Oscillations and Waves

Which of the following mathematical expressions correctly represents the restoring force $F$ in SHM for a displacement $x$ and force constant $k$?

For a particle executing SHM with amplitude $A$, the total mechanical energy of the system is proportional to:

If the length of a simple pendulum is increased by four times, its time period of oscillation will:

Which of the following graphs correctly represents the variation of the total mechanical energy ($E$) of a system in SHM with respect to its displacement ($x$)?

If the mass of a simple harmonic oscillator is doubled while keeping its amplitude and force constant ($k$) the same, what happens to its total energy?

At which point in the path of a particle performing SHM is its kinetic energy maximum?

What happens to the amplitude of a system when the frequency of the external force matches its natural frequency?

A simple pendulum oscillating in a room eventually comes to a halt due to air resistance. This phenomenon is known as:

In the case of forced oscillations, the frequency of the oscillating body is equal to:

In a longitudinal wave, the regions where the particles of the medium are crowded together are called:

Which of the following properties of a wave remains unchanged when it travels from one medium to another (e.g., sound moving from air into water)?

A tuning fork produces a sound wave with a frequency of $250\text{ Hz}$. If the speed of sound in air is $340\text{ m/s}$, what is the wavelength of the sound wave?

If the angular frequency $\omega$ of a wave is $100\pi\ rad/s$, what is the frequency $f$ of the wave?

Identify the labels A and B in the provided wave profile description.

In the displacement relation $y(x, t) = a \sin(kx - \omega t + \phi)$, what are the SI units of the wave number $k$?

Which of the following is a necessary condition for the formation of standing waves?

In a stationary wave, the specific points where the particles of the medium undergo the maximum displacement are known as:

When a transverse wave pulse traveling on a string is reflected from a rigid support (fixed boundary), what is the phase change introduced in the reflected wave?

When beats are heard, the periodic variation in the loudness of sound is due to the variation in:

The maximum frequency difference between two sound sources for the human ear to distinguish beats clearly is approximately:

What is the beat frequency produced by two tuning forks with frequencies $f_1 = 440$ Hz and $f_2 = 444$ Hz?

In astronomy, the 'Redshift' of light from distant galaxies is an application of the Doppler Effect. This phenomenon indicates that these galaxies are:

A source of sound and an observer are both moving in the same direction with the same velocity $v$. If the actual frequency of the source is $f$, the apparent frequency heard by the observer will be:

The Doppler Effect for wave motion is applicable to which of the following?