###### Waves

Which type of waves do not require a medium to travel?

Electromagnetic waves can exist in empty space.

###### Waves - 2

A moving wave which is made up of oscillations happening perpendicular to the direction of travelling is called

A transverse wave is a moving wave that is made up of oscillations happening perpendicular to the direction of propagation.

###### Waves - 3

A moving wave which is made up of oscillations happening in the same direction as the wave propagates is called

In longitudal wave oscillations occur parallel to the direction of wave propagation.

###### Waves - 4

What type of wave is shown in the picture below?

A transverse wave is a moving wave that is made up of oscillations happening perpendicular to the direction of propagation.

###### Waves - 5

A wave that transfers energy as it moves is called

Progressive wave transfers energy with propagating.

###### Waves - 6

Choose the incorrect statement.

Choose the incorrect statement.

Continuous wave is a scientific model in which a wave has no beginning and no end, but real-life waves always have limited duration.

###### Waves - 7

The number of cycles of an oscillation that occur in current time is called

Frequency is the number of cycles of an oscillation that occur in current time.

###### Frequency

Choose the incorrect statement.

Period is the time taken to complete one oscillation. Frequency is a number of cycles of an oscillation that occur in unit time. The unit is the Hertz (Hz, 1/s)

###### Frequency - 2

The figure below shows displacement versus time plot of a material point of the wave. What is the frequency of the wave?

The graph shows that the period of oscillation of the body is 4 seconds. Hence  the frequency is $$v = {1\over T} = {1\over {4s}} = 0.25\space Hz$$

###### Speed of sound

To determine the speed of sound a student stood up at a distance of 30 m from the wall and clapped his hands. At the moment of the clap an electronic timer was turned on. It was turned off by the reflected sound. Stopwatch showed the time 0.18s. What is the speed of sound that was determined by student?

The sound made its way to the wall and back before turning off the stopwatch. Therefore, the speed of sound that was determined by the student is $$v = {2s\over T} = 2*30/0.18 \approx333\space m/s$$

###### Speed of sound - 2

Question: The ship moving at a speed of 5.5 m/s gave a beep. The sound was heard on the bridge after 3 seconds. Then, after 3 minutes the ship passed under the bridge. Determine the speed of sound in air.

Input the correct answer in m/s.

Firstly, find the distance from the ship to the bridge as $$s = v*t = 5.5m/s*180 = 990m$$

Secondly, find the speed of sound using the previously found distance to the bridge:

$$v = s/t = {990m \over 3s} = 330 \space m/s$$

###### Speed of sound - 3

What is the frequency of acoustic oscillations in the medium, if the speed of sound in the medium is $$v = 500 \space m/s$$ , and the wavelength of oscillations is $$\lambda = 2m$$?

Frequency f, wavelength $$\lambda$$ and speed of propagation of sound  waves in the medium $$v$$ are related with each other by the formula $$\lambda*f = v$$. Hence, the frequency of acoustic oscillations is $$f = v/\lambda={500m/s\over2m}= 250\space Hz$$

###### Wavelength

Bass saxophone can produce sound with frequencies from $$f1 = 80Hz$$ to $$f2 = 8000Hz$$. What is the ratio of corresponding wavelenghts, $$\lambda1/\lambda2$$?

Wavelength of sound, frequency and speed if propagation are connected by formula $$\lambda f = v$$.

Hence, $$\lambda_1/\lambda_2 = {v/f_1\over v/f_2}=8000Hz/80Hz =100$$

###### Principle of superposition

The principle of superposition could be applied for

Select the correct statement.

When two or more waves meet, the total displacement at any point is the sum of the displacements that each individual wave would cause at the point. The principle of superposition applies to all waves.

###### Standing waves

Select the correct statement:

Select the correct statement.

1. Standing waves do not transfer energy – by definition.
2. Standing wave could exist as a result of interference between two waves travelling in opposite directions – i.e. electromagnetic waves in space.
3. Standing always has points where the oscillation amplitude is zero. They are called nodes
4. Standing waves can exist in a vacuum despite there being no reflecting medium (as a result of interference between electromagnetic waves)
###### String

What is the wavelength of a wave that could exist in a string stretched between two fixed points?

The length of a string is l, n is a whole number.

For a string stretched between two points, theamplitude of vibration at each end must be zero. It can be shown that the only waves that are possible under this restriction are those where $$\lambda={ {2l}\over n}$$, where l is the lenghth of the string and n is a whole number.

###### Standing waves - 2

Select the correct statement.

1. Standing wave does not transfer energy – by definition.
2. Standing wave could exist as a result of interference between two waves travelling in opposite directions – i.e. electromagnetic waves in space.
3. Standing wave always has points where the amplitude of oscillation is zero. These points are called nodes.
4. Standing waves can exist in a vacuum despite there being no reflecting medium (as a result of interference between electromagnetic waves).
###### String - 2

What is the wavelength of a wave that could exist in a string stretched between two fixed points? l is a length of the string, n is an integer.

Expression $$\lambda = {2l\over n}$$ is correct for any n that is an integer.

###### String - 3

A string is stretched between two fixed points. Which set shows the distances (from the end of string) at which nodes can occur?

$$\lambda$$ is a wavelength of a standing wave in this string.

The distance between neighboring nodes is $$\lambda/2$$.

###### Fundamental mode wavelength

For a string with a length $$l$$ that is stretched between two fixed points, the fundamental mode wavelength is

According to an expression for modes that can exist in a string with fixed ends, $$\lambda ={2l\over n}$$, the fundamental mode wavelength is obtained at n = 1: $$\lambda_{fund} = 2l$$.

###### Light waves

The four statements are given:

1. Light waves are reflected with a 90° phase change when travelling from less dense to more dense medium.
2. Light waves are reflected with a 180° phase change when travelling from less dense to more dense medium.
3. Light waves are reflected without phase change when travelling from less dense to more dense medium.
4. Light waves are reflected without phase change when travelling from more dense to less dense medium.

Select the set in which all the statements are correct.

Light waves are reflected with a 180° phase change when travelling from less dense to more dense medium.

Light waves are reflected without phase change when travelling from more dense to less dense medium.

###### Reflection and refraction

There are several statements.

1. Angle of incidence is equal to angle of refraction.
2. Angle of incidence is measured from horizontal ray.
3. Angle of reflection and angle of refraction are measured from normal ray.
4. When a light ray moves to a less optical dense medium it speeds up.
5. When a light ray moves to a less optical dense medium it slows down.

Select the row in which all the listed statements are correct.

1/2/3  Angle of reflection, angle of incidence and angle of refraction are measured from normal ray. 4/5. When a light ray moves to a less optically dense medium, it speeds up. When it moves to the optically denser medium, it slows down.

###### Reflection and refraction - 2

A ray of light in air is approaching the boundary with water. A piece of glass is located under the water surface. It is known that the refractive index of glass is greater than the refractive index of water. Which figure depicts correctly the course of the ray?

At the air-water and water-glass borders the light beam is travelling from less optically dense medium to more optically dense medium. Refractive index increases at each of the boundaries..

###### Refraction

A ray of light in the air approaches the boundary with glass.

What will happen to the frequency of electromagnetic oscillations in the light wave?

When a ray of light passes from glass to air, the frequency of electromagnetic oscillations in the light wave is not changed because it does not depend on the environment in which the wave propagates.

###### Refraction

A ray of light in the air approaches the boundary with glass.

What will happen to the speed of propagation of a light wave?

Since glass is an optically denser medium than the air, the propagation speed of a light wave decreases when the beam enters glass.

###### Refraction - 3

A ray of light in the air approaches the boundary with glass.

What will happen to the wavelength of electromagnetic oscillations in the light wave?

The wavelength is connected with the frequency and the speed of propagation of a wave: $$\lambda f =b$$. As the frequency of the wave is invariant and the speed of propagation of the wave decreases, the wavelength decreases proportionally with the speed of propagation.

###### Refraction - 4

A ray of light enters a thick horizontal glass plate at $$\alpha^{\circ}$$to normal and passes through it. What is the angle between its final and initial directions?

A ray is refracted at the same angle when it enters and escapes the glass plate. The direction of the beam remains the same.

###### Total internal reflection

Which of the pictures shows the case of total internal reflection?

Total internal reflection is observed in the case when a wave moves from a more optically dense medium to a less optically dense medium and strikes the boundary between these mediums at some critical angles. At these angles, the angle between refracted angle and normal is greater than $$90^{\circ}$$ by Snell's law, and all the light is effectively reflected back.

###### Total internal reflection - 2

There are several statements.

1. Total internal reflection can occur when a light ray moves to a less optical dense medium.
2. Total internal reflection can occur when a light ray moves to the denser optical medium.
3. At any boundary between mediums some energy of a wave always passes across the boundary.
4. When a ray of light moves to a less optically dense medium it slows down.

Select the set in which all the statements are correct.

1/2: Total internal reflection can occur when a light ray moves to a less optical dense medium.

3: At any boundary some wave energy always passes across the boundary. This is called a transmission.

4: When a ray of light moves to a less optically dense medium, it slows down.

###### Total internal reflection - 3

Light travels from acrylic glass to air. Acrylic glass has an index of refraction of approximately 1.5. Calculate the value of critical angle.

Input the correct answer to 1 d.p. in degrees

The critical angle will be when the refracted ray leaves at $$90^{\circ }$$ to the vertical.

By Snell's law, $$n_1Sin(\theta_i) = n_2Sin(\theta_r)$$, where $$n_1$$is the index of refraction for acrylic glass, $$n_2$$ is the index of refraction for air, $$\theta_i$$ is an angle of incedence and $$\theta_r$$ is an angle of refraction.

As  $$\theta_r = 1$$$$\theta_i=ArcSin(n_2/{n_1}) = ArcSin(1/1.5)\approx41.8^\circ$$

###### Total internal reflection - 4

Ligth travels from a substance with an index of refraction of $$n_1 = 1.2$$ to a substance with an index of refraction of $$n = 1.5$$. What is the critical angle for this pair of substances?

The phenomenon of total internal reflection occurs only in the case when light travels from a more optically dense medium to a less optically dense medium.

###### Speed of light

A beam of light travels from air to glass. The refractive index of a glass relative to air is n. The speed of light in the air is c. Select the expression that corresponds to speed of light in glass.

Because glass is an optically denser medium than air, the speed of light in glass is reduced and equals $$c/n$$.

###### Nonlinear effects

Select the correct definition of interference.

Interference is a phenomenon in which two waves superpose to form a resultant wave of greater, lower, or the same amplitude.

###### Nonlinear effects - 2

Select the correct definition of diffraction.

Diffraction is defined as the bending of light around the corners of an obstacle or aperture into the region of geometrical shadow of the obstacle.

###### Nonlinear effects - 3

Select the correct definition of refraction.

Refraction is the change in direction of propagation of a wave due to a change in its transmission medium.

###### Nonlinear effects - 4

Select the correct definition of dispersion.

Dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency.

###### Coherent waves

Select the correct definition of coherent waves.

Waves that are of the same frequency and phase are coherent. Waves are incoherent if the phase difference between them keeps changing.

###### Coherent waves -2

Select the correct definition of incoherent waves.

Waves are coherent if they are of a same frequency and phase. If the phase difference between the waves keeps changing, the waves are incoherent.

###### Polarisation

Which of the listed waves can be polarized?

Polarization is a property of waves that can oscillate with more than one orientation. Only transverse waves (electromagnetic or gravitational) can be polarized.

###### Polarisation - 2

Which source of radiation can emit polarized waves?

Television transmitters are engineered to emit polarized waves in order to avoid interference between signals with similar frequencies. Other sources from the list emit waves with random orientations.

###### Electromagnetic waves

Which number shows the part of the electromagnetic spectrum that corresponds to X-rays?

X-rays are high-energy short-wavelength electromagnetic waves that are produced during the collision of high-speed electrons with a metal target.
X-rays are positioned in a spectrum of electromagnetic waves between gamma rays that have shorter wavelength and UV-rays that have longer wavelength.

###### Electromagnetic waves - 2

Which number shows the part of an electromagnetic spectrum that corresponds to gamma rays?

Gamma rays are generated by energy shifts inside the nuclei of atoms. There is a crossover between the frequency ranges of X-rays and gamma rays at lower energies, but the X-rays are produced in another way - during the rapid deceleration of electrons.

###### Electromagnetic waves - 3

Which number shows the part of an electromagnetic spectrum that corresponds to ultraviolet?

Ultraviolet waves have higher frequencies than visible light, but lower than X-rays, ranging from $$7.5\times10^{14}Hz$$ up to $$3\times10^{16}Hz$$. Higher-energy ultraviolet is wideliy used to kill bacteria in recycled water because it damages the DNA of these organisms.

###### Electromagnetic waves - 4

Which number shows the part of an electromagnetic spectrum that corresponds to infrared?

Infrared lies between the visible light region and microwaves in the spectum of electromagnetic waves. Infrared is responsible for heat radiation; for example, if you feel warmth while sitting beside a campfire, most of the heat is being carried to you by infrared waves. Also, infrared waves are used in communications, they transfer information alone or along the visible light in optical fibers.

###### Electromagnetic waves - 5

Which number shows the part of an electromagnetic spectrum that corresponds to microwaves?

Microwaves have shorter wavelengths than radio waves. Microwaves effectively pass through the ionosphere. This type of electromagnetic waves is used in communication with satellites. Small dimensions of aerials needed to transmit or receive microwaves ensure the usage of this type of waves in portable devices, like cell phones, navigators and so on.

###### Usage of electromagnetic waves

Set the correspondence between electromagnetic waves and their possible practical applications.

1.​ Cancer therapy

2.​ Communication with satellites, mobile phones

3.​ Destroying microorganisms in water

4.​ Materials science

A.​ X-Rays

B.​ Microwaves

C.​ Ultraviolet

D.​ Gamma rays

Select the correct set.

Gamma rays are widely used as a part of cancer therapy. They are also used to sterilize surgical instruments.

Microwaves have shorter wavelength than radio waves - there is no need for a large aerial for transmitting and receiving and that makes them ideal for handled communication devices. They are also not reflected by the ionosphere and thus are used for communication with satellites.

The DNA of various types of microorganisms could be fatally damaged by ultraviolet waves, so it is used for water sterilizing.

X-Rays have many practical applications. X-rays can go through many solid materials. For this reason, taking photograms with X-rays is used in medicine in order to see bones and other things inside the body. They are also widely used in material science: X-rays radiography, X-rays crystallography etc.

###### Human eye

Select the range of wavelengths that can be detected by the human eye.

A typical human eye will be sensitive to wavelengths from about 400 to 700 nm. $$1\space nm =10^{-9}\space m$$.