Calculating Length of Pipe Open at Both Ends

[soulja101]

Homework Statement

A pipe organ playing in a concert produces a 440 Hz signal with a pipe open at both ends.if the ideal temperature is 20degrees, what is the length of the pipe(first harmonic)

Homework Equations

f=N/T
f=1/T
v=f*wavelength
sound equation

The Attempt at a Solution

332ms*0.59*20
=332ms+0.118ms
=332.118ms
i don't know where to go from there

 

[Kurdt]

You know the velocity of sound at 20 degrees C (at least I hope you have the right equation) and you know the frequency. Its simply a matter of rearranging this v=f*wavelength for wavelength.

Also remember that the first harmonic in an open pipe has a wavelength of twice the pipes length.

 

[m2003]

I would suggest approaching this problem by using the formula for the wavelength of a sound wave, which is given by λ = v/f, where λ is the wavelength, v is the speed of sound, and f is the frequency. In this case, we are given the frequency (440 Hz) and the temperature (20 degrees), but we need to determine the speed of sound in order to calculate the wavelength.

The speed of sound in air can be calculated using the equation v = √(γRT), where γ is the adiabatic index for air (which is approximately 1.4), R is the gas constant (8.314 J/molK), and T is the temperature in Kelvin. Plugging in the given temperature of 20 degrees Celsius (293.15 Kelvin), we get v = √(1.4*8.314*293.15) = 331.5 m/s.

Now, we can use this value for the speed of sound in our equation for the wavelength: λ = v/f = (331.5 m/s) / (440 Hz) = 0.753 m. This is the wavelength of the sound wave produced by the pipe organ.

However, we are looking for the length of the pipe, not the wavelength. So, we need to take into account that the pipe is open at both ends, which means that the length of the pipe is equal to half of the wavelength. Therefore, the length of the pipe for the first harmonic would be L = 0.753 m / 2 = 0.3765 m.

In conclusion, the length of the pipe for the first harmonic in this scenario would be approximately 0.3765 meters. It is important to note that this is an ideal calculation based on given parameters and may differ slightly from the actual length in a real-life scenario.