Physics, 17.07.2020 16:01 djgunderson

The clarinet is well modeled as a cylindrical pipe that is open at one end and closed at the other. Find the wavelength and frequency of the third normal mode of vibration of a clarinet's air column with effective length of 0.401 m. Take 342 m/s for the speed of sound inside the instrument.

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Answer from: snicklegirlp4isqr

The characteristics of standing waves in tubes allows to find the results for the third harmonic of the clarinet are:

The wavelength is λ = 0.5365 m. The frequency is: f = 639.7 Hz.

Standing waves are formed when a wave collides with an obstacle and is reflected, the sum of the incident wave and the reflected wave forms a standing wave that does not move in time. There are several types of obstacles:

Fixed. When it collides with a wall a node is formed at this point. Open. When it collides with a change in density, it is considered a moving obstacle, at this point a belly or antinode is produced.

They indicate that the clarinet is approximated to a tube with one end open and the other closed, therefore at the closed end we have a node and at the open end a antinode, in the adjoint we see a diagram of the resonance, the expression for the resonance should be:

L = $\frac{\lambda}{4}$ 1st harmonic

L = $3 \frac{\lambda}{4}$ 3th harmonic

L = $(2n-1) \frac{\lambda}{4}$ General term

where L is the length of the tube, λ the wavelength and n an integer.

Ask for the wavelength of the third harmonic m = 3

λ = $\frac{4L}{3}$

λ = $\frac{4 \ 0.401}{3}$

λ = 0.5365 m

The speed of the wave is related to the product of the wavelength and the frequency.

v = λ f

f = $\frac{v}{\lambda}$

Let's calculate.

f = $\frac{342}{0.5365}$

f = 639.7 Hz

In conclusion, using the characteristics of standing waves in tubes we can find the results for the third harmonic of the clarinet are:

The wavelength is λ = 0.5365 m The frequency is: f = 639.7 Hz

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Answer from: drcarver

wavelength is = 0.05m

frequency is = 639.65 Hz

Explanation:

F= 3V/4L

(3 x 342)/(4 x 0.401) = 639.65Hz

Wavelenght =4L/3

wavelength =(4x0.401)/3 = 0.05m

The clarinet is well modeled as a cylindrical pipe that is open at one end and closed at the other.

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Answer from: Quest

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