Work, Energy and Sound
Work, Energy and Sound links force and displacement with energy transfer, then applies wave ideas to sound. Expect numericals on work, kinetic and potential energy, power, echo timing, and speed of sound.
Core ideas
- Work W = F s cos(theta), where theta is the angle between force and displacement. Work is zero if force is perpendicular to displacement.
- Kinetic energy KE = 1/2 mv^2; gravitational potential energy PE = mgh near Earth.
- Mechanical energy is conserved when only conservative forces act. Power P = work/time; unit watt.
- Sound is a longitudinal mechanical wave. It needs a medium and cannot travel through vacuum.
- Frequency determines pitch; amplitude determines loudness. Speed of sound is greater in solids than in gases.
- Echo: total distance travelled by sound is 2d, so d = v t / 2. Human audible range is about 20 Hz to 20 kHz; ultrasound is above 20 kHz.
Worked example
A force of 20 N pulls a box 3 m along a floor at 60 degrees to the displacement. Find the work done. W = F s cos(60) = 20 x 3 x 0.5 = 30 J. Reasoning: only the component of force along the displacement does work. If the force were vertical while the box moves horizontally, cos 90 = 0 and the work would be zero.
Traps that cost marks
Use metres, not centimetres, in energy calculations. In echo problems, do not forget to divide by 2. Sound does not travel in vacuum, so an explosion cannot be heard in space. Power and energy are different: watt is joule per second.