05 · 18 min
Waves and sound
Frequency, wavelength, the wave equation, echoes, and a timed pendulum.
v = fλ
The idea
A wave transfers energy without transferring the material. In a transverse wave the oscillation is across the direction of travel, as on a rope or a light wave. In a longitudinal wave, such as sound in air, the oscillation is along the direction of travel.
Frequency is the number of waves passing a point each second, in hertz. The period is the time for one wave, T = 1/f. Wavelength is the distance from one crest to the next. They are tied together by v = fλ.
An echo is a reflection. The sound goes to the wall and back, so the distance to the wall is vt/2, not vt. A simple pendulum is a slow oscillator you can time: for small swings, T = 2π√(L/g). Time several swings and divide.
| Change | What you notice |
|---|---|
| Larger amplitude | Louder. Pitch and speed stay the same. |
| Higher frequency | Higher pitch. Wavelength gets shorter if the speed is unchanged. |
| Warmer air, typically | A slightly higher speed of sound. |
Formulas
Wave speed
v = fλ
Any wave. If the medium fixes v, frequency and wavelength trade off.
- v
- wave speed
- m/s
- f
- frequency
- Hz
- λ
- wavelength
- m
Period and frequency
T = 1 / f
One complete oscillation. A frequency of 4 Hz means a period of 0.25 s.
- T
- period
- s
- f
- frequency
- Hz
Echo distance
d = vt / 2
d is the distance to the reflector. t is the time to go there and back.
- d
- distance to the wall
- m
- v
- speed of sound
- m/s
- t
- time for the echo
- s
Simple pendulum
T = 2π√(L / g)
Small angles, roughly under 10°. The period does not depend on the mass of the bob.
- T
- period
- s
- L
- length to the centre of the bob
- m
- g
- gravitational field strength
- m/s²
Worked examples
Speed in a ripple tank
Eight ripples pass a point in 4.0 s. The wavelength is 5.0 cm. Find the wave speed.
- Waves counted
- 8 in 4.0 s
- Wavelength
- 5.0 cm
Try it on paper first. Then open the working one step at a time.
How far is the lightning?
You see lightning and hear the thunder 5.0 s later. Take the speed of sound as 340 m/s and ignore the time the light takes. How far away was the strike?
- Time
- 5.0 s
- Speed of sound
- 340 m/s
Try it on paper first. Then open the working one step at a time.
Checks
A wave has frequency 50 Hz and wavelength 6.0 m. What is its speed, in m/s?
A wave has frequency 4.0 Hz. What is its period, in seconds?
A shout returns from a cliff after 1.2 s. The speed of sound is 340 m/s. How far away is the cliff, in metres?
Increasing only the amplitude of a sound wave increases the
Easy places to lose a mark
- Using the echo time as if the sound only travelled one way.
- Leaving wavelength in centimetres when the speed should be in m/s.
- Timing one pendulum swing. Time five or ten and divide — the error is shared out.
Practical
Ripple tank
Measure frequency and wavelength, then check the wave speed.