Mathematical Representation of Harmonic Waves
Physics ⇒ Waves and Sound
Mathematical Representation of Harmonic Waves starts at 10 and continues till grade 12.
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A wave is given by y(x,t) = 0.5 cos(2x + 4t). What is the direction of propagation of the wave?
If the amplitude of a wave is doubled, what happens to the maximum displacement of the particles?
If the frequency of a wave is doubled, what happens to its period?
If the phase constant φ in a wave equation is zero, what is the initial displacement of the particle at x = 0 and t = 0?
The mathematical representation of a harmonic wave is an example of which type of function? (1) Linear, (2) Exponential, (3) Trigonometric, (4) Logarithmic
Which of the following best describes the physical meaning of the wave number k in the harmonic wave equation? (1) Number of waves per second, (2) Number of waves per meter, (3) Number of meters per wave, (4) Number of seconds per wave
Which of the following equations represents a harmonic wave traveling in the negative x-direction? (1) y(x,t) = A sin(kx - ωt), (2) y(x,t) = A sin(kx + ωt), (3) y(x,t) = A sin(-kx + ωt), (4) y(x,t) = A sin(-kx - ωt)
Which of the following is a correct expression for the displacement of a harmonic wave at position x and time t? (1) y(x,t) = A sin(kx + ωt), (2) y(x,t) = A sin(kx - ωt), (3) y(x,t) = A sin(kx), (4) y(x,t) = A sin(ωt)
Which of the following is NOT a parameter in the mathematical representation of a harmonic wave? (1) Amplitude, (2) Wavelength, (3) Mass, (4) Frequency
Which of the following is the correct SI unit for wave number k? (1) m, (2) m-1, (3) s, (4) s-1
Which of the following quantities does NOT affect the speed of a harmonic wave on a string? (1) Tension in the string, (2) Mass per unit length, (3) Amplitude, (4) Frequency
Which of the following statements is true about the amplitude of a harmonic wave? (1) It determines the speed of the wave, (2) It determines the maximum displacement from equilibrium, (3) It determines the wavelength, (4) It determines the frequency
The displacement of a particle in a wave is maximum when the phase (kx - ωt + φ) is equal to _______.
The frequency f of a harmonic wave is related to its period T by the equation f = _______.
The phase constant in the wave equation y(x,t) = A sin(kx - ωt + φ) is represented by _______.
The phase difference between two points separated by a distance d in a harmonic wave is given by _______.
True or False: The angular frequency ω is related to the period T by the equation ω = 2π/T.
True or False: The mathematical representation of a harmonic wave assumes that the medium is perfectly elastic and non-dissipative.
True or False: The mathematical representation of a harmonic wave can be used to describe both transverse and longitudinal waves.
True or False: The mathematical representation of a harmonic wave can be written using either sine or cosine functions.
