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.
- What is the amplitude of the waves?
- 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.