General Physics (42104) Chapter 16: Wave Motion PDF

General Physics (42104) Chapter 16: Wave Motion Ms. Ghadeer Qawasmi, M.Sci. Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 1 ...

General Physics (42104) Chapter 16: Wave Motion Ms. Ghadeer Qawasmi, M.Sci. Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 1  CH 16: Wave Motion Introduction of Waves  A wave is a propagation of a disturbance into space.  All mechanical waves require: some source of disturbance a medium that can be disturbed some physical mechanism through which elements of the medium can influence each other  The waves must be corresponding to the propagation of a disturbance through a medium.  The central feature of wave motion: energy is transferred over a distance, but matter is not. Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 2  CH 16: Wave Motion 16.1 Propagation of a Disturbance Types of Waves Mechanical Waves Electromagnetic Waves Require a medium to disturbed Do not require a medium Longitudinal Transverse Transverse Waves Waves Waves Visible light x-rays Sound Waves Water Waves infrared rays Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 3  CH 16: Wave Motion 16.1 Propagation of a Disturbance Longitudinal waves Vs. Transverse waves  A traveling wave that causes the elements of the disturbed medium to move perpendicular to the direction of propagation is called a transverse wave.  A traveling wave that causes the elements of the medium to move parallel to the direction of propagation is called a longitudinal wave. Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 4  CH 16: Wave Motion 16.1 Propagation of a Disturbance Longitudinal waves Vs. Transverse waves Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 5  CH 16: Wave Motion 16.1 Propagation of a Disturbance Wave Function Consider a pulse traveling to the right on a long string:  The wave function y(x, t) represents the y coordinate (the transverse position) of any element located at position x at any time t: if the pulse travels to the right if the pulse travels to the left Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 6  CH 16: Wave Motion 16.1 Propagation of a Disturbance Example: A pulse moving to the right along the x-axis is represented by the wave function where x and y are measured in centimeters and t is measured in seconds. Find expressions for the wave function at t = 0, t = 1.0 s, and t = 2.0 s.  Write the wave function expression at t = 0:  Write the wave function expression at t = 1:  Write the wave function expression at t = 2: Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 7  CH 16: Wave Motion 16.2 Sinusoidal Waves Wave Characteristics Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 8  CH 16: Wave Motion 16.2 Sinusoidal Waves Wave Characteristics A wave is usually described by the following terms:  Amplitude (A): the maximum displacement of a vibrating particle in a wave from its equilibrium point.  Wavelength (λ): the wavelength is the minimum distance between any two identical points on adjacent waves (such as from crest to crest or from trough to trough). It is usually measured in cm.  Period (T): The time it takes for any of the vibrating particles in a wave to complete one cycle. It is measured in seconds per cycle.  Frequency ( f ): the number of crests (or troughs) that pass a given point in a unit time interval. So, it is the number of complete cycles per unit time (usually 1 sec). The frequency of a sinusoidal wave is related to the period by the expression: The SI unit is the hertz (Hz) or s-1  Wave velocity (v): is the displacement traveled by the wave in one second and is related to frequency and wavelength. Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 9  CH 16: Wave Motion 16.2 Sinusoidal Waves  The shorter the wavelength (λ), the higher the frequency ( f ).  Energy of the wave increases as frequency increases. Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 10  CH 16: Wave Motion 16.2 Sinusoidal Waves The amount of energy carried by a wave is related to the amplitude of the wave:  The amplitude of a transverse pulse is related to the energy which that pulse transports through the medium.  A high energy wave is characterized by a high amplitude; a low energy wave is characterized by a low amplitude. Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 11  CH 16: Wave Motion 16.2 Sinusoidal Waves The wave function for a transverse wave can be expressed by k From the wave function expression, there are 6 parameters that can be studied and calculated:  Amplitude: is a maximum value of y.   k  Phase constant ( ), can be determined from the initial conditions  The direction of the propagation; depending on the sign ( ).  Speed of a sinusoidal wave: k Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 12  CH 16: Wave Motion 16.2 Sinusoidal Waves  If the wave moves to the right with a speed v, we can express generally the wave function in the form k Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 13  CH 16: Wave Motion 16.2 Sinusoidal Waves For your information  Power of wave: The power (rate of energy transfer) transmitted by a sinusoidal wave is proportional to the square of the angular frequency and to the square of the amplitude: (where μ is the mass per unit length of the string)  Wave Intensity: the Intensity of any wave is proportional to its amplitude: Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 14  CH 16: Wave Motion 16.2 Sinusoidal Waves Example 1: A sinusoidal wave traveling in the positive x direction has an amplitude of 15.0 cm, a wavelength of 40.0 cm, and a frequency of 8.00 Hz. The vertical position of an element of the medium at t = 0 and x = 0 is also 15.0 cm, as shown in the Figure. (A) Find the wave number k, period T, angular frequency v, and speed v of the wave.  The wave number:  The period of the wave:  The angular frequency of the wave: Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 15  CH 16: Wave Motion 16.2 Sinusoidal Waves  The wave speed: (B) Determine the phase constant Φ and write a general expression for the wave function.  Imagine this wave moving to the right and maintaining its shape  Substitute A = 15.0 cm, y = 15.0 cm, x = 0, and t = 0  the wave function: Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 16  CH 16: Wave Motion 16.2 Sinusoidal Waves Example 2: A wave has a wavelength of 3.00 m. Calculate the frequency of the wave if it is (a) a sound wave (b) a light wave. Take the speed of sound as 343 m/s and the speed of light as 3 * 108 m/s.  Find the frequency of a sound wave with λ = 3.00 m: Find the frequency of a light wave with λ = 3.00 m: Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 17  CH 16: Wave Motion 16.2 Sinusoidal Waves Example 3: The displacement of a wave traveling in the positive x-direction is where x is in m and t is in s. What are the (a) frequency, (b) wavelength, and (c) speed of this wave?  The wavenumber of the wave: k 2.7 rad/m  The angular frequency of the wave: 124 rad/s  The frequency:  The wavelength: k  The speed of the wave: Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 18  CH 16: Wave Motion 16.2 Sinusoidal Waves Example 4: The wave function for a traveling wave on a taut string is (in SI units)  We compare the given equation with k  We note that sin(θ) = −sin(–θ) = sin(−θ + π)  Thus we find that k = 3π rad/m and ω = 10π rad/s (a) What are the speed and direction of travel of the wave? (b) What is the vertical position of an element of the string at t = 0, x = 0.100 m? Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 19  CH 16: Wave Motion 16.2 Sinusoidal Waves (c) What are the wavelength of the wave? (d) What are the frequency of the wave? Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 20  CH 16: Wave Motion 16.2 Sinusoidal Waves Example 5: A sinusoidal wave is traveling along a rope. The oscillator that generates the wave completes 40.0 vibrations in 30.0 s. A given crest of the wave travels 425 cm along the rope in 10.0 s. What is the wavelength of the wave?  The frequency is  The wave speed is Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 21  CH 16: Wave Motion 16.2 Sinusoidal Waves At Home A wave is modeled with the function −1 −1 Find the (a) amplitude, (b) wave number, (c) angular frequency, (d) wave speed, (e) phase shift, (f) wavelength, and (g) period of the wave. Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 22  CH 16: Wave Motion Choose the correct answer A sinusoidal wave of frequency f is traveling along a stretched string. The string is brought to rest, and a second traveling wave of frequency 2f is established on the string. The wave speed of the second wave is (a) twice that of the first wave (b) half that of the first wave (c) the same as that of the first wave (d) impossible to determine The wavelength of the second wave is (a) twice that of the first wave (b) half that of the first wave (c) the same as that of the first wave (d) impossible to determine The amplitude of the second wave is (a) twice that of the first wave (b) half that of the first wave (c) the same as that of the first wave (d) impossible to determine Ms. Ghadeer Qawasmi / General Physics (42104) / Hebron University / 2024-2025 23