A trombone player stands at the end zone (x=0) of a football field and begins to play its fundamental tone. Assume the trombone is a half open tube that is 3 m long. How long does it take, in seconds, for the sound to travel to the other end zone (x=300 ft)?
We can calculate the speed of sound in air using the formula:
v = f * λ
where v is the speed of sound (343 m/s in air), f is the frequency of the fundamental tone played by the trombone, and λ is the wavelength of the fundamental tone.
The fundamental frequency (f) of a trombone playing at its fundamental tone is 233 Hz. To find the wavelength (λ) of the fundamental tone, we can use the formula:
λ = 2L
where L is the length of the half open tube (3 m).
λ = 2(3) = 6 m
Now we can calculate the speed of sound in air using the formula:
v = f * λ
v = 233 Hz * 6 m
v = 1398 m/s
To calculate the time it takes for the sound to travel from one end zone to the other, we can use the formula:
t = d / v
where d is the distance between the two end zones (300 ft = 91.44 m) and v is the speed of sound in air (1398 m/s).
t = 91.44 m / 1398 m/s
t = 0.0655 seconds
Therefore, it takes approximately 0.0655 seconds for the sound to travel from one end zone to the other.