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Mathematics of Waves
Harmonics
Conceptual wave problem
Light
100
Two waves are traveling through the same container of nitrogen gas. Wave A has a wavelength of 1.5 m. Wave B has a wavelength of 4.5 m. The speed of wave B must be ________ the speed of wave A.
same
100
If the frequency in the first harmonic is 250 Hz what is the frequency in the third harmonic?
750Hz
100
A __________ is a wave in which particles of the medium move in a direction parallel to the direction that the wave moves.
longitudinal wave
100
Which color of the visible light spectrum has the highest frequency
violet
200
Frieda the fly flaps its wings back and forth 121 times each second. The period of the wing flapping is ____ sec.
.00826s
200
A frequency of the first harmonic is 587 Hz (pitch of D5) is sounded out by a vibrating guitar string. The speed of the wave is 600 m/sec. Find the length of the string.
λ = v / f = (600 m/s) / (587 Hz) = 1.02 m For the first harmonic, the length of the string is one-half the wavelength of the wave (see Tutorial page). Thus, the following calculation can be performed: L = 0.5 • 1.02 m = 0.51 m
200
In a diagram of a wave, how do you get wavelength.
measure crest to crest
200
Which color of the visible light spectrum has the longest wavelength
red
300
Mac and Tosh are resting on top of the water near the end of the pool when Mac creates a surface wave. The wave travels the length of the pool and back in 25 seconds. The pool is 25 meters long. Determine the speed of the wave.
2 m/s
300
Determine the length of guitar string required to produce a fundamental frequency (1st harmonic) of 256 Hz. The speed of waves in a particular guitar string is known to be 405 m/s.
.791m
300
The ____ of a wave refers to how often the particles of the medium vibrate when a wave passes through the medium.
frequency
300
Which region of the electromagnetic spectrum has the highest frequency
gamma
400
Ocean waves are observed to travel along the water surface during a developing storm. A Coast Guard weather station observes that there is a vertical distance from high point to low point of 4.6 meters and a horizontal distance of 8.6 meters between adjacent crests. The waves splash into the station once every 6.2 seconds. Determine the frequency
.161 Hz
400
A guitar string with a length of 80.0 cm is plucked. The speed of a wave in the string is 400 m/sec. Calculate the frequency of the first harmonic.
Let λ = wavelength. λ = 2• L = 2 • (0.80 m) = 1.6 m Now rearrange the wave equation v = f • λ to solve for frequency. f1 = v / λ = (400 m/s) / (1.6 m) = 250 Hz
400
The amount of energy carried by a wave is related to the ___ of the wave. A high energy wave is characterized by a high ____
amplitude
400
Which region of the electromagnetic spectrum has the longest wavelength
radio
500
Ocean waves are observed to travel along the water surface during a developing storm. A Coast Guard weather station observes that there is a vertical distance from high point to low point of 4.6 meters and a horizontal distance of 8.6 meters between adjacent crests. The waves splash into the station once every 6.2 seconds. Determine speed of these waves.
1.4 m/s
500
A flute is played with a first harmonic of 196 Hz The length of the air column is 89.2 cm (quite a long flute). Find the speed of the wave resonating in the flute
350 m/s
500
______is a type of interference that occurs at any location along the medium where the two interfering waves have a displacement in the same direction
Constructive interference
500
Which region of the electromagnetic spectrum will travel with the fastest speed
same speed