The laws of reflection are the same for all types of waves, including light and sound. The video below shows light reflecting in a mirror.

#### Laws of Reflection

1. The angle of incidence is equal to the angle of reflection
2. The incident ray, the reflected ray, and the normal all lie in the same plane

Note: the normal is a line drawn at 90 degrees to the surface of the reflector, at the point where the incident ray hits. Angles of incidence and reflection are normally (no pun intended!) measured between the ray and the normal, not between the ray and the surface of the reflector.

This all works OK for flat surfaces – normal mirrors around the house, or flat walls reflecting sound waves in an acoustic application. What if the mirror is not flat?

## Curved Reflectors

If a curved surface is used to reflect waves, they can be focused onto a point. The diagrams below show both a spherical and parabolic mirror shape:

Parabolic mirrors are especially useful, and they have one focus point. If a bulb or LED is placed at the focus, a straight beam of light can be formed which travels for long distances (e.g. in torches and car headlamps). Curved satellite dishes are used to transmit or receive radio waves. Even sound can be focused with a curved surface, like the old sound mirrors created by the military and described in the video below.

## Case study: Improving a music room

The photo below shows a music recital room. There is a big concave wall. Without treatment sound would be focused to a particular place in the room leading to the sound being too loud there. To deal with this I designed an acoustic diffuser; if you look carefully you can see that the surface is wiggly. This breaks up the focus by reflecting sounds in all directions. This removes the distortion that the curved surface would have caused.

Trevor Cox, Professor of Acoustical Engineering

✓ Career Case Study: Read about why Trevor Cox works in Acoustical Engineering.

# Echoes

When you shout near a tall building or under a bridge, the sound is reflected back from the walls. You hear this reflected sound as an echo. The time it takes for the echo to reach you can be used to calculate your distance from the wall.

#### Question

If the sound takes one second to go to the wall and back again how far away is the wall? Speed of sound = 330 m/s

• Time taken for sound to travel to the wall = 1 seconds / 2 = 0.5 seconds
• Speed = 330m/s
• Distance = speed x time taken = 330 x 0.5 = 165 metres

Echoes are a problem in large concert halls. If a trumpet plays on the stage, the sound can reflect off the back wall and return to the front of the seating (stalls) still quite loud. Sometimes this sound can be heard by the audience as an echo. To overcome this problem, absorbers can be put on the rear wall to stop the sound reflecting, as was done in the Royal Festival Hall, London shown below. Diffusers could also help the problem by dispersing the reflection causing the echo.

The problem is even worse when there is a curved surface. This is the sound underneath the dome of a mosque in Iran.

Echoes are used in Sonar and Radar. Both systems send out waves (sound waves in water and electromagnetic waves in air, respectively) and record the time it takes for the reflections to arrive back. From this they can detect nearby reflective objects. Stealth devices are those which attempt to make an object non-reflective – if the waves do not bounce off your aircraft, then no-one will know it is there! You also get sound radar, called SODAR which plays chirping sounds and use these to detect wind speed and temperature in the atmosphere!

# Ultrasound

An adaptation of sonar is used to create images of structures inside the human body – this is called medical ultrasound. Ultrasound is very high-frequency acoustic waves, typically between 1 and 3 MHz – much higher than the frequency range audible to humans (20 Hz -20 kHz). Ultrasound is chosen because high frequency sounds have small wavelength. This small wavelength allows a very high degree of image detail to be recorded.

The speed of sound in air is much less than that in water (and the human body is mostly water!). This means that there is an acoustic impedance difference between the air and the body. This difference would normally mean that a large part of the ultrasound energy is reflected away from the body and wasted. To prevent this, the transducer that produces the ultrasonic waves is placed on the skin using a special gel. The speed of sound in the gel is part way between that in air and water, and it therefore creates a smooth transition for the sound waves resulting in less reflected (wasted) energy. This is an example of impedance matching.

Next: Superposition