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
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?
A wave is described by the equation y(x, t) = 0.05 sin(4πx - 200πt), where x is in meters and t in seconds. What is the speed of the wave?
A wave is described by y(x, t) = 0.1 cos(2πx - 6πt). What is its frequency?
A wave on a string is given by y(x, t) = 0.2 sin(5x - 20t). What is the amplitude of the wave?
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 a wave travels 600 m in 3 seconds, what is its speed?
If the displacement of a wave is given by y(x, t) = A sin(kx - ωt), what does the parameter k represent?
State the physical meaning of the term 'wave speed' in the context of the wave equation.
What is the general form of the one-dimensional wave equation for a wave traveling along the x-axis?
A sound wave in water has a wavelength of 0.75 m and a speed of 1500 m/s. Calculate its frequency.
A wave is described by the equation y(x, t) = 0.03 cos(8πx + 400πt). Determine the direction in which the wave is traveling and calculate its frequency.
A wave on a string is given by y(x, t) = 0.1 sin(6x - 18t). Calculate the wavelength and the period of the wave.
A wave pulse is moving along a string with speed v. If the string is replaced with another string of the same length but with four times the mass per unit length and the same tension, what will be the new speed of the wave?
Derive the wave equation for a stretched string using Newton’s second law, stating all assumptions clearly.
Explain how the principle of superposition applies to the solutions of the wave equation and provide an example.
