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Wave Speed

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===About Wave Speed===
: [[Wave Speed]] is measured in [[metres per Second|metres per second]].
: The '''wave speed''' states how quickly [[energy]] and [[information]] can be transferred by a [[wave]].
 
===Equation===
====Equation 1====
<math>v = \dfrac{x}{t}</math>
 
Where:
 
v = '''Wave Speed'''
 
x = distance traveled
 
t = time taken to travel
 
====Equation 2====
 
<math>v = f \lambda</math>
 
<math>v = f \times \lambda</math>
 
Where:
 
v = '''Wave Speed'''
 
f = [[frequency]] of the [[wave]]
 
λ = [[wavelength]] of the [[wave]]
 
==Key Stage 4==
===Meaning===
[[Wave Speed]] is how quickly a [[wave]] travels through a [[medium]].
 
===About Wave Speed===
: '''Wave speed''' is a [[scalar]] because it has [[magnitude]] only.
: The [[SI Unit]] of [[Wave Speed|wave speed]] is [[Metres per Second|metres per second]].
: The '''wave speed''' states how quickly [[energy]] and [[information]] can be transferred by a [[wave]].
: '''Wave speed''' can change depending on the [[medium]] the [[wave]] is travelling through.
: When a [[wave]] enters a new [[medium]] it will change in [[speed]].
 
===Equation===
====Equation 1====
<math>v = \dfrac{x}{t}</math>
 
Where
 
v = '''Wave Speed'''
 
x = distance traveled
 
t = time taken to travel
 
====Equation 2====
<math>v = f \lambda</math>
 
Where:
 
v = '''Wave Speed'''
 
f = [[frequency]] of the [[wave]]
 
λ = [[wavelength]] of the [[wave]]
 
===Example Calculations===
 
====Finding Wave Speed from Distance Travelled and Time Taken====
{| class="wikitable"
| style="height:20px; width:300px; text-align:center;" |A scientist [[observe]]s a [[wave]] in a ripple tank. The length of the tank is 0.75m and it takes the [[wave]] 1.2 seconds to get from one end of the tank to the other. Calculate the '''wave speed''' of the [[wave]] correct to two [[Significant Figures|significant figures]].
| style="height:20px; width:300px; text-align:center;" |A surfer wants to know how fast the [[wave]]s are travelling on a windy day. The surfer observes a [[wave]] takes 15 [[second]]s to travel between two buoys. The surfer knows the distance between the buoys is 63m. Calculate the [[speed]] of the [[wave]] correct to two [[Significant Figures|significant figures]].
|-
| style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
 
x = 0.75m
 
t = 1.2s
| style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
 
x = 63m
 
t = 15s
|-
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].'''
 
<math>v = \dfrac{x}{t}</math>
 
<math>v = \dfrac{0.75}{1.2}</math>
 
<math>v = 0.625m/s</math>
 
<math>v \approx 0.63m/s</math>
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].'''
 
<math>v = \dfrac{x}{t}</math>
 
<math>v = \dfrac{63}{15}</math>
 
<math>v = 4.2m/s</math>
|}
 
====Finding Wave Speed from Wavelength and Frequency====
{| class="wikitable"
| style="height:20px; width:300px; text-align:center;" |A [[Water Wave|water wave]] has a [[wavelength]] of 1.6m and a frequency of 1.5Hz. Calculate the [[speed]] of the [[wave]].
| style="height:20px; width:300px; text-align:center;" |A ray of [[ultraviolet]] [[light]] with a [[frequency]] of 7.5x10<sup>14</sup>Hz and [[wavelength]] of 0.30μm in an [[Optical Fibre|optical fibre]]. Calculate the [[speed]] of the [[wave]] through that [[Optical Fibre|optical fibre]] correct to 2 [[Significant Figures|significant figures]].
|-
| style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
 
f = 1.5Hz
 
λ = 1.6m
| style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
 
f = 7.5x10<sup>14</sup>Hz
 
λ = 0.30μm = 0.30x10<sup>-6</sup>m
|-
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].'''
 
<math>v = f \lambda</math>
 
<math>v = 1.5 \times 1.6</math>
 
<math>v = 2.4m/s</math>
 
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].'''
 
<math>v = f \lambda</math>
 
<math>v = 7.5 \times 10^14 \times 0.30 \times 10^{-6}</math>
 
<math>v = 225000000m/s</math>
 
<math>v \approx 2.3 \times 10^8 m/s</math>
|}
 
====Finding Wavelength using Wave Speed and Frequency====
 
{| class="wikitable"
| style="height:20px; width: 300px; text-align:center;" |A [[wave]] with [[frequency]] 700Hz travels at a [[speed]] of 340m/s. Calculate the [[wavelength]] of the [[wave]] correct to two [[Significant Figures|significant figures]].
| style="height:20px; width: 300px; text-align:center;" |A 630MHz [[radiowave]] travels at 300,000,000m/s in a [[vacuum]]. Calculate the [[wavelength]] of this [[radiowave]] correct to two [[Significant Figures|significant figures]].
|-
| style="height:20px; width: 300px; text-align:left;" |'''1. State the known quantities'''
 
f = 700Hz
 
v = 340m/s
| style="height:20px; width: 300px; text-align:left;" |'''1. State the known quantities'''
 
f = 630MHz = 630x10<sup>6</sup>Hz
 
v = 300,000,000m/s = 3x10<sup>8</sup>m/s
|-
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
 
<math>v = f \lambda</math>
 
<math>340 = 700 \times \lambda</math>
 
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
 
<math>v = f \lambda</math>
 
<math>3 \times 10^8 = 630 \times 10^6 \times \lambda</math>
|-
| style="height:20px; width: 300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
 
<math> \lambda = \dfrac{340}{700}</math>
 
<math> \lambda = 0.48571m</math>
 
<math> \lambda \approx 0.48m</math>
 
| style="height:20px; width: 300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
 
<math> \lambda = \dfrac{630 \times 10^6}{3 \times 10^8}</math>
 
<math> \lambda = 2.1m</math>
|}
 
====Finding Frequency using Wave Speed and Wavelength====
 
{| class="wikitable"
| style="height:20px; width:300px; text-align:center;" |A [[microwave]] travelling at a speed of 3.0x10<sup>8</sup>m/s has a [[wavelength]] of 0.051m. Calculate the [[frequency]] of the [[wave]] correct to two [[Significant Figures|significant figures]].
| style="height:20px; width:300px; text-align:center;" |An [[ultrasound]] [[wave]] of [[wavelength]] 0.125m passes through an [[Iron]] block at a [[speed]] of 5000m/s. Calculate the [[frequency]] of the [[wave]] correct to two [[Significant Figures|significant figures]].
|-
| style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
 
v = 3.0x10<sup>8</sup>m/s
 
λ = 0.051m
| style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
 
v = 5000m/s
 
λ = 0.125m
|-
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
 
<math>v = f \lambda</math>
 
<math>3.0 \times 10^8 = f \times 0.051</math>
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
 
<math>v = f \lambda</math>
 
<math>5000 = f \times 0.125</math>
|-
| style="height:20px; width:300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
 
<math> f = \dfrac{3.0 \times 10^8}{0.051}</math>
 
<math> f = 5882352941Hz</math>
 
<math> f \approx 5900000000Hz</math>
| style="height:20px; width:300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
 
<math> f = \dfrac{5000}{0.125}</math>
 
<math> f = 40000Hz</math>
|}
 
===References===
====AQA====
 
:[https://www.amazon.co.uk/gp/product/019835939X/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=019835939X&linkCode=as2&tag=nrjc-21&linkId=57e96876985fc39b1a3d8a3e3dc238b6 ''Wave speed, pages 176-177, 186-187, 190-191, GCSE Physics; Third Edition, Oxford University Press, AQA '']
:[https://www.amazon.co.uk/gp/product/1782945598/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945598&linkCode=as2&tag=nrjc-21&linkId=ad276ad49df77ab4b40ab4fd0fe10425 ''Wave speed, pages 220, 221, GCSE Combined Science; The Revision Guide, CGP, AQA '']
:[https://www.amazon.co.uk/gp/product/1471851362/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1471851362&linkCode=as2&tag=nrjc-21&linkId=7d78d70a2044ee9982dae010c94af92a ''Wave speed, pages 258, GCSE Combined Science Trilogy 2, Hodder, AQA '']
:[https://www.amazon.co.uk/gp/product/178294558X/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=178294558X&linkCode=as2&tag=nrjc-21&linkId=f0dfb66dafcb0c6e9449e7b1a4ae1ac499 ''Wave speed, pages 73, 74, 76, GCSE Physics; The Revision Guide, CGP, AQA '']
:[https://www.amazon.co.uk/gp/product/1471851362/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1471851362&linkCode=as2&tag=nrjc-21&linkId=7d78d70a2044ee9982dae010c94af92a ''Wave speed; Electromagnetic waves, pages 262, GCSE Combined Science Trilogy 2, Hodder, AQA '']
:[https://www.amazon.co.uk/gp/product/1471851370/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1471851370&linkCode=as2&tag=nrjc-21&linkId=01c69b0ae058f809cf636033e6ba793e ''Wave speed; measurement of, pages 185-6, GCSE Physics, Hodder, AQA '']
:[https://www.amazon.co.uk/gp/product/1471851362/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1471851362&linkCode=as2&tag=nrjc-21&linkId=7d78d70a2044ee9982dae010c94af92a ''Wave speed; Measurement of, pages 259, GCSE Combined Science Trilogy 2, Hodder, AQA '']
:[https://www.amazon.co.uk/gp/product/1471851370/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1471851370&linkCode=as2&tag=nrjc-21&linkId=01c69b0ae058f809cf636033e6ba793e ''Waves speed, page 184, GCSE Physics, Hodder, AQA '']
:[https://www.amazon.co.uk/gp/product/1782945598/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945598&linkCode=as2&tag=nrjc-21&linkId=ad276ad49df77ab4b40ab4fd0fe10436
 
====OCR====
:[https://www.amazon.co.uk/gp/product/1782945695/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945695&linkCode=as2&tag=nrjc-21&linkId=ceafcc80bcad6b6754ee97a0c7ceea53 ''Wave speed, pages 187, 188, Gateway GCSE Combined Science; The Revision Guide, CGP, OCR '']
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