Frequency and time period

The frequency of a wave can also be calculated using this equation:

\text{frequency =}~\frac{\text{1}}{\text{time period}}

\text{f =}~\frac{\text{1}}{\text{T}}

where:

f = frequency = number of waves produced by a source per second, in hertz Hz.

T = period = time it takes for one complete vibration or oscillation, in seconds s.

Example

A sound wave has a time period of 0.0001 seconds. What is its frequency?

Answer

\text{f =}~\frac{\text{1}}{\text{T}}

\text{f =}~\frac{\text{1}}{\text{0.0001 s}}

f = 10,000 Hz

The frequency of the sound wave is 10,000 Hz.

Question

A radio wave has a frequency of 3 MHz. What is its period?

\text{T =}~\frac{\text{1}}{\text{f}}

f = 3 MHz = 3 x 106 Hz

\text{T =}~\frac{\text{1}}{\text{3}\times{10}^{6}{Hz}}

T = 0.00000033 s

T = 0.33 x 10-6 = 0.33 μs

The period of the radio wave is 0.33 μs

Question

A boat at sea bobs up and down as waves pass. The vertical distance between a crest and a trough is 52 cm and 20 waves pass the boat in 30 seconds.

  1. What is the amplitude of the waves?
  2. What is the frequency of the waves?

1. The amplitude of a wave is the maximum displacement of a point of a wave from its rest position. This is exactly half the distance between a crest and trough.

The distance between a crest and trough = 52 cm.

\text{amplitude =}~\frac{\text{distance between a crest and trough}}{\text{2}} = \frac{\text{52 cm}}{\text{2}} = 26 cm.

The amplitude of the wave is 26 cm.

2. \text{frequency f =}~\frac{\text{number of waves to pass a point}}{\text{time taken in seconds}}

number of waves = 20

time taken = 30 s

\text{f =}~\frac{\text{20}}{\text{30}}

f = 0.67 Hz

The frequency of the waves is 0.67 Hz.