P1.5 – Measuring Waves

P1.5 – Measuring Waves Learning Objectives: Calculate how fast a wave travels Skills objective: Checking units

How big??

Units and size

SI Units To avoid problems like these we came up with the International System of Units (SI units) These are a set of units that everyone must use when carrying out calculations.

Meters, kilometers or centimeters? Units tell us what type of number we are talking about. For example, 2m means we are talking about a distance. Sometimes that unit has a prefix. This tells us about how big or small the value is. For example, 2mili-meters is a smaller distance than 2kilo-meters. The most common prefixes are, (in order of size) Meters (m) Millimeters (mm) Thousandths Centimeters (cm) Hundredths Kilometers (km) Thousands Megameters (Mm) Millions

Changing between prefixes • It’s hard to remember all of the rules (do you divide by 1000 or times? Is it 100 or 1000?) • Instead, try to remember what each means

Converting between pre-fixes Kilo = thousand, so 1km is “1 thousand meters” Or 2.5km is “2.5 thousand meters” 1 km = 1000m What do you have to do to get from m to km? What do you have to do to get from km to m?

Converting between pre-fixes Mega = a million, so 1Mm is “1 million meters” Or 2.5Mm is “2.5 million meters” 1 Mm = 1,000,000m What do you have to do to get from m to Mm? What do you have to do to get from Mm to m?

Converting between pre-fixes Milli is a thousandth, so 1mm is “1 thousandth of a meter” Or 1000mm is meter 1000mm = 1m What do you have to do to get from m to mm? What do you have to do to get from mm to m?

Converting between pre-fixes Centi is a hundredth, so 1cm is “1 hundredth of a meter” Or 100cm is meter 100cm = 1m What do you have to do to get from m to cm? What do you have to do to get from cm to m?

Converting between pre-fixes Try these together • How many m in 1000km? • How many cm in 5m? • How many mm in 500m? • How many m in 2000Mm?

Wave speed You can also calculate how fast a wave will travel using this equation: • Wavespeed = wavelength x frequency (m/s) (m) (Hz) If a wave has a wavelength of 2m and a frequency of 1Hz, what will the wave speed be?

Putting it all together • We are going to apply all of these new rules to a new formula • The Silly Wave Formula

Wavespeed = wavelength x frequency (m/s) (m) (Hz) What is the frequency of a wave of wavelength 2km travelling at 0.5m/s. • Are there any difficult units? • Do I need to rearrange the equation? • Now I can put the numbers in!

Answers • The speed of a wave with a frequency of 1kHz and a wavelength of 2m. v = f x λ v = 1000 x 2 v = 2000m/s

Answers • The speed of a wave with a wavelength of 50m and a frequency of 4Hz v = f x λ v = 4 x 50 v = 200m/s

Answers • The frequency of a wave travelling at 500m/s with a wavelength of 25m f = v ÷ λ f = 500 ÷ 25 f = 20Hz

Answers • The speed of a radio wave with a wavelength of 3000m and a frequency of 100Hz v = f xλ v = 100 x 3000 v = 300,000 m/s

Answers • The speed of a wave with a frequency of 30kHz and wavelength of 10cm v = f xλ v = 30,000 x 0.1 v = 3,000 m/s

Answers • The wavelength of a wave travelling at 11km/s with a frequency of 5.5kHz λ = v ÷ f λ = 11,000 ÷ 5,500 λ = 2m

Answers • The frequency of the wave below, which is travelling at 9km/s f = v ÷ λ f = 9,000 ÷ 0.03 f = 300,000Hz or 300kHz 3cm = 0.03m

Plenary • Make a flow chart for the steps you would take to solve this problem Q1. A wave is travelling at 5mm/s and it has a frequency of 4KHz. What is the wavelength of this wave? Write the equation that I need to answer this question

P1.5 – Measuring Waves