Wave Equation 8.1

The Wave Equation The wave equation relates the speed of the wave to its frequency and wavelength: Wave speed (v) = frequency (f) x wavelength ( ) in m/s in Hz in m

Wave Equation Wave velocity - the velocity at which wave crests (or any other part of the wave) move. v = λfv = λf But f = 1/T so… v = λ/T Velocity of electromagnetic waves is 3.0x10 8 m/s

Wave Speed Example 1 A spring vibrates at 2.8 Hz. This produces a wave with wavelength 36cm. Calculate the speed of the wave. Answer: v = fλ v = (2.8)(0.36) = m/s = 1.0m/s

Example 2 Water waves with wavelength 1.8m produced in a wave tank travel with a speed of 2.50 m/s. What is the frequency of the vibrations that produced them? Answer: v = fλ  f = v/ λ f = 2.50/1.8 f = 1.4 Hz

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Solution

Try These Page 349, questions 5, 6 Page 350, questions 7, 8a/b, 9

Question 5

Worksheet – all but question 10 (specifically questions 8 and 9)

Quick Review of Waves 1) What type(s) of wave is a sound wave? 2) What type(s) of wave is a light wave? 3) What do all waves need? 4) What is the difference between electromagnetic waves and mechanical waves?

1) Longitudinal, mechanical 2) Transverse, electromagnetic 3) Wave pulse/vibration/disturbance/force to start wave AND energy to transfer via the wave 4) Electromagnetic waves don’t need a medium for energy to travel through

Quick Review Part 2 5) Draw a surface wave. 6) Draw a transverse wave and label the following: –Amplitude, wavelength, crest, trough, period, equilibrium position 7) Write the wave equation.

5) Circles going outward 6) Perpendicular wave (wave goes up/down while energy goes left/right) 7) v = lambda x f

Question 1 a)What is the amplitude of this wave? b)What is the wavelength? c)What is the frequency of the waves (hint: how many waves are shown here for this 2 second diagram)? d) What is the wave speed?

Question 1 Answers a)Amp = 0.4m b)Lambda = 2m c)2 waves per 2 second = 1 Hz d) V = (1)(2) = 2 m/s

Question 2

Question 2 Answers a)f = 10 Hz (10 waves per second) b)V = d/t = 30/6 = 5 m/s c)Wavelength = 0.5 m

Question 3 ** For this question you need to know the speed of radio waves = 300,000,000 m/s

Question 3 Answers ** For this question you need to know the speed of radio waves = 300,000,000 m/s a)0.001 s b) Hz

Question 4 While hiking through a canyon, Noah Formula lets out a scream. An echo (reflection of the scream off a nearby canyon wall) is heard 0.82 seconds after the scream. The speed of the sound wave in air is 342 m/s. Calculate the distance from Noah to the nearby canyon wall.

Answer If it takes 0.82 s to travel to the canyon wall and back (a down-and-back time), then it takes 0.41 s to travel the one-way distance to the wall. Now use d = v t d = v t = (342 m/s) (0.41 s) = 140 m

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Worksheet HW Probe