Electromagnetic and mechanical waves are both studied in GCSE Science. This is the fourth of six quizzes on waves and it looks at the wave equation, which describes the relationship between velocity, frequency and wavelength.

There are two types of wave - transverse and longitudinal. Each has its own properties but all waves have one thing in common - they obey the **wave equation**. This shows how the speed of the wave is related to the frequency and the wavelength, and knowing any two of them can be used to calculate the missing value. It allows you to predict what effect making any changes will have on the wave. The wave equation is:

**v = fλ**, using the scientific symbols, or **speed of the wave = frequency of the wave x wavelength of the wave** in plain English.

1 .

Wave frequency is measured in which unit?

Hertz

Seconds

Wave-seconds

Gauss

One Hz = one wave passing per second. Gauss are the units of magnetism and wave-seconds don't exist

2 .

A keyboard player plays a note of 440 Hz. What does this mean?

It is painfully loud

It cannot be heard by human ears

440 waves reach the listener's ear each second

It has an amplitude of 440 cm

The normal range of human hearing is 20 Hz to 20 kHz. The frequency tells you how many waves reach a given point (or go past an observer) in a second

3 .

If a wave of 440 Hz travels at 340 m/s, what is its wavelength?

0.772 m

0.772 Hz

1.29 m

14.96 km

You need to rearrange the wave equation to ë = v/f

4 .

What is the wavelength of the microwaves used by a mobile phone operator that uses microwaves with a frequency of 1.8 x 10^{9} Hz and which travel at a speed of 3.0 x 10^{8} m/s to transmit their signals?

17 cm

17 m

1.7 cm

1.7 m

Working with powers of ten can be tricky. Make sure you do a rough calculation using the powers of ten so that you know if your final answer is in the right area

5 .

Electromagnetic waves travel through space at a speed of 3.0 x 10^{8} m/s. The radio waves emitted from a distant galaxy have a wavelength of 25 metres. What is the frequency of the radio waves emitted from the galaxy?

8.33 MHz

8.33 x 10^{8} Hz

12 MHz

12 mhz

The difference between the last two answers is the units - mhz is wrong because the capitalisation is incorrect. As well as checking that you can rearrange the wave equation, it tests if you are aware of the correct way to write units

6 .

Electromagnetic waves travel at a speed of 3.0 x 10^{8} m/s through the air. A radio station transmits using waves with a wavelength of 1.9 x 10^{2} m. At what frequency would you need to set your radio to receive this particular station's programmes?

1578 m

1578 Mhz

1578 kHz

1.578 kHz

Did you get the rearranged equation the correct way up?

7 .

A group of students carried out an experiment using a ripple tank. They measured the frequency of a wave as being 14 Hz with a total of 20 wave crests in the tank. The tank was 40 cm long. How fast was the wave travelling?

28 m/s

2.8 m/s

0.28 cm/s

0.28 m/s

When dealing with complex questions like this, you need to break them down into smaller steps. To do that, start from the equation you need to work out the speed v = fë. You have the frequency and need the wavelength. So you then look at the other information to see how you can work out the wavelength from the data. Once you have that, it is a simple matter of plugging the figures into the equation

8 .

What is the wavelength of the musical note middle C? It has a frequency 256 Hz and the speed of sound is 335 m/s.

131 cm

13.1 m

0.76 m

7.6 cm

You will see various different values for the speed of sound because it varies according to the air pressure

9 .

Waves are diffracted when they pass through a gap that is about the same width as their wavelength. What width of gap would be required to cause microwaves of frequency 1.5 x 10^{10} Hz to diffract?

1 m

2 cm

3 km

4 mm

This is a wavelength question, but slightly disguised! We didn't give you the speed of the waves because, by now, you should know that microwaves travel at the same speed as all electromagnetic waves - 3 x 10^{8} m/s. That is actually the speed they travel in a vacuum but it isn't much different in other media

10 .

Snakes swim by vibrating their body from side to side, just like a transverse wave. The faster they vibrate, the faster they move through the water. A 90 cm long snake in a lake travels with a velocity of 1.8 m/s. At what frequency does it vibrate its body?

1 Hz

2 Hz

3 Hz

4 Hz

A nice easy finish for you, hopefully you did this one using mental arithmetic - 1.8 (m/s) divided by 0.9 (m). Mental arithmetic can save time in the exams but is not always possible

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