Wave Behaviour

At the equilibrium position, what is the magnitude of the restoring force acting on the mass?

If the frequency of an oscillation is tripled, what happens to the period?

Which formula represents the kinetic energy of an object of mass $m$ in SHM at any instant?

If the angular frequency of a system is $10\pi\text{ rad s}^{-1}$, what is its frequency in $\text{Hz}$?

A spring with spring constant $k$ is cut into two equal halves. If one half is used to support the same mass $m$, how does the period of oscillation change?

The displacement of a particle is $x = A \cos(\omega t)$. At which time $t$ is the particle first at the equilibrium position?

An object in SHM has a maximum acceleration $a_{max}$ and maximum velocity $v_{max}$. What is the angular frequency $\omega$ of the motion?

A mass $m$ is attached to a spring $k$. When the mass is $m$, the period is $T$. When an unknown mass $M$ is added to $m$, the period becomes $2T$. What is the value of $M$?

A particle in SHM has displacement $x = A/2$ and is moving towards the equilibrium position. What is its phase in the cycle, if $x = A \sin(\omega t + \phi)$ and the motion starts at $t=0$?

A particle of mass $0.1$ kg oscillates with SHM. If the frequency is 5 Hz and the amplitude is 0.1 m, what is the total energy of the system?

What is the period of a wave that has a frequency of $100\text{ Hz}$?

If 10 crests of a water wave pass a buoy in 2 seconds, what is the frequency of the wave?

What is the highest point on a transverse wave called?

A wave is a process that transfers:

For a travelling wave, which of the following is the correct unit for intensity?

If a wave source moves such that it produces $10$ crests every $2$ seconds, and the crests are $5\text{ m}$ apart, what is the wave speed?

A wave has a speed of $300\text{ m s}^{-1}$ and a frequency of $50\text{ Hz}$. What is the phase difference between two particles $2.0\text{ m}$ apart?

Which of the following is a characteristic of all electromagnetic waves but not all mechanical waves?

A travelling wave passes through a medium. A particle in the medium completes $10$ oscillations in $2$ seconds. If the wavelength is $5\text{ m}$, what is the speed of the wave?

Two waves of frequencies $500\text{ Hz}$ and $505\text{ Hz}$ interfere. What is the period of the resulting beats?

If a light ray passes from glass ($n=1.5$) to water ($n=1.33$), it will:

Total internal reflection is used in which of the following technologies?

Which of the following is the correct formula for the refractive index $n$ of a material?

What is the effect of increasing the width of a slit on the diffraction pattern of light passing through it?

A student measures the refractive index of a block to be $1.40$. If the speed of light in vacuum is $c$, what is the speed of light in the block?

What happens to the wavefronts of a plane wave when they pass through a very large opening (relative to the wavelength)?

A light ray is incident on a glass-air interface from the glass side at an angle of $30^{\circ}$. If the refractive index of the glass is $1.50$, what is the angle of refraction in the air?

A source of waves is placed at the focus of a parabolic reflector. The reflected waves are:

A ray of light is incident on a transparent plate at the Brewster angle. Which of the following is true about the reflected and refracted rays?

White light passes through a single slit. Which statement correctly describes the resulting diffraction pattern?

In a standing wave, the energy is:

A string is fixed at both ends and its fundamental frequency is $f$. If the length of the string is cut to $L/2$ while keeping tension constant, what is the new fundamental frequency?

The second harmonic of a pipe closed at one end is:

What happens to the frequency of the fundamental mode of an air column if the speed of sound increases (e.g., due to temperature increase)?

When a string fixed at both ends is vibrating in its fundamental mode, every point on the string (except the nodes) has the same:

A standing wave is formed by the interference of $y_1 = A \sin(kx - \omega t)$ and $y_2 = A \sin(kx + \omega t)$. At which values of $x$ do the nodes occur?

The third harmonic of an open pipe of length $L_1$ has the same frequency as the second overtone of a closed pipe of length $L_2$. What is the ratio $L_1 / L_2$?

The fundamental frequency of an open organ pipe is $300\text{ Hz}$. The first overtone of a closed organ pipe has the same frequency as the first overtone of the open pipe. How long is the closed pipe? (Speed of sound $v = 330\text{ m s}^{-1}$)

An air column in a glass tube is open at one end and closed at the other by a movable piston. The smallest length of the column for resonance with a tuning fork of $500\text{ Hz}$ is $16\text{ cm}$. What is the next length at which resonance will occur?

A standing wave on a string is given by $y = 5 \sin(0.1\pi x) \cos(100\pi t)$, where $x$ and $y$ are in cm and $t$ is in seconds. What is the distance between the first and the third nodes?

For a moving source, the Doppler effect is primarily caused by a change in the wave's:

An observer is stationary. A source moves towards the observer. What happens to the wavefronts between the source and observer?

How does the speed of a wave in a medium change due to the Doppler effect?

If a galaxy shows a very large redshift, it indicates that the galaxy is:

A source of frequency $1000 \text{ Hz}$ moves at $50 \text{ m s}^{-1}$ towards an observer who is moving at $20 \text{ m s}^{-1}$ away from the source. What frequency does the observer hear? ($v = 340 \text{ m s}^{-1}$)

Which of the following does NOT depend on the speed of the source in the Doppler effect for sound?

For a source of light moving away from an observer at $0.1c$, the fractional change in frequency $\frac{\Delta f}{f}$ is approximately:

Calculate the redshift $z$ of a galaxy that is receding at $0.6c$.

A stationary observer hears a frequency of $560\text{ Hz}$ from a whistle on a train approaching a tunnel in a cliff. After the train enters the tunnel, the observer hears an echo of $480\text{ Hz}$ from the cliff. If $v_{sound} = 340\text{ m s}^{-1}$, what is the train's speed?

A ship uses sonar to find its speed relative to the seabed. It sends a $30\text{ kHz}$ signal and receives a reflection shifted by $60\text{ Hz}$. If the speed of sound in water is $1500\text{ m s}^{-1}$, what is the ship's speed?

Which phenomenon proves that light is a transverse wave?

What does a ray represent in the context of waves?

If the amplitude of a wave is doubled, by what factor does its intensity increase?

In a longitudinal wave, what is a region of high pressure called?

A beam of light travels from a medium with refractive index $n_1$ to $n_2$. If $n_2 > n_1$, which of the following is true?

If the phase difference between two points on a wave is $2\pi$ radians, what is the distance between them?

For destructive interference to occur between two waves of wavelength $\lambda$, the path difference must be:

A wave source moves in a circle at a constant speed $u$. A stationary observer is located far away in the plane of the circle. The maximum frequency heard by the observer is $f_{max}$ and the minimum is $f_{min}$. What is the source frequency $f_0$ in terms of $f_{max}$ and $f_{min}$?

In a standing wave on a string, the energy is:

The second-order maximum of a diffraction grating for light of wavelength $400\text{ nm}$ occurs at the same angle as the first-order maximum for an unknown wavelength. What is the unknown wavelength?

Two coherent point sources, $S_1$ and $S_2$, emit waves of wavelength $\lambda$ that are in phase with one another. The waves meet at a point $P$. The distance $S_1P$ is $4.0\lambda$ and the distance $S_2P$ is $4.5\lambda$. Which phenomenon occurs at point $P$ due to the superposition of these waves?

A wave has a wavelength of $2\text{ m}$ and a frequency of $5\text{ Hz}$. What is its speed?

Which of the following is NOT a property of all electromagnetic waves?

Which of the following best describes 'destructive interference'?

A diffraction grating has $400$ lines/mm. If light containing two wavelengths $500\text{ nm}$ and $501\text{ nm}$ is used, what is the angular separation between the first-order maxima of these two wavelengths?

A non-reflective coating ($n = 1.38$) is applied to a glass lens ($n = 1.50$). For destructive interference of reflected light with wavelength $\lambda$ in air, what is the minimum thickness required?

A sound source moves away from a stationary observer at $20\%$ of the speed of sound. What is the ratio of the observed frequency to the source frequency?

Two polarizers have their transmission axes at an angle $\theta$. Unpolarized light of intensity $I$ is incident on the first. If the final intensity is $I/4$, what is $\theta$?

A sound source is moving away from a stationary observer at a speed equal to half the speed of sound. What is the ratio of the observed frequency to the source frequency?

A diffraction grating has $N$ lines illuminated. If $N$ is doubled, how do the intensity of the principal maxima and their angular width change?

Which of the following is NOT a property shared by all electromagnetic waves in a vacuum?

A wave has a wavelength of $2\text{ m}$ and a period of $0.5\text{ s}$. What is its speed?

The orientation of the oscillations in a transverse wave is called its:

Which of the following is the correct order of electromagnetic waves from longest to shortest wavelength?

Calculate the frequency of a light wave with a wavelength of 600 nm in a vacuum.

Which of the following is a unit of intensity?

When light travels from a medium with $n=1.5$ to one with $n=1.2$, what is the ratio of the speed of light in the first medium to the speed in the second?

A wave is described by $y = 0.05 \sin(10\pi t - 2\pi x)$. What is the speed of the wave?

A polarizer-analyzer set is adjusted so that the transmitted intensity is $I_{max}$. By what angle should the analyzer be rotated to reduce the intensity to $0.1 I_{max}$?

Two waves with amplitudes $A$ and $2A$ interfere. What is the ratio of the maximum possible intensity to the minimum possible intensity?

In medical imaging, the Doppler effect is used with ultrasound to measure:

An observer is moving away from a stationary siren. The speed of the sound waves relative to the observer is:

The frequency of a wave is $f$. If the period $T$ of the wave increases, the frequency $f$:

A star's spectral line is measured at $600 \text{ nm}$ in the lab but is observed at $602 \text{ nm}$ from a distant star. This is an example of:

A star is moving towards Earth. The emitted wavelength is $\lambda_0$ and the observed wavelength is $\lambda$. The velocity $v$ of the star is approximately:

A sound source $S$ moves away from a stationary observer $O$ at speed $v_s$. The frequency heard by the observer is $f'$. If the speed of sound is $v$, which of the following is true?

Which of the following is true for the Doppler effect of light from a receding galaxy?

The formula for the Doppler effect in light is often given as $\Delta f / f \approx v/c$. Under what condition is this approximation most accurate?

A galaxy is observed to have its light blueshifted. What does this imply about its motion relative to Earth?

If a source of frequency $f$ moves toward an observer at $0.9v$, what is the ratio of the observed wavelength to the original wavelength?