of waves are associated with electrons, protons, atoms, and molecules?
Matter waves
In a transverse wave, how does a typical string element move as the pulse passes?
Moves up and down continuously
How would you describe the displacement of oscillating string elements in a transverse wave?
Perpendicular to the wave's direction of travel
What type of wave is set up in an air-filled pipe by moving a piston back and forth?
Longitudinal wave
Which waves are described as traveling waves in the text?
Both transverse and longitudinal waves
What determines how fast a wave can travel on a string?
Mass and elasticity
What is the average power of a sinusoidal wave on a stretched string dependent on?
Linear density, wave speed, angular frequency, and amplitude
What does the principle of superposition for waves state?
The displacement of a particle is the sum of the displacements from individual waves.
In interference of waves, what happens when two sinusoidal waves on the same string overlap?
They add or cancel out based on the principle of superposition.
What quantities are involved in determining the speed of a wave on a string?
Tension and linear density
What type of energy is transported by a wave as it moves along a string?
Kinetic energy and elastic potential energy
What type of waves are governed by Newton's laws?
Transverse mechanical waves
How are transverse mechanical waves characterized?
Particles oscillate perpendicular to the wave's direction of travel
In describing a wave on a string, what is needed to give the shape of the wave?
A function that relates transverse displacement to time and position
What mathematical form represents a sinusoidal wave moving in the positive direction of an x-axis?
$ym \sin(kx - \omega t)$
What does the frequency of a wave represent?
Number of occurrences of a repeating event per unit of time
Which function can be used to describe a sinusoidal shape like a wave on a string?
Both sine and cosine functions
What is the relationship between the displacement of two waves traveling alone and their displacement when they overlap?
They algebraically add to each other.
If two identical sinusoidal waves interfere with a phase difference φ of π rad or 180°, what kind of resultant wave is produced?
A completely canceled wave
What phase difference between two interfering waves results in a net wave that is what is actually observed on the string?
0 rad or 0°
What effect do two sinusoidal waves of the same amplitude and wavelength traveling in the same direction have when they interfere?
They generate a resultant sinusoidal wave.
If a string has a linear density of 0.7 kg/m and is under 80 N of tension, what is the angular frequency of a sinusoidal wave if the average power is 30W and the amplitude is 0.18 m?
$2\pi$ rad/s
In the context of waves on a string, what happens when two waves overlap?
They produce a resultant wave.
Study Notes
Types of Waves
- Matter waves are associated with electrons, protons, and other fundamental particles, and even atoms and molecules.
- Mechanical waves are common examples of waves, including water waves, sound waves, and seismic waves.
- Electromagnetic waves are less familiar, but include visible and ultraviolet light, radio and television waves, microwaves, x-rays, and radar waves.
- Electromagnetic waves require no material medium to exist and travel through a vacuum at the same speed c = 3x10^8 m/s.
Transverse Waves and Longitudinal Waves
- A transverse wave is a wave in which the particles of the medium oscillate perpendicular to the wave's direction of travel.
- A longitudinal wave is a wave in which the particles of the medium oscillate parallel to the wave's direction of travel.
- Examples of transverse waves include a single pulse sent along a stretched string, and a sinusoidal wave sent along a string.
- Examples of longitudinal waves include a sound wave set up in an air-filled pipe by moving a piston back and forth.
Wave Speed on a Stretched String
- The speed of a wave on a string with tension τ and linear density μ is determined by the wave's velocity equation.
- The velocity equation is: v = √(τ/μ)
Power of a Wave Traveling Along a String
- The average power of a wave traveling along a string is: Pavg = (1/2)μvω^2y_m^2
- Where: Pavg is the power (Watt), μ is the linear density (kg/m), v is the speed of the wave (m/s), ω is the angular frequency (rad/s), and y_m is the amplitude (magnitude of the maximum displacement) of the wave (m).
Interference of Waves
- When two or more waves traverse the same medium, the displacement of any particle of the medium is the sum of the displacements that the individual waves would give it, an effect known as the principle of superposition for waves.
- The principle of superposition states that the resultant disturbance is equal to the algebraic sum of the individual disturbances.
- When two waves overlap, the displacement of the string is the algebraic sum of the individual displacements: y(x, t) = y1(x, t) + y2(x, t)
- Interference can result in either constructive or destructive interference, depending on the phase difference between the two waves.
This quiz covers the basics of waves, including types of waves, wave speed on a stretched string, power of a wave traveling along a string, and interference of waves. It is based on the lecture by Dr. Suhail Alshahrani for BMT 201 at King Saud University, College of Applied Medical Sciences.
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