List of top Physics Questions on Wave Motion

A wave disturbance in a medium is described by \[ y(x,t)=0.02\cos\left(50\pi t + \frac{\pi}{2}\right)\cos(10\pi x), \] where \( x,y \) are in meters and \( t \) in seconds. Which statements are correct?
The equation of a stationary wave along a stretched string is \[ y = 5\sin\left(\frac{\pi x}{3}\right)\cos(40\pi t), \] where \( x,y \) are in cm and \( t \) in seconds. The separation between two adjacent nodes is
The variation of displacement with time of a simple harmonic motion is \[ y = 2\sin\left(\frac{\pi t}{2}+\phi\right)\text{ cm}. \] The maximum acceleration of the particle is
Statement-1: Kinetic energy of system = \( \frac{1}{2} m_1 v_1^2 + \frac{1}{2} m_2 v_2^2 + \dots + \frac{1}{2} m_n v_n^2 \) Statement-2: Kinetic energy of system = Kinetic energy of center of mass + kinetic energy with respect to center of mass.
A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the x-direction in 0.3 sec. The crest P is at $ x = 0 $ at $ t = 0 $ sec and maximum displacement of the wave is 2 cm. Which equation correctly represents this wave?
The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, $ y_1 (x, t) = 4 \sin(kx - \omega t) $ and $ y_2 (x, t) = 2 \sin(kx - \omega t + \frac{2\pi}{3}) $, are: (Take the angular frequency of initial waves same as $ \omega $)
Two strings with circular cross section and made of same material are stretched to have same amount of tension. A transverse wave is then made to pass through the strings. The velocity of the wave in the first string having the radius of cross section $ R $ is $ v_1 $, and that in the other string having radius of cross section $ R/2 $ is $ v_2 $. Then, $ \frac{v_2}{v_1} $ is:
The equation of a transverse wave travelling along a string is \( y(x, t) = 4.0 \sin \left( 20 \times 10^{-3} x + 600t \right) \) mm, where \( x \) is in mm and \( t \) is in seconds. The velocity of the wave is:
A wave disturbance in a medium is described by \[ y(x,t) = 0.02 \cos\left(50 \pi t + \frac{\pi}{2}\right) \cos(10 \pi x) \] where \( x \) and \( y \) are in meters and \( t \) is in seconds. Which statement(s) is/are correct?
The frequency of a wave is 500 Hz and its wavelength is 0.66 m. What is the speed of the wave?
If $ V $ is the velocity of wave in a rope having tension $ T $, find the velocity when the tension becomes $ 8T $.

The figure shows a system of two equal masses \( m \) and three massless horizontal springs with spring constants \( k_1 \), \( k_2 \), and \( k_1 \). Ignore gravity. The masses can move only in the horizontal direction, and there is no dissipation. If \( m = 1 \), \( k_1 = 2 \), and \( k_2 = 3 \) (all in appropriate units), the frequencies of the normal modes of the system in the same system of units are:


 

In the wave equation $ y = 3 \cos \pi (100t - x) \, \text{cm}$, the wavelength is
A transverse wave is described by the equation \( y = A \sin \left( 2 \pi \left( \frac{r}{\lambda} - \frac{t}{T} \right) \right) \). The maximum particle velocity is equal to four times the wave velocity if:
The ratio of radii of two wires is 1:2 and the density of their materials are in the ratio 1:4. If same tension is applied to both the wires then the ratio of the speed of transverse waves produced in them is:
If the speed of a wave doubles as it passes from shallow water into deeper water, its wavelength will be
Prove that the frequency of beats is equal to the difference between the frequencies of the two sound notes giving rise to beats.
What are harmonics and overtones (Two points)?
The equation of a simple harmonic progressive wave travelling on a string is \( y = 8 \sin (0.02 x - 4 t) \) cm. The speed of the wave is ______.
What is the wavelength of a sound wave with a frequency of \( 500 \, \text{Hz} \) in air (speed of sound \( v = 343 \, \text{m/s} \))?