The wave equation GCSE physics lesson: v = f λ, frequency, wavelength and period

The wave equation: from readings to a speed

Each question is a reading from the required practical on waves, or from measuring the speed of sound. Turn readings into hertz, metres and seconds first, and show your working on paper.

1. In a ripple tank, Amira counts 30 waves passing a mark in 10 seconds. What is their frequency, in Hz?
2. With the strobe on, the waves look still. Five whole waves cover 40 cm on her ruler. What is the wavelength, in metres?
3. Use her frequency (3 Hz) and wavelength (0.08 m). What is the speed of the waves, in m/s?
4. Why does Amira measure across five waves and divide by 5, not measure one wave?
   1. One wave is short, so a small slip with the ruler is a big part of it; across five, the slip is shared out
   2. The waves further from the bar are longer, so she needs an average
   3. Measuring across five waves gives the frequency as well
5. A vibration generator shakes a string at 40 Hz. The still pattern has 4 loops along 1.2 m of string, and each loop is half a wavelength. What is the speed of the waves on the string, in m/s?
6. Kai stands 85 m from a tall wall and claps. The echo comes back 0.50 s later. What is the speed of sound, in m/s?
7. Two microphones are 1.36 m apart, in line with a loudspeaker. A timer shows the sound reaches the second one 4.0 ms after the first. What is the speed of sound, in m/s?

The wave equation: practice

Show your working on paper. Turn kHz into Hz and cm into m first. Give speeds in m/s, wavelengths in m, frequencies in Hz and periods in s. The stretch is optional.

Diagnostic question: choose and explain

1. A sound has a frequency of 2 kHz and a wavelength of 17 cm. What is its speed?
   1. 34 m/s
   2. 340 m/s
   3. 34 000 m/s
   4. 0.34 m/s

Practice questions

1. A wave has a frequency of 5 Hz and a wavelength of 2 m. What is its speed, in m/s?
2. A wave has a frequency of 50 Hz. What is its period, in seconds?
3. Which of these is a longitudinal wave?
   1. Ripples on a pond
   2. A wave on a guitar string
   3. Sound travelling through air
4. A wave has a frequency of 0.25 kHz and a wavelength of 60 cm. In hertz, f = ___ Hz; in metres, λ = ___ m; so its speed is v = ___ m/s.
5. Sound travels at 330 m/s in cold air. A note has a wavelength of 1.5 m. What is its frequency, in Hz?
6. A singer goes from a low note to a higher note in the same room. Compared with the low note, the higher note's sound waves…
   1. go faster, with the same wavelength
   2. go at the same speed, with a shorter wavelength
   3. go at the same speed, with a longer wavelength
   4. go faster, with a longer wavelength
7. A cork floats on a pond. Ripples pass it for a minute. What does the cork do?
   1. It is carried along with the ripples to the edge of the pond
   2. It bobs up and down, staying about where it was
   3. It stays completely still while the ripples pass under it
8. Ben shakes a rope harder, but just as often each second. What changes?
   1. The amplitude: each wave is taller and carries more energy
   2. The wavelength: each wave gets longer
   3. The speed: the waves move along faster
9. A ship's sonar sends a pulse of sound down to the seabed. The echo comes back 0.80 s later. Sound travels at 1500 m/s in seawater. How deep is the sea there, in metres?
10. A radio station broadcasts at 100 MHz. Radio waves travel at 300 000 000 m/s. What is the wavelength, in metres?
11. Stretch: a wave's period is 0.04 s and its wavelength is 0.5 m. Its frequency is ___ Hz, so its speed is ___ m/s.

Support: Write the three quantities in a line with their units: v = ? m/s, f = ? Hz, λ = ? m. Change each into those units before anything else, then put them into v = f λ.

The wave equation: exit

Write v = f λ with each quantity and its unit first.

1. A wave on a rope has a frequency of 2.5 Hz and a wavelength of 1.6 m. What is its speed, in m/s?
2. The same rope is now shaken at 5 Hz. What is the wavelength now, in metres?

Exit check

A wave's speed, then the same rope shaken faster, shows who keeps the speed and shortens the wavelength.

A wave on a rope has frequency 2.5 Hz and wavelength 1.6 m: its speed?

The wave equation

Write v = f λ (or T = 1 ÷ f) first, turn every reading into Hz, m and s, then work it out. Give units with every answer.