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Define amplitude, frequency, period, wavelength, and velocity of a wave; Relate wave frequency, period, wavelength, and velocity; Solve problems involving wave properties
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13.2 Wave Properties: Speed, Amplitude, Frequency, and...
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13.2 Wave Properties: Speed, Amplitude, Frequency, and...
- 17.1 Understanding Diffraction and Interference
Begin with the equation of the time-averaged power of a sinusoidal wave on a string: P = 1 2μA2ω2v. The amplitude is given, so we need to calculate the linear mass density of the string, the angular frequency of the wave on the string, and the speed of the wave on the string.
The above equation is known as the wave equation. It states the mathematical relationship between the speed (v) of a wave and its wavelength (λ) and frequency (f). Using the symbols v, λ, and f, the equation can be rewritten as. v = f • λ.
If the velocity of the sinusoidal wave is constant, the time for one wavelength to pass by a point is equal to the period of the wave, which is also constant. For a sinusoidal mechanical wave, the time-averaged power is therefore the energy associated with a wavelength divided by the period of the wave.
The period describes the time it takes for a particle to complete one cycle of vibration. The frequency describes how often particles vibration - i.e., the number of complete vibrations per second. These two quantities - frequency and period - are mathematical reciprocals of one another.
To find the amplitude, wavelength, period, and frequency of a sinusoidal wave, write down the wave function in the form \(y(x, t)=A \sin (k x-\omega t+\phi)\). The amplitude can be read straight from the equation and is equal to \(A\). The period of the wave can be derived from the angular frequency \( \left(T=\frac{2 \pi}{\omega}\right)\).
9 paź 2024 · The frequency calculator will let you find a wave's frequency given its period or its wavelength and velocity in no time. You can choose a wave velocity from the preset list, so you don't have to remember.
