Wave Equation
Physics ⇒ Waves and Sound
Wave Equation starts at 9 and continues till grade 12.
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See sample questions for grade 11
Derive the relationship between wave speed, frequency, and wavelength.
Describe the difference between a traveling wave and a standing wave in terms of the wave equation.
Explain why the wave equation is called a 'partial' differential equation.
If the displacement of a wave is given by y(x, t) = A sin(kx - ωt), what does the parameter k represent?
A sound wave travels at 340 m/s in air. If its frequency is 1700 Hz, what is its wavelength?
A string of length 2 m is fixed at both ends and vibrates in its fundamental mode. If the speed of the wave on the string is 100 m/s, what is the frequency of the fundamental mode?
A wave has a frequency of 500 Hz and a wavelength of 0.6 m. Calculate its speed.
A wave has a period of 0.01 s. What is its frequency?
Which of the following best describes a transverse wave?
(1) The particles of the medium move parallel to the direction of wave propagation.
(2) The particles of the medium move perpendicular to the direction of wave propagation.
(3) The particles do not move at all.
(4) The wave does not transfer energy.
Which of the following best describes the principle of superposition as it applies to the wave equation?
(1) The sum of two solutions is also a solution.
(2) Only one solution can exist at a time.
(3) The wave equation is non-linear.
(4) The amplitude of a wave cannot change.
Which of the following is a necessary condition for a function y(x, t) to be a solution to the wave equation?
(1) It must be linear in x and t.
(2) It must be twice differentiable with respect to x and t.
(3) It must be periodic in x.
(4) It must have constant amplitude.
Which of the following is NOT a solution to the one-dimensional wave equation?
(1) y(x, t) = sin(x - vt)
(2) y(x, t) = cos(x + vt)
(3) y(x, t) = x² + t²
(4) y(x, t) = e^{i(kx - ωt)}
Fill in the blank: The general solution to the wave equation can be written as y(x, t) = f(x - vt) + g(x + vt), where f and g are ______ functions.
Fill in the blank: The quantity ω in the wave equation y(x, t) = A sin(kx - ωt) is called the ______.
Fill in the blank: The term 'homogeneous' in the context of the wave equation means that the equation has ______ on the right-hand side.
Fill in the blank: The wave equation is satisfied by any function of the form f(x ± vt), where v is the ______ of the wave.
True or False: The general solution to the wave equation can represent both traveling and standing waves.
True or False: The wave equation applies only to mechanical waves and not to electromagnetic waves.
True or False: The wave equation can be derived from Newton's laws for a vibrating string.
True or False: The wave equation can be used to describe both longitudinal and transverse waves.
