Physics lo6
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A standing wave is composed of two harmonic waves of equal amplitude, wavelength, and frequency that move in opposite directions. Nodes occur where the amplitude is zero and do not move. Antinodes occur at points of maximum amplitude. For a standing wave with wavelengths of 0.80m and frequencies of 95Hz, the equation is D(x,t) = 6sin(7.85x)cos(596.9t). The nodes occur at 0m, 0.40m, and 0.80m, and the antinodes occur at 0.20m, 0.60m, and 1.0m. The amplitude at any point x is given by A(x)=6sin(7.
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Standing waves occur when two waves of equal wavelength, frequency, and amplitude traveling in opposite directions interfere. The points of no displacement are called nodes, and the points of maximum displacement are called antinodes. A standing wave can be described by the equation D(x,t) = A(x)cos(ωt), where A(x) is the position-dependent amplitude. The distance between nodes and antinodes is λ/2, where λ is the wavelength. Standing waves are confined to a given space and do not transport energy like traveling waves.
Standing waves
Standing waves are harmonic waves with equal amplitude, wavelength, and frequency that are moving in opposite directions. Nodes are points where the amplitude is zero, while antinodes are points where the amplitude is at a maximum. For a standing wave pattern in a water pipe, if there are 4 nodes and 4 antinodes, and the sound wave speed is 300m/s and frequency is 250Hz, the length of the pipe can be calculated using the relationship that the distance between nodes or antinodes is one quarter of the wavelength.
Standing waves
Standing waves are harmonic waves with equal amplitude, wavelength, and frequency that are moving in opposite directions. They have a phase constant of 0. Standing waves have nodes where the amplitude is 0 and antinodes where the amplitude is at a maximum of 2A. The distance between nodes is half the wavelength, as is the distance between antinodes. An example problem calculates the length of a water pipe with a standing wave pattern by determining the wavelength from the given frequency and speed, and using the node and antinode spacing to relate the length to the wavelength.
Standing Waves on a String
This document discusses standing waves on strings. It explains that when a string with fixed ends is plucked, waves travel back and forth along the string creating standing waves. The allowed wavelengths are λ=2L/m, where L is the string length and m is a positive integer. These standing waves are called the normal modes of vibration, and their frequencies are given by fm=mf1, where f1 is the fundamental frequency. The document provides an example problem involving calculating the wave speed, number of reflections, wavelengths, frequencies, and node spacing for the first two normal modes of a plucked guitar string.
PHYSICS MAHARASHTRA STATE BOARD CHAPTER 6 - SUPERPOSITION OF WAVES EXERCISE S...
The document discusses superposition of waves and properties of progressive and stationary waves. It provides explanations and derivations of key concepts related to wave interference and standing waves. Specifically, it defines progressive and stationary waves, derives the equation for a stationary wave on a stretched string, and shows that only odd harmonics are present in an air column vibrating in a pipe closed at one end.
Learning objects 1
The document provides the wave function for a harmonic wave traveling in the negative x-direction with a velocity of 2 m/s, period of 1 Hz, and amplitude of 1 m. The wave function is D(x, t)=sin((pi)x+(2pi)t+pi/2), where the phase constant pi/2 is determined using the information that the displacement at t=0 when x=0 is 1 m.
Chapter 3 wave_optics
The document discusses wave optics and electromagnetic waves. It defines key concepts like wavefronts, which connect points of equal phase, and rays, which describe the direction of wave propagation perpendicular to wavefronts. It explains Huygens' principle, which states that each point on a wavefront acts as a secondary source of spherical wavelets to determine the new wavefront position. The principle of superposition states that multiple waves add linearly at each point in space to determine the resulting disturbance. Interference occurs when waves are out of phase and their amplitudes diminish or vanish.
15Waves ppt 1.pdf
This document discusses different types of mechanical waves and their properties. It defines mechanical waves as oscillations that transfer energy through a medium. Key points include:
- Mechanical waves can be transverse (perpendicular to direction of travel) or longitudinal (parallel to direction of travel).
- They transport energy through the medium and require a medium, like air or water, to propagate.
- Examples of mechanical waves include water waves, sound waves, and waves on a string or rope.
- Harmonic waves have a sinusoidal shape described by a mathematical function involving amplitude, wavelength, frequency, and phase.
Harmonic waves
A harmonic wave is a sinusoidal wave that undergoes simple harmonic motion. It has a smooth, repetitive oscillation described by a sine function. The key characteristics of a harmonic wave are its amplitude, wavelength, period, frequency, and phase shift. The speed of a harmonic wave can be calculated by multiplying its wavelength by its frequency. An increase in frequency would cause the velocity of a harmonic wave to increase as well, since these factors are directly correlated.
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Physics lo6
- 1. Standing Waves By: Priya Suresh
- 2. Let’s Start With A Definition… What is a standing wave? A standing wave is composed of 2 harmonic waves with EQUAL amplitude, wavelength, and frequency but the waves move in OPPOSITE directions *for simplicity we may assume that the phase constants are 0 for both waves
- 3. Some Other Key Terms… NODE: points on the wave that have zero amplitude and remain at rest ANTINODE: points on the wave that have maximum amplitude *since nodes do not move, energy is conserved in a standing wave
- 4. Amplitude Of A Standing Wave The amplitude of the wave at a specific point can be described with the following equation A(x) = 2Asin(kx) = 2Asin(2π*x/λ) Antinodes have maximum amplitude at 2A Nodes have zero amplitude All other points have amplitude between 0 and 2A
- 5. Equation For Position Of Wave As A Function of Time D(x,t) D(x,t) = 2Asin(kx)cos(ωt) Or another form is… D(x,t) = A(x)cos(ωt)
- 6. Nodes And Antinodes Nodes occur at x= …-λ,-λ/2, 0, λ/2, λ… Antinodes occur at x=…-3λ/4, -λ/4, λ/4, 3λ/4… The distance between 2 consecutive nodes/antinodes is λ/2 An antinode is λ/4 apart from a node Speed of a wave is greatest at antinodes Speed of a wave is zero at nodes
- 7. Now Lets Use What We Know To A Solve A Problem Two sinusoidal waves with wavelengths 0.80m, amplitudes 3.0m and frequencies 95Hz are moving in opposite directions to produce a standing wave. (Assume the phase constants are 0). a) Determine the equation of the standing wave. b) If the wave starts at x=0, at what values of x will there be nodes? (Give the first 3 locations) c) At what values of x will there be antinodes? (Give the first 3 locations) d) Determine the equation to find the amplitude at a given x value e) What is the amplitude at x=5
- 8. Solving The Problem Step by Step a) The equation for a standing wave is D(x,t) = 2Asin(kx)cos(ωt) k = 2π/λ= 2π/0.80 = 7.85 rad/m ω = 2πf = 2π(95) = 596.90 rad/s A = 3 2A = 6m Therefore the equation is… D(x,t) = 6sin(7.85x)cos(596.9t)
- 9. b) The first 3 nodes occur at x=0, λ/2, λ x=0m, x=0.80/2=0.40m x=0.80m Therefore the nodes occur at: 0m, 0.40m, 0.80m c) The first 3 antinodes occur at x= λ/4, 3λ/4, 5λ/4 x=0.80/4=0.20m x=3(0.80)/4=0.60m x=5(0.80)/4=1.0m Therefore the antinodes occur at: 0.20m, 0.40m, 1.0m
- 10. d) The equation to determine the amplitude is: A(x) = 2Asin(kx) A= 3.0m k= 7.85rad/m Therefore the amplitude is given by… A(x)= 6sin(7.85x) e) At x=5 the amplitude is… A(5)= 6sin(7.85*5) =5.99m
- 11. Thank You