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Example Which type of wave requires a material medium to travel through? a) Television b) Light c) Sound d) Radio e) X-ray Sound is a mechanical wave, and mechanical waves require a medium to travel through. Example A periodic wave transfers? a) Mass and Energy b) Mass only c) Energy only d) Neither Mass and Energy e) Sound Light, does not have mass, or sound effects, but any periodic wave does transfer energy, since energy was given to it to make it oscillate Example A periodic wave is produced when you hit one of the prongs of a tuning fork. To increase the amplitude of the wave, you would need to: a) Hit the prong harder b) Hit the prong faster c) Hit the prong slower d) Nothing, amplitude it fixed e) Shorten the prong When you hit the fork harder, you are transferring more energy to the fork, increasing the amplitude of the wave Example What is the period of a 50-Hz electromagnetic wave travelling at 3x108 m/s? a) 20s b) 2s c) 0.2s d) 0.02s e) 0.002s 1 1 T 0.02s f 50 Hz Example A periodic wave with a frequency of 10 Hz and a speed of 20 m/s has a wavelength of: a) 20m b) 2m c) 0.2m d) 0.02m e) 0.002m m v s 2m f 10 Hz 20 Example An electromagnetic wave with a wavelength of 2.0x10-1 m is travelling through a vacuum, What is its period? a) 20s b) 5s c) 3.0x108s d) 2.0x10-1s e) 6.7x10-10s 2.0 10 1 m v f T 6.7 10 10 s T v 3.0 108 m s Example The phenomenon that cause sound waves to shatter a glass cub is? a) Reflection b) Refraction c) Resonance d) Diffraction e) Interference Example If you have two waves travelling in the same medium with the same frequency and amplitude. The maximum destructive interference will occur when the phase difference between the two waves is: a) 0o b) 90o c) 180o d) 270o e) 360o Example When tuning a piano, a key produces a note of 150 Hz, when the next key is hit a beat pattern twice a second is heard. What could the frequency be for the second out of tune key? a) 152 Hz b) 75 Hz c) 300 Hz d) 148 Hz e) 2 Hz fbeat f2 f1 Example Two children create a standing wave when skipping. If the children are 4.60 metres apart, then determine the wavelength of this standing wave. a) 9.20 m b) 4.60 m c) 1.50 m d) 13.8 m e) 2.30 m This standing wave is ½ of the actual wavelength Example You design a string instrument in which the speed of the travelling waves are 400m/s. How long should the string be to produce the first fundamental frequency at 300Hz. a) 1.42 m b) 0.42 m c) 1.50 m d) 1.8 m e) 0.67 m v n f L 2 2 n Hint: m 1 400 nv s L 0.67m 2f 2 300 Hz Example You are given a 1m length of rope and you record the velocity of a pulse along this rope as 400 m/s. What frequency or frequencies could not be produced by the rope. a) 200 Hz b) 400 Hz c) 500 Hz d) 600 Hz e) 1200Hz Hint: 200 Hz is the fundamental frequency (or first harmonic), 400 Hz is the Second Harmonic (or first overtone), 600 Hz is the 3rd Harmonic (or second overtone, and 1200 Hz is the fourth Harmonic (or 3rd overtone). nv f 2L Example You are given four organ pipes with standing waves of the air displacement. Given that the speed of sound is 343 m/s. 2m a) Which pipe has the highest frequency and what is that frequency b) Which pipe has the lowest frequency and what is that frequency c) Which pipe has the longest wavelength and what is that wavelength d) Which pipe has the shortest wavelength and what is that wavelength Example You are given four organ pipes with standing waves of the air displacement. Given that the speed of sound is 343 m/s. a) Which pipe has the highest frequency and what is that frequency? b) Which pipe has the lowest frequency and what is that frequency? 2m nv 4L f f f f nv 4L nv 4L nv 2L f f f f 5 343 m s 214 Hz 3 343 m s 129 Hz 1 343 m s 42.9 Hz 3 343 m s 257 Hz 4 2m 4 2m 4 2m 2 2m Example You are given four organ pipes with standing waves of the air displacement. Given that the speed of sound is 343 m/s. c) Which pipe has the longest wavelength and what is that wavelength d) Which pipe has the shortest wavelength and what is that wavelength 2m 4L n 4 2m 8 m 4L n 4 2m 8 m 4L n 2L n 5 3 5 3 4 2m 8m 1 4 2m 8 m 3 3 Example You have a pipe that is closed at one end and open at the other. A tuning fork resonates when the pipe is 11 cm long. The same tuning fork does not resonate at any pipe smaller than this. At what other pipe length with the tuning fork resonate? a) 22 cm b) 33 cm c) 44 cm d) 55 cm e) 66 cm Solution You have a pipe that is closed at one end and open at the other. A tuning fork resonates when the pipe is 11 cm long. The same tuning fork does not resonate at any pipe smaller than this. At what other pipe length with the tuning fork resonate? 11 cm The wavelength of the wave then must be 44 cm Since the pipe is open at one end and closed at the other it has a node at the closed end and a antimode at the other The next harmonic oscillation occurs when there again is a anti-node at the open end, or 3 x 11cm = 33cm Example An ambulance’s siren produces a sound wave of constant frequency. As the ambulance accelerates away from you, you notice that the sound wave: a) Increases in amplitude and decreases in frequency b) Increases in amplitude and increases in frequency c) decreases in amplitude and decreases in frequency d) decreases in amplitude and increases in frequency e) Remains fixed in amplitude and decreases in frequency Because the ambulance is moving away, the frequency of the wave is decreasing, plus the sound gets lower in volume, so the amplitude also decreases. Example You inhale some helium, as a result, the pitch of your voice rises. What happens to the standing waves of your vocal cords to cause this effect a) The frequency of the waves decrease b) The speed of the waves decrease c) The speed of the waves increase d) The wavelength of the waves decrease e) The wavelength of the waves increase Since the pitch of your voice increases, the frequency must increase. The wavelength does not change (wavelength depends upon physicsal structure of your voice box). Therefore by v=λf, the speed of the waves must increase. (the speed of sound in helium is faster than in air) Example A siren is emitting sound at a frequency of 1500Hz and an observer is moving away from the siren at 100 m/s. Given that the speed of sound in the air is 340 m/s, determine the observed frequency of the siren. v v0 Hint: f f v vs m m 340 s 100 s f 1500 Hz m 340 s 12 f 1500 Hz 17 Since you and the source are moving away from each other, the frequency must be lower f 1060 Hz Example A rope is tied between two poles that are 8 m apart. Give two allowed standing wavelengths for this rope. Hint: 2 n L n 2 1 8m 1 16m 2 8m 2 8m 2 Use this formula for Fixed-Fixed conditions Example The distance between two successive nodes in a vibrating string is 10cm. Given that the frequency of the source is 30 Hz. What is there wavelength? Hint: d node 1 2 1 10cm 2 20cm Example A lightning flash is seen in the sky and 8.2 seconds later the boom of thunder is heard. The temperature of the air is 12.0 C. (a) What is the speed of sound in air at that temperature? v 331 0.606TC m/s The speed of sound in air of this temperature is 338 m/s. (b) How far away is the lightning strike? d vt 338 m/s 8.2 s 2800 m 2.8 km Example The speed of light is 3.00105 km/s. How long does it take the light signal to reach the observer? d t v 2.8 km 3.0 105 km/s 9.3 10 6 sec Example Two wave pulses with amplitude A are travelling towards each other along a rope. When they interfere, what is the maximum amplitude of the resulting collision when the wavelength of one wave is twice the wavelength of the other? AT A1 A2 2A Wavelength plays no role in determining the resultant amplitude. Example Given that a human’s ear vibrates with an amplitude of 2.0x10-10 m. when listening to a 4 kHz sound. What is the total distance will the eardrum move in 1 minute? Hint: Find number of cycles in 1 minute cycles cycles 60 s 4000 s 240000 d 2 2.0 10 10 m 240000 9.6 10 5 m Example A sound wave in air moves at a speed of 340 m/s. Which is the closest to the wavelength of middle C (f=256 Hz) v f m 340 s 256 Hz 1.33m Wavelength plays no role in determining the resultant amplitude.