A human wave. During sporting events within large, densely packed stadiums, spectators will send a wave (or pulse) around the stadium (Fig. below). As the wave reaches a group of spectators, they stand with a cheer and then sit. At any instant, the width w of the wave is the distance from the leading edge (people are just about to stand) to the trailing edge (people have just sat down). Suppose a human wave travels a distance of 859 seats around a stadium in 40.0 s, with spectators requiring about 1.80 s to respond to the wave's passage by standing and then sitting. What are (a) the wave speed v (in seats per second) and (b) width w (in number of seats)?
To find the wave speed v, we need to calculate the distance the wave travels (d) and the time it takes (t):
(a) Wave speed v is calculated using the formula: v = d / t
First, let's calculate the distance the wave travels. It's given as 859 seats.
Next, we'll find the time it takes for the wave to travel this distance. It's given as 40.0 s.
Now, substitute these values into the formula to solve for v:
v = 859 seats / 40.0 s
v ≈ 21.5 seats/s
Therefore, the wave speed is approximately 21.5 seats per second.
To find the width of the wave, we need to calculate the time it takes for the wave to pass a group of spectators, including the time for them to stand and sit. Let's call this time interval T.
The time interval T is the wave period, which is the time for one complete wave cycle (from standing to sitting and back to standing) to pass through a group of spectators. In this case, the wave period is given as 1.80 s.
The width w of the wave is then the product of the wave speed v and the time interval T:
(b) Width w = v * T
Substitute the calculated values to find w:
w = 21.5 seats/s * 1.80 s
w ≈ 38.7 seats
Therefore, the width of the wave is approximately 38.7 seats.
To find the wave speed and width, we can use the formula:
v = d/t
where v is the wave speed, d is the distance traveled, and t is the time taken.
Given:
Distance traveled, d = 859 seats
Time taken, t = 40.0 s
(a) To find the wave speed, we can substitute the values into the formula:
v = 859 seats / 40.0 s
Using a calculator, we get:
v ≈ 21.475 seats/s
Therefore, the wave speed is approximately 21.475 seats per second.
(b) To find the width, we need to consider the time it takes for spectators to respond to the wave's passage and stand/sit. Let's calculate the number of waves that can occur in the given time.
Time for one wave = 1.8 s
Total time = 40.0 s
Number of waves in the given time = Total time / Time for one wave = 40.0 s / 1.8 s = 22.222...
Since a whole number of waves cannot occur, we round down to the nearest whole number wave. Therefore, 22 waves occur in the given time.
The width of the wave is the distance traveled divided by the number of waves:
w = distance / number of waves
w = 859 seats / 22 waves
Using a calculator, we get:
w ≈ 39 seats
Therefore, the width of the wave is approximately 39 seats.
wave speed=859/40 seats/second
Width=speed*timestanding
I am wondering what this is doing with the title physics, it is basic high school math.