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Fred is standing outside the SAU when an earthquake hits the RIT campus, coming from the east. Looking towards the dorms (1/4 mile = 0.4 km away), Fred sees ripples in the walkway, coming towards him.

**Question 1:** Is this a transverse or longitudinal wave?

Answer: Since the ripples are visible to Fred, they must be in the vertical plane -- up and down. The wave is travelling east to west, perpendicular to the displacement. -> transverse

The first ripple reaches him 1.5 seconds after it first appeared at the dorms.

**Question 2: **What is the speed of the wave?

Answer: the wave travels 400 meters in 1.5 seconds 400 meters speed = -------------- = 267 m/s 1.5 sec

Just before the first crest reaches him, he can see 4 other crests in the walkway behind it.

**Question 3:** What is the wavelength of the wave?

Answer: there are two ways to interpret this question (my mistake). One way is to imagine that, just as one crest reaches Fred, he can see three others, plus one more _just_ exactly at the dorm. In that case, 4 crests span the entire distance 400 m -> wavelength = ----------- = 100 m 4 crests The other way to interpret the question is to imagine that, just as one crest reaches Fred, he can see clearly 4 other crests in the walkway between himself and the dorm. There could be a fifth crest _just_ about to emerge from under the dorm. In this case, 400 m -> wavelength = ----------- = 80 m 5 crests I accepted any answer between these two limits.

The crest of the wave raises Fred 30 cm above its trough.

**Question 4:** What is the amplitude of the wave?

Answer: the amplitude is the maximum displacement of the wave from the rest position. The distance crest-to-rest is one amplitude, and the distance rest-to-trough is also one amplitude; thus, crest-to-trough is two times the amplitude amplitude A = 0.5 * 30 cm = 15 cm

**Question 5: **The earthquake lasts for 10 seconds. How many times is
Fred raised upwards during that span of time?

Answer: the frequency of a wave is the number of times per second that wave crests pass a fixed point. If the frequency of the wave is "f", Fred will be raised upwards "f" times each second. In 10 seconds, he'll be raised upwards 10*f times. speed of wave frequency f = ------------- wavelength 267 m/s if wavelength = 100 m, f = ------- = 2.67 cycles/sec 100 m -> Fred raised (10 sec)*(2.67 cycles/sec) = 26.7 times 267 m/s if wavelength = 80 m, f = ------- = 3.33 cycles/sec 80 m -> Fred raised (10 sec)*(3.33 cycles/sec) = 33.3 times

**Question 6:** Write an equation which describes Fred's height above the
walkway's level as a function of time.

Answer: The equation of simple harmonic motion describes the displacement as a function of time: height = A * sin(2*pi*f*t) where A = amplitude of wave = 15 cm f = frequency of wave = 2.67 cycles/sec or 3.33 cycles/sec One can also define omega = 2*pi*f = 20.9 radians/sec or 16.8 radians/sec and write height = A * sin(omega*t) One can also write 2*pi*t height = A * sin(------) T where T = period of wave = 0.30 seconds or 0.38 seconds In order to get credit for this question, a student had to write the equation as above, _and_ define (here or earlier) the numerical values of "A" and "f" (or "T").

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This page maintained by Michael Richmond.
Last modified Feb 6, 1997.
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Copyright © Michael Richmond. This work is licensed under a Creative Commons License.