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The Universal Wave Equation

The Universal Wave Equation. There is a relationship between frequency (f), speed (v) and wavelength ( λ ) If the source vibrates faster (greater frequency), the wavelength changes. This relationship is described by the universal wave equation v = f λ v – speed (m/s)

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The Universal Wave Equation

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  1. The Universal Wave Equation

  2. There is a relationship between frequency (f), speed (v) and wavelength (λ) • If the source vibrates faster (greater frequency), the wavelength changes

  3. This relationship is described by the universal wave equation v = fλ v – speed (m/s) f – frequency (Hz or 1/s) λ – wavelength (m)

  4. Sample Problem # 1: The wavelength along a rope is 3.5 m and the crests travel 11 m in 2.9 s. What is the frequency of the waves? Answer: f = 1.1 Hz

  5. Sample Problem # 2 The period of a wave from the radio is 8.3 x 107. If the speed of the wave in the air was 3.5 x 10-6 m/s, what is its wavelength? Answer: λ = 2.9 x 102 m

  6. Open End Reflection • Reflects back on the same side! http://surendranath.tripod.com/Applets/Waves/TWaveRefTran/TWRT.html

  7. Fixed End Reflection • Reflects back on the opposite side! http://surendranath.tripod.com/Applets/Waves/TWaveRefTran/TWRT.html

  8. Other Animations • http://paws.kettering.edu/~drussell/Demos/reflect/reflect.html • http://www.upscale.utoronto.ca/PVB/Harrison/Flash/#waves

  9. Transmission and Reflection of Waves

  10. As a wave goes in between mediums • Frequency is constant (depends on source) • Speed and wavelength will change depending on the medium http://faraday.physics.utoronto.ca/PVB/Harrison/Flash/Waves/TwoMediums/TwoMediums.html

  11. At a boundary between two mediums • Some reflection occurs at this boundary (called partial reflection) but the majority of the energy is transmitted

  12. Heavy Medium to Light Medium •  increases – speed increases • Acts like an open end reflection point (crest reflects as a crest) http://surendranath.tripod.com/Applets/Waves/TWaveRefTran/TWRT.html

  13. Light Medium to Heavy Medium •  decreases – speed decreases • Acts like a closed end reflection point (crest reflects as a trough) http://surendranath.tripod.com/Applets/Waves/TWaveRefTran/TWRT.html

  14. http://paws.kettering.edu/~drussell/Demos/reflect/reflect.htmlhttp://paws.kettering.edu/~drussell/Demos/reflect/reflect.html

  15. http://paws.kettering.edu/~drussell/Demos/reflect/reflect.htmlhttp://paws.kettering.edu/~drussell/Demos/reflect/reflect.html

  16. Practice – Universal Wave Equation 1.A machine with a frequency of 15.0 Hz produces water waves that have a wavelength of 4.0 cm. What is the speed of the waves? 2.A wave in a rope travels at a speed of 1.4 m/s. If the wavelength is 0.75 m, what is the period of the waves? 3.Waves travel along a wire at a speed of 10.0 m/s. Find the frequency and the period of the source if the wavelength is 0.10 m. 4.A given crest of water wave requires 2.6 s to travel between two points located 9.5 m apart on a fishing dock. It is noted in a series of waves that 26.4 crests pass the first point in 22 s. What is wavelength of the waves? 5.A sound wave travels at 347 m/s. What is the wavelength of a sound with a frequency of 1.2 x 103 Hz? 6.An FM station broadcasts radio signals with a wavelength of 2.904 m. What is the frequency in MHz? The speed of light (and radio waves) is 3.00 x 108 m/s. 7.What is the wavelength of Kiss 92.5 radio waves?

  17. Case 1: A pulse in a more dense medium is traveling towards the boundary with a less dense medium. 1. The reflected pulse in medium 1 ________ (will, will not) be inverted because _______. 2. The speed of the transmitted pulse will be ___________ (greater than, less than, the same as) the speed of the incident pulse. 3. The speed of the reflected pulse will be ______________ (greater than, less than, the same as) the speed of the incident pulse. 4. The wavelength of the transmitted pulse will be ___________ (greater than, less than, the same as) the wavelength of the incident pulse. 5. The frequency of the transmitted pulse will be ___________ (greater than, less than, the same as) the frequency of the incident pulse.

  18. Case 2: A pulse in a less dense medium is traveling towards the boundary with a more dense medium. 6. The reflected pulse in medium 1 ________ (will, will not) be inverted because _____________. 7. The speed of the transmitted pulse will be ___________ (greater than, less than, the same as) the speed of the incident pulse. 8. The speed of the reflected pulse will be ______________ (greater than, less than, the same as) the speed of the incident pulse. 9. The wavelength of the transmitted pulse will be ___________ (greater than, less than, the same as) the wavelength of the incident pulse. 10. The frequency of the transmitted pulse will be ___________ (greater than, less than, the same as) the frequency of the incident pulse.

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