Wave Motion and Sound: v = fλ, Speed of Sound and Echo
This section tests wave terminology, the v = fλ relation, the nature and speed of sound, echo calculations and ultrasound applications.
Wave basics
A wave transfers energy without transferring matter. In a transverse wave the particles vibrate perpendicular to the direction of propagation; sound is longitudinal, travelling as compressions and rarefactions. Amplitude determines loudness, frequency determines pitch, and the relation v = fλ with T = 1/f links the quantities.
Sound
Sound is mechanical, so it needs a medium and never travels through a vacuum. It travels fastest in solids and slowest in gases; in air at room temperature v ≈ 340 m/s, and the speed increases with temperature and humidity. The audible range is 20 Hz to 20 kHz; above that is ultrasound, used in sonar, medical scanning and cleaning; below it is infrasound.
For an echo, the sound travels to the reflector and back: 2d = vt. The sensation of sound persists for about 0.1 s, so the reflector must be at least about 17 m away in air. Reverberation is the persistence of many overlapping reflections.
Worked example
A sonar pulse returns 0.8 s after transmission and the speed of sound in water is 1500 m/s. Total distance = 1500 × 0.8 = 1200 m, so the depth = 1200/2 = 600 m. Dividing by two is essential because the pulse travelled down and back up.
Traps that cost marks
- Forgetting the factor of 2 in echo and sonar problems.
- Saying sound travels in vacuum, or is faster in air than in steel.
- Confusing pitch with loudness.
- Using 20 kHz as the lowest audible frequency instead of the highest.