Tsunamis are fast-moving waves often generated by underwater earthquakes. In the deep ocean their amplitude is barely noticable, but upon reaching shore, they can rise up to the astonishing height of a six-story building. One tsunami, generated off the Aleutian islands in Alaska, had a wavelength of 747 km and traveled a distance of 3830 km in 5.03 h. (a) What was the speed (in m/s) of the wave? For reference, the speed of a 747 jetliner is about 250 m/s. Find the wave's (b) frequency and (c) period.
change units to m and second.
speed= distancetraveled/time
frequency=speed/wavelength
period= 1/frequency.
a) 3830km * 1000m/km / ( 5.03h * 3600s/h)
b) 3830km * 1000m/km / (5.03h * 3600s/h) / (747km * 1000m/km)
c) 1 / (3830km* 1000m/km / (5.03h*3600s/h) / (747km * 1000m/km))
Sure, let's calculate that!
(a) To find the speed of the wave, we can use the formula:
Speed = Distance Traveled / Time
Converting the given values to meters and seconds:
Distance Traveled = 3830 km = 3830 * 1000 m = 3,830,000 m
Time = 5.03 h = 5.03 * 3600 s ≈ 18,108 s
Speed = 3,830,000 m / 18,108 s
Speed ≈ 211.39 m/s
So, the speed of the tsunami wave is approximately 211.39 m/s.
(b) To find the frequency of the wave, we can use the formula:
Frequency = Speed / Wavelength
Given values:
Wavelength = 747 km = 747 * 1000 m = 747,000 m
Frequency = 211.39 m/s / 747,000 m
Frequency ≈ 0.000283 Hz
So, the frequency of the wave is approximately 0.000283 Hz.
(c) To find the period of the wave, we can use the formula:
Period = 1 / Frequency
Period = 1 / 0.000283 Hz
Period ≈ 3536.69 s
So, the period of the wave is approximately 3536.69 seconds.
To find the speed of the wave, we can use the formula:
speed = distance traveled / time
Converting the given distance of 3830 km to meters and time of 5.03 hours to seconds:
distance = 3830 km * 1000 m/km = 3,830,000 m
time = 5.03 h * 3600 s/h = 18,108 s
Now we can calculate the speed:
speed = 3,830,000 m / 18,108 s = 211.56 m/s
Therefore, the speed of the wave is approximately 211.56 m/s.
To find the frequency, we use the formula:
frequency = speed / wavelength
Converting the given wavelength of 747 km to meters:
wavelength = 747 km * 1000 m/km = 747,000 m
Now we can calculate the frequency:
frequency = 211.56 m/s / 747,000 m = 0.000283 Hz
Therefore, the frequency of the wave is approximately 0.000283 Hz.
Finally, to find the period, we use the formula:
period = 1 / frequency
Calculating the period:
period = 1 / 0.000283 Hz = 3532.85 s
Therefore, the period of the wave is approximately 3532.85 s.
To find the speed of the tsunami wave, we need to calculate the distance traveled and the time it took.
(a) The distance traveled is given as 3830 km. Let's convert it to meters by multiplying by 1000: 3830 km x 1000 m/km = 3,830,000 m.
The time taken is given as 5.03 hours. However, we need to convert this to seconds. We know that there are 60 minutes in an hour and 60 seconds in a minute. Therefore, 5.03 hours x 60 minutes/hour x 60 seconds/minute = 18,108 seconds.
Now we can calculate the speed:
speed = distance traveled / time taken
speed = 3,830,000 m / 18,108 s ≈ 211.5 m/s
The speed of the tsunami wave is approximately 211.5 m/s.
(b) To find the frequency, we can use the speed and the wavelength:
frequency = speed / wavelength
frequency = 211.5 m/s / 747,000 m ≈ 0.283 Hz
The frequency of the tsunami wave is approximately 0.283 Hz.
(c) The period is the reciprocal of the frequency:
period = 1 / frequency
period = 1 / 0.283 Hz ≈ 3.53 s
The period of the tsunami wave is approximately 3.53 seconds.