{"id":2137,"date":"2022-12-29T10:00:00","date_gmt":"2022-12-29T04:30:00","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=2137"},"modified":"2022-12-30T09:45:04","modified_gmt":"2022-12-30T04:15:04","slug":"relation-between-wave-velocity-frequency-wavelength","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/relation-between-wave-velocity-frequency-wavelength\/","title":{"rendered":"What Is The Relation Between Wave Velocity, Frequency And Wavelength"},"content":{"rendered":"

Relation Between Wave Velocity, Frequency And Wavelength\u00a0For A Periodic Wave<\/strong><\/h2>\n

\\( \\text{wave velocity}=\\frac{\\text{distance covered}}{\\text{Time}\\,\\,\\text{taken}} \\)
\n\\( =\\frac{\\text{wave}\\,\\text{length}}{\\text{Time}\\,\\text{taken}} \\)
\n\\( \\text{or v}=\\frac{\\lambda }{T}\\text{ }……\\text{ (1)} \\)
\n\\( \\text{since }\\!\\!~\\!\\!\\text{ }v=\\frac{\\text{1}}{\\text{T}}\\text{, equation }\\left( \\text{1} \\right)\\text{ can also be written as} \\)
\n\\( \\text{v}=v\\lambda \\text{ }……\\text{ (2)} \\)
\nWave Velocity = Frequency \u00d7 Wave Length<\/strong><\/p>\n

Relation Between Wave Velocity, Frequency And Wavelength Example Problems With Solutions<\/strong><\/h2>\n

Example 1:<\/strong> \u00a0 \u00a0If 50 waves are produced in 2 seconds, what is its frequency ?
\nSolution:<\/strong>\u00a0 \u00a0 Frequency,
\n\\( v=\\frac{\\text{Number}\\,\\text{of}\\,\\text{wave}\\,\\text{produced}}{\\text{Time}\\,\\text{taken}} \\)
\n\\( =\\frac{50}{2}=25\\text{ Hz} \\)<\/p>\n

Example 2:<\/strong> \u00a0 \u00a0A source produce 50 crests and 50 troughs in 0.5 second. Find the frequency.
\nSolution:<\/strong>\u00a0 \u00a0 1 crest and 1 trough = 1 wave
\n\u2234 50 crests and 50 troughs = 50 waves
\n\\( \\text{Now, Frequency, }v=~\\frac{\\text{Number}\\,\\text{of}\\,\\text{wave}}{\\text{Time}} \\)
\n\\( =\\frac{50}{0.5}=100\\text{ Hz} \\)<\/p>\n

Example 3:<\/strong> \u00a0 \u00a0Sound waves travel with a speed of 330 m\/s. What is the wavelength of sound waves whose frequency is 550 Hz ?
\nSolution:<\/strong>\u00a0 \u00a0 Given velocity, v = 330 m\/s,
\nFrequency, \\(\\upsilon\\)\u00a0= 550 Hz
\n\\(\\therefore \\text{ }wavelength,~~\\text{ }\\lambda =\\frac{\\text{v}}{\\upsilon }\\)
\n\\( =\\frac{330}{550}=0.6\\text{ }m \\)<\/p>\n

Example 4:<\/strong> \u00a0 \u00a0The wave length of sound emitted by a source is 1.7 \u00d7 10-2<\/sup> m. Calculate frequency of the sound, if its velocity is 343.4 ms-1<\/sup>.
\nSolution:<\/strong>\u00a0 \u00a0 The relation ship between velocity, frequency and wave length of a wave is given by the formula v = \\(\\upsilon\\)\u00a0\u00d7 \u03bb
\nHere, velocity, v = 343.4 ms-1<\/sup>
\nfrequency \\(\\upsilon\\)\u00a0= ?
\nand wavelength, \u03bb= 1.7 \u00d7 10-2<\/sup> m
\nSo, putting these values in the above formula, we get :
\n343.4 = \\(\\upsilon\\)\u00a0\u00d7 1.7 \u00d7 10-2<\/sup>
\n\\( v=\\frac{343.4}{1.7\\times {{10}^{-2}}} \\)
\n\\( =\\frac{343.4\\,\\times {{10}^{2}}}{1.7} \\)
\n= 2.02 \u00d7 104<\/sup> Hz
\nThus, the frequency of sound is 2.02 \u00d7 104<\/sup> hertz.<\/p>\n

Example 5:<\/strong> \u00a0 \u00a0A wave pulse on a string moves a distance of 8m in 0.05 s.
\n(i) Calculate the velocity of the pulse.
\n(ii) What would be the wavelength of the wave on the same string, if its frequency is 200 Hz ?
\nSolution:<\/strong>\u00a0 \u00a0 (i) Velocity of the wave,
\n\\( \\text{v}=\\frac{\\text{Distance covered}}{\\text{Time}\\,\\text{taken}}=\\frac{8m}{0.05s}=160\\text{ m\/s} \\)
\n(ii) Periodic wave has the same velocity as that of the wave pulse on the same string.
\n\\( \\therefore \\text{ Wavelength, }\\lambda =~\\frac{\\text{v}}{v}=~\\frac{160\\,m\/s}{200\\,Hz}~=0.8\\text{m} \\)
\nThus, the wavelength of the wave is 0.8 m.<\/p>\n

Example 6:<\/strong> \u00a0 \u00a0A person has a hearing range of 20 Hz to 20 kHz. What are the typical wavelengths of sound waves in air corresponding to these two frequencies ? Take the speed of sound in air as 340 m\/s.
\nSolution:<\/strong>\u00a0 \u00a0 Given : \\({{v}_{1}}\\)\u00a0= 20 Hz, V = 340 m\/s
\n\\( \\therefore \\text{ }{{\\lambda }_{1}}=\\frac{\\text{v}}{{{v}_{1}}}=\\frac{340}{20}=17\\text{ m} \\)
\n\\({{v}_{2}}\\) = 20 kHz = 20,000 Hz, v = 340 m\/s
\n\\( \\therefore \\text{ }{{\\lambda }_{2}}=\\frac{\\text{v}}{{{v}_{2}}}=\\frac{340}{20,000}=1.7\\times {{10}^{-2}}m=1.7cm \\)
\n\u2234 The typical wavelengths are 17 m and 1.7 cm.<\/p>\n

Example 7:<\/strong> \u00a0 \u00a0A longitudinal wave is produced on a toy string. The wave travels at a speed of 30 cm\/s and the frequency of the wave is 20 Hz. What is the minimum separation between the consecutive compressions of the string ?
\nSol. Given, Velocity, v = 30 cm\/s
\nFrequency, \\(\\upsilon\\)\u00a0= 20 Hz
\nMinimum separation between the two consecutive compressions is equal to one wavelength \u03bb and
\n\\(\\lambda =\\frac{\\text{v}}{v}=\\frac{30\\,cm\/s}{20\\,Hz}=1.5\\text{ cm}\\)<\/p>\n

Example 8:<\/strong> \u00a0 \u00a0Wave of frequency 200 Hz produced in a string is represented in figure. Find out the following
\n\"Wave-of-frequency\"
\n(i) amplitude
\n(ii) wavelength
\n(iii) wave velocity
\nSolution:<\/strong>\u00a0 \u00a0 (i) Amplitude = Maximum displacement = 10 cm
\n(ii) Wavelength \u03bb = Distance between two successive crests = 40 cm
\n(iii) Now, frequency, n = 2 Hz
\nWavelength, \u03bb= 40cm = 0.4 m
\n\u2234 Wave velocity, v = \\(\\upsilon\\)\u03bb
\n= 200 \u00d7 0.4 m\/s
\n= 80m\/s<\/p>\n

Example 9:<\/strong> \u00a0 \u00a0A stone is dropped into a well 44.1 m deep. The sound of splash is heard 3.13 seconds after the stone is dropped. Calculate the velocity of sound in air.
\nSolution:<\/strong>\u00a0 \u00a0 First we calculate the time taken by the stone to reach the water level by using the relation:
\ns = ut + \\(\\frac { 1 }{ 2 }\\) gt2<\/sup>
\nHere s = 44.1 m, u = 0, g = 9.8 m\/s2<\/sup>
\n\u2234 44.1 = 0 \u00d7 t + \\(\\frac { 1 }{ 2 }\\) \u00d7 9.8 \u00d7 t2<\/sup>
\n\\( {{t}^{2}}=\\frac{44.1\\times 2}{9.8}=9 \\)
\nor t = 3 s
\nTime taken by the sound to reach the top of the well
\nt2<\/sub>\u00a0= 3.13 \u2013 3 = 0.13 s
\nNow, speed of sound
\n\\( \\frac{\\text{Distance}}{\\text{Time}}=\\frac{44.1\\,m}{0.13\\,s}=339.2\\text{ m\/s} \\)<\/p>\n","protected":false},"excerpt":{"rendered":"

Relation Between Wave Velocity, Frequency And Wavelength\u00a0For A Periodic Wave Wave Velocity = Frequency \u00d7 Wave Length Relation Between Wave Velocity, Frequency And Wavelength Example Problems With Solutions Example 1: \u00a0 \u00a0If 50 waves are produced in 2 seconds, what is its frequency ? Solution:\u00a0 \u00a0 Frequency, Example 2: \u00a0 \u00a0A source produce 50 crests […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[404],"tags":[585,882,881,895,584],"yoast_head":"\nWhat Is The Relation Between Wave Velocity, Frequency And Wavelength - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/relation-between-wave-velocity-frequency-wavelength\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What Is The Relation Between Wave Velocity, Frequency And Wavelength\" \/>\n<meta property=\"og:description\" content=\"Relation Between Wave Velocity, Frequency And Wavelength\u00a0For A Periodic Wave Wave Velocity = Frequency \u00d7 Wave Length Relation Between Wave Velocity, Frequency And Wavelength Example Problems With Solutions Example 1: \u00a0 \u00a0If 50 waves are produced in 2 seconds, what is its frequency ? 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