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 3m long.
How much would the trombone player have to move the slider in cm to play 25 Hz?
I calculated the frequency of the fundamental tone - 28.58 Hz. A previous part of the problem said that the end zone is 300ft.
But..what's with the trombone? How do I quantify the amount of slide? What should I be solving for?
But how do you relate frequency and length of the trombone together?
Well, it seems like the trombone is the life of the party here! To figure out how much the trombone player would have to move the slider to play 25 Hz, we need to look at the relationship between frequency and the length of the tube.
The fundamental frequency of a half-open tube is given by the equation:
f = (v / 2) * (1 / L),
where f is the frequency, v is the speed of sound, and L is the length.
Now, we have the frequency (25 Hz) and the length of the tube (3 m), but we need to find the speed of sound to plug into the equation. Without that information, we can't calculate how much the slider needs to be moved.
So, while the trombone may be a jazzy addition to the football field, we need more details to give you a specific answer. Otherwise, it's all just a bunch of musical notes hanging in the air!
To calculate the amount the trombone player would have to move the slider to play a specific frequency, we need to use the equation for the fundamental frequency of a half-open tube. The equation is:
f = (v/2L) * m
Where:
- f is the frequency of the fundamental tone,
- v is the speed of sound (approximately 343 m/s),
- L is the length of the trombone (3m in this case),
- m is the mode or harmonic number (1 for the fundamental tone).
Since you already calculated the frequency of the fundamental tone to be 28.58Hz, we can rearrange the equation to solve for m:
m = (f * 2L) / v
Substituting the values, we get:
m = (28.58 * 2 * 3) / 343
m = 1.984
Since the mode or harmonic number should be a whole number, let's round the value of m to the nearest whole number, which is 2.
Now that we know the mode or harmonic number, we can calculate the position of the slide using the formula:
x = (λ/4) * (m - 1)
Where:
- x is the position of the slide in relation to the length of the tube,
- λ is the wavelength of the sound produced by the trombone.
To find the wavelength, we can use the formula:
λ = v/f
Substituting the values, we get:
λ = 343 / 28.58
λ = 11.98 m
Now, substituting the values into the equation for the slide position:
x = (11.98 / 4) * (2 - 1)
x = 2.995 m
To convert the slide position to centimeters, multiply it by 100:
x = 2.995 * 100
x = 299.5 cm
Therefore, the trombone player would have to move the slider by approximately 299.5 cm to play a frequency of 25 Hz.
To solve this problem, we need to understand the relationship between the fundamental frequency of a half-open tube and the length of the tube. In a half-open tube, such as a trombone, the fundamental frequency is determined by the length of the tube and the speed of sound in the medium (in this case, air).
The fundamental frequency (f) can be calculated using the formula:
f = (v/2L)
Where:
- f is the frequency
- v is the speed of sound in air (approximately 343 m/s)
- L is the length of the tube
In this case, we are given the frequency (25 Hz) and the length of the trombone (3 m). We need to solve for the amount the trombone player should move the slide.
To solve for the slide position, we rearrange the formula to solve for L:
L = v / (2f)
Plugging in the given values:
L = 343 m/s / (2 * 25 Hz)
L = 343 m/s / 50 Hz
L = 6.86 m
The length of the trombone when playing the desired frequency is 6.86 meters. Since the original length of the trombone is 3 meters, the trombone player would need to extend the slide by:
Slide extension = (6.86 m - 3 m) * 100 cm/m
Slide extension = 3.86 m * 100 cm/m
Slide extension ≈ 386 cm
Therefore, the trombone player would need to move the slider approximately 386 cm to play a frequency of 25 Hz.
at 3 meters (300 cm) you got 28.58 Hz
What length gives 25 Hz? (a bit longer)
subtract