1. A woman is standing in the ocean, and she notices that after a wave crest pas
ID: 1505781 • Letter: 1
Question
1. A woman is standing in the ocean, and she notices that after a wave crest passes by, five more crests pass in a time of 58.5 s. The distance between two successive crests is 32.6 m. What is the wave's (a) period, (b) frequency, (c) wavelength, and (d) speed?
2.The drawing shows a graph of two waves traveling to the right at the same speed. (a) Using the data in the drawing, determine the wavelength of each wave. (b) The speed of the waves is 18 m/s; calculate the frequency of each one. (c) What is the maximum speed for a particle attached to each wave?
3. A wave traveling along the x axis is described mathematically by the equation y = 0.17sin(8.7?t + 0.67?x), where y is the displacement (in meters), t is in seconds, and x is in meters. What is the speed of the wave?
4. A hunter is standing on flat ground between two vertical cliffs that are directly opposite one another. He is closer to one cliff than the other. He fires a gun and, after a while, hears three echoes. The second echo arrives 1.20 s after the first, and the third echo arrives 0.851 s after the second. Assuming that the speed of sound is 343 m/s and that there are no reflections of sound from the ground, find the distance (in m) between the cliffs.
Explanation / Answer
Part 1)
is the distance between two consecutive peaks
a) The period We have 5 peaks at 58.5 s relationship to know we made a time of two consecutive crest
T = 58.5/5 = 11.7 s
b)
f = 1/T
f = 1/11.7
f = 0.0855 Hz
c) = 32.6 m
d) v= f
v= 32.6 0.0855
v = 2.786 m/s
Part 2)
a)
The wavelength gives A is the distance to the wave repeats A = 2 m
for the wavelength B B = 4 m
b) v = f
f = v/
wavelength A fA = 18 / 2 fA = 9 Hz
wavelength B fB = 18/ 4 fB = 4.5 Hz
c) v = -w A Sin (wt)
v maximum Sin(wt) = -1
Vmax = w A = 2f A
wavelength A Vmax = 2 9 0.5 Vmax= 28.27 m/s
wavelength B Vmax = 2 4.5 0.25 Vmax = 7.07 m/s
Part 3)
the wave velocity is
Y = a Sin (2f t + x 2/)
v= f
for this expression
2f = 8.7
f = 8.7/2
f = 4.35 Hz
2/ = 0.67
= 2/0.67
= 2.985 m
V = 4.35 2.985
V= 12.985 m/s
Part 4)
t1 first echo from the nearest wall
second echo t2 = t1 + 1.20 farthest wall
third echo t3 = t2 + 0.850 nearest wall
V = d/t
total distance L
distance to nearest wall x
distance far wall L-x
V = x/t1
V= (L-x)/t2
V= (( L-x) +L +x)/t3
x = V t1 x = 343 t1 (1)
L-x = V (t1+1.2) L- x = 343 t1 + 343 1.2 (2)
2L = V (t1 +1.2 + 0.85) 2L = 343 t1 + 343 (2.05) (3)
We have three equations and three unknowns which can solve the system
replace 1 in 2
L – 343 t1 = 343 t1 + 411.6
L = 2 343t1 + 411.6
t1 = (L – 411.6)/686
replace in 3
2L = 343 t1 + 703.15
2L = 343 (L – 411.6)/2 343 + 703.15
2L = L/2 – 411.6/2 + 703.15
2L -L/2 = 497.35
¾ L = 497.35
L = 4/3 497.35
L = 663.13 m
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