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Questions and Answers
If $F(t)$ is an even periodic function, what can you say about its Fourier series?
If $F(t)$ is an even periodic function, what can you say about its Fourier series?
The Fourier series of an even function consists only of cosine terms.
Given the transverse wave equation $\psi(x, t) = 0.001\sin 2\pi(100t - x)$, determine the wavelength of the wave.
Given the transverse wave equation $\psi(x, t) = 0.001\sin 2\pi(100t - x)$, determine the wavelength of the wave.
1 meter
Given the transverse wave equation $\psi(x, t) = 0.001\sin 2\pi(100t - x)$, what is the frequency of the wave?
Given the transverse wave equation $\psi(x, t) = 0.001\sin 2\pi(100t - x)$, what is the frequency of the wave?
100 Hz
Given the transverse wave equation $\psi(x, t) = 0.001\sin 2\pi(100t - x)$, calculate the velocity of the wave.
Given the transverse wave equation $\psi(x, t) = 0.001\sin 2\pi(100t - x)$, calculate the velocity of the wave.
Given the transverse wave equation $\psi(x, t) = 0.001\sin 2\pi(100t - x)$, what is the time period of oscillation of the point $x = 0.25$?
Given the transverse wave equation $\psi(x, t) = 0.001\sin 2\pi(100t - x)$, what is the time period of oscillation of the point $x = 0.25$?
A transverse wave on a wire is described by $\psi(x, t) = 0.001\sin 2\pi(100t - x)$. Determine the velocity of the point $x = 0.25$ at time $t = 0.1$.
A transverse wave on a wire is described by $\psi(x, t) = 0.001\sin 2\pi(100t - x)$. Determine the velocity of the point $x = 0.25$ at time $t = 0.1$.
A transverse wave on a wire is described by $\psi(x, t) = 0.001\sin 2\pi(100t - x)$. Calculate the acceleration of the point $x = 0.25$ at time $t = 0.1$.
A transverse wave on a wire is described by $\psi(x, t) = 0.001\sin 2\pi(100t - x)$. Calculate the acceleration of the point $x = 0.25$ at time $t = 0.1$.
A transverse wave on a wire of linear density 0.1 kg/m is described by $\psi(x, t) = 0.001\sin 2\pi(100t - x)$. Determine the tension in the wire.
A transverse wave on a wire of linear density 0.1 kg/m is described by $\psi(x, t) = 0.001\sin 2\pi(100t - x)$. Determine the tension in the wire.
A transverse wave on a wire of linear density 0.1 kg/m is described by $\psi(x, t) = 0.001\sin 2\pi(100t - x)$. What is the characteristic impedance of the wire?
A transverse wave on a wire of linear density 0.1 kg/m is described by $\psi(x, t) = 0.001\sin 2\pi(100t - x)$. What is the characteristic impedance of the wire?
An ultrasonic plane wave in a liquid of density $\rho_0$ and bulk modulus $B$ is described by $\psi(x, t) = A\sin(kx)\cos(\omega t)$. Express the wave speed in terms of $\rho_0$ and $B$.
An ultrasonic plane wave in a liquid of density $\rho_0$ and bulk modulus $B$ is described by $\psi(x, t) = A\sin(kx)\cos(\omega t)$. Express the wave speed in terms of $\rho_0$ and $B$.
Flashcards
Wavelength
Wavelength
The distance between two successive crests or troughs of a wave.
Wave Velocity
Wave Velocity
The speed at which a wave propagates through a medium.
Frequency of a Wave
Frequency of a Wave
The number of complete oscillations per unit of time, typically measured in Hertz (Hz).
Time Period of Oscillation
Time Period of Oscillation
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Fourier Series
Fourier Series
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Tension in the Wire
Tension in the Wire
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Characteristic Impedance
Characteristic Impedance
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Study Notes
- To determine the steady state solution for F(t) = F₀cosωt.
- To determine the steady state solution for F(t) = F₀.
- To determine the steady state solution for F(t) = F₀sin²ωt.
- If F(t) is an even periodic function, its Fourier series can be described.
- Wave is on a wire of linear density 0.1 kgm⁻¹.
- The wave is described by ψ(x, t) = 0.001sin2π(100t - x).
- ψ(x, t) represents the displacement of point x at time t.
- ψ(x, t) and x are in meters, and t is in seconds.
Wave Properties to Determine
- Frequency of the wave.
- Time period of oscillation of point x = 0.25.
- Wavelength of the wave.
- Velocity of the wave.
- Velocity of the point x = 0.25 at time t = 0.1.
- Acceleration of the point x = 0.25 at time t = 0.1.
- Total external force on the string element lying between x = 0.2449 and x = 0.2501 at time t = 0.1.
- Tension in the wire.
- Characteristic impedance of the wire.
- Transverse component of the force at time t = 0.1, exerted by the transmitter on the wire at the point x = 0.
- Transverse component of the force at time t = 0.1, exerted by the wire at the point x = 0 on the transmitter.
- An ultrasonic plane wave in a liquid of density ρ₀ and bulk modulus B is described by ψ(x, t) = Asinkxcosωt.
- ψ(x, t) denotes the displacement at time t of the plane labeled by its undisturbed position x.
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