4.3 Waves at material interfaces — Learn

Prerequisites: Section 4.1, especially the wave equation and the difference between a transverse wave and a longitudinal wave; Section 3.1 for speed as distance divided by time; measuring an angle with a protractor.

By the end of this section you can: describe what happens to a wave at the boundary between two materials; state the law of reflection; draw a ray diagram to show reflection; and explain what happens to the speed, frequency and wavelength when a wave is transmitted into a new material.

1. A boundary between two materials

The boundary between two different materials is called a material interface. When a wave reaches an interface, three things can happen to it.

It can be reflected: the wave bounces back from the boundary.
It can be transmitted: the wave passes through the boundary into the second material.
It can be absorbed: the energy of the wave is transferred to the material.

Usually all three happen at once. Some of the wave is reflected, some passes through, and some is absorbed. How much of each depends on the two materials and on the type of wave.

2. Reflection

Reflection happens when a wave bounces off a surface. To describe it, we draw a normal: the line at right angles to the surface at the point where the wave hits.

The ray arriving at the surface is the incident ray.
The ray leaving the surface is the reflected ray.
The angle of incidence is the angle between the incident ray and the normal.
The angle of reflection is the angle between the reflected ray and the normal.

The law of reflection states that the angle of incidence equals the angle of reflection.

An echo is a reflected sound wave. Light reflecting from a mirror is a reflection of a light wave, and a water ripple reflecting from the side of a tank is a reflection of a water wave.

Worked example 1. A ray of light meets a mirror at an angle of incidence of 35 degrees. State the angle of reflection, and say what line the angles are measured from.

The angle of reflection is 35 degrees, because the angle of reflection equals the angle of incidence. Both angles are measured from the normal, which is the line at right angles to the mirror at the point where the ray hits it.

Try it: the law of reflection

The figure shows a ray meeting a flat surface. You can change the angle of incidence.

Predict first. Do not move the slider yet. Write down your answers.

What is the angle of reflection when the angle of incidence is 40 degrees?
What happens to the reflected ray when the incident ray travels along the normal?

Test. Set the angle of incidence to 40 degrees and read the angle of reflection. Now set it to 70 degrees, and then to 0 degrees.

Explain. The angle of incidence and the angle of reflection are always equal. Why does the reflected ray go straight back along the incident ray when the angle of incidence is 0 degrees? Write your answer in two or three sentences.

3. Transmission and the speed of a wave

When a wave is transmitted into a new material, its speed can change. The frequency does not change, because the frequency is set by the source. The wave equation $v = f\lambda$ then tells you what happens to the wavelength.

If the wave speeds up, the wavelength gets longer.
If the wave slows down, the wavelength gets shorter.

This is why a wave can change direction when it crosses a boundary at an angle. The change of direction is called refraction. You will meet refraction again when you study lenses.

Worked example 2. A sound wave of frequency 500 Hz passes from air into water. The speed of sound is 330 m/s in air and 1500 m/s in water. Calculate the wavelength in each material.

\begin{aligned} \text{in air:}\quad \lambda &= \frac{v}{f} = \frac{330}{500} = 0.66\,\text{m} \\ \text{in water:}\quad \lambda &= \frac{v}{f} = \frac{1500}{500} = 3.0\,\text{m} \end{aligned}

The frequency stays at 500 Hz. The higher speed in water gives the longer wavelength.

Worked example 3. When a wave meets a boundary, 15% of its energy is reflected and 25% is absorbed. Calculate the percentage of the energy that is transmitted.

100\% - 15\% - 25\% = 60\%

4. Absorption

Absorption happens when a material takes in the energy of a wave. The energy is transferred to the material and usually warms it a little.

Soft, rough materials absorb sound well. That is why a room lined with thick curtains or carpets has a quieter echo than a room with bare walls. Dark, matt surfaces absorb light well, which is why they look black.

Worked example 4. A water wave travels at 4.0 m/s and reflects from a wall 30 m away. Calculate the time taken for the wave to travel to the wall and back.

\begin{aligned} \text{total distance} &= 2 \times 30 = 60\,\text{m} \\ t &= \frac{s}{v} \\ &= \frac{60}{4.0} \\ &= 15\,\text{s} \end{aligned}

Worked example 5. A ripple tank contains water to a depth of 25 cm. Convert this depth to metres.

25\,\text{cm} = 0.25\,\text{m}

Worked example 6. A person claps and hears the echo from a wall after 0.80 s. The speed of sound in air is 330 m/s. Calculate the distance from the person to the wall.

\begin{aligned} d &= \frac{v t}{2} \\ &= \frac{330 \times 0.80}{2} \\ &= \frac{264}{2} \\ &= 132\,\text{m} \end{aligned}

5. Using boundaries to explore hidden structures

Different materials reflect, transmit and absorb waves by different amounts, and they can change the speed of a wave by different amounts. Scientists and engineers use these differences to explore structures that cannot be seen directly.

An ultrasound pulse sends back a reflection from a boundary inside the body, such as the edge of an organ.
A seismic wave from an earthquake changes speed and direction as it crosses the boundary of the Earth's core.
An echo sounder detects the sea floor or a shoal of fish from the reflection of a high-frequency sound pulse.

The reflection tells you where the boundary is, and the change in speed tells you something about the material on each side.

Watch out. The angle of incidence and the angle of reflection are measured from the normal, not from the surface. A common error is to measure the angle between the ray and the surface, which gives a different number. The normal is the dashed line at right angles to the surface. Also remember that the frequency does not change when a wave crosses a boundary: only the speed and the wavelength can change.

Progress check

Return to the chapter problem. The echo sounder sends a pulse of sound down to the sea floor. Part of the pulse is reflected back to the boat. Describe what happens to the rest of the pulse at the sea floor, and explain why the reflection is useful for measuring the depth.

You should now be able to

describe reflection, transmission and absorption at a material interface;
state the law of reflection and say what the normal is;
draw a ray diagram to show a wave reflecting from a flat surface;
explain why the frequency does not change when a wave crosses a boundary, and what happens to the speed and the wavelength;
describe how soft materials absorb sound and reduce an echo;
calculate the time for a wave to travel to a boundary and back;
explain how differences between materials are used to explore hidden structures (Higher tier).