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)?
A humming bird beats its wings up and down with a frequency of 80 Hz. What is the period of the humming bird's flaps.
time period= 1/frequency
To find the wave speed and width, we can use the given information.
Let's start with finding the wave speed.
(a) Wave speed (v) can be calculated using the formula:
v = d / t
Where:
- d is the distance traveled by the wave (859 seats)
- t is the time taken for the wave to travel that distance (40.0 s)
Plugging in the values:
v = 859 seats / 40.0 s
Calculating:
v ≈ 21.48 seats/s
So, the wave speed is approximately 21.48 seats per second.
Moving on to finding the width of the wave:
(b) The width of the wave can be determined by considering the time required for spectators to respond to the wave's passage.
Given that spectators take about 1.80 s to respond, we need to find the number of seats covered by the wave in that time.
To do that, we multiply the wave speed (v) by the response time (1.80 s):
w = v * t
Where:
- v is the wave speed (21.48 seats/s)
- t is the response time (1.80 s)
Plugging in the values:
w = 21.48 seats/s * 1.80 s
Calculating:
w ≈ 38.66 seats
So, the width of the wave is approximately 38.66 seats.