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.
Amplitude = \(\frac{52}{2}\)
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.
Question
A tuning fork has a frequency of 440 Hz.
- What does a frequency of 440 Hz mean?
- Calculate the period of vibration.
- A frequency of 440 Hz means that the prongs of the tuning fork vibrate 440 times every second.
- \(\text{T =}~\frac{\text{1}}{\text{f}}\)
\(\text{T =}~\frac{\text{1}}{\text{440}}\)
T = 0.0023 s = 2.3 x 10-3 s or 2.3 m/s.
The period of vibration is 0.0023 s.
Key point
There are three equations for calculating frequency:
- \(\text{frequency f =}~\frac{\text{number of waves to pass a point}}{\text{time taken in seconds}}\)
- \(\text{f =}~\frac{\text{v}}{\text{λ}}\)
- \(\text{f =}~\frac{\text{1}}{\text{T}}\)
Use the information given in the question to select the appropriate equation to use.