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)?

Question

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)?

Answer 1

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)? i got the wave speed right but cant get the value of width correct

Answer 2

To find the wave speed (v), we need to divide the distance traveled around the stadium (859 seats) by the time it takes (40.0 s):

v = distance / time = 859 seats / 40.0 s = 21.475 seats/s

So, the wave speed is 21.475 seats per second.

Now, to find the width of the wave (w), we need to consider the time it takes for spectators to respond to the wave's passage.

First, we need to find the total time it takes for one complete wave cycle, which includes the time for spectators to stand and sit. This will be the sum of the time it takes for the wave to travel a distance of one wavelength and the time for spectators to respond.

The wavelength in this case is the distance traveled in one complete wave cycle, which is equal to the distance around the stadium (859 seats).

Time for one complete wave cycle = time for the wave to travel distance + time for spectators to respond

Time for one complete wave cycle = 40.0 s + 1.80 s = 41.8 s

Now, we can find the width of the wave (w), which is the distance traveled by the wave during the time spectators are standing. This can be calculated using the wave speed (v) and the time for one complete wave cycle (41.8 s):

w = v * time for one complete wave cycle = 21.475 seats/s * 41.8 s = 896.30 seats

So, the width of the wave is approximately 896.30 seats.