A pipe organ is an aerophone with open ended tubes, with esssentially the same physics as the flute. (a) for normal room temperature, where the speed of sound is about 340 m/s how long is the pipe for the A440 note. (b) Suppose someone wanted to install an outdoor pipe organ at the South Pole that would be in tune when the temperature is -80 degrees Celcius. How long would the pipe be for the A440 note for that organ?

Question

A pipe organ is an aerophone with open ended tubes, with esssentially the same physics as the flute. (a) for normal room temperature, where the speed of sound is about 340 m/s how long is the pipe for the A440 note. (b) Suppose someone wanted to install an outdoor pipe organ at the South Pole that would be in tune when the temperature is -80 degrees Celcius. How long would the pipe be for the A440 note for that organ?

For A do I just use the equation wavelength= frequency x velocity and get 149,600 meters or how would I find the outdoor pipe organ length?

Answer 1

To find the length of the pipe for the A440 note in normal room temperature, you can use the equation for wavelength:

wavelength = velocity / frequency.

In this case, the velocity is the speed of sound, which is approximately 340 m/s, and the frequency is 440 Hz (A440).

So, plugging in the values:

wavelength = 340 m/s / 440 Hz = 0.77 m or 77 cm.

Therefore, the length of the pipe for the A440 note in normal room temperature would be about 77 cm.

For the outdoor pipe organ at the South Pole, where the temperature is -80 degrees Celsius, you need to consider the change in the speed of sound due to temperature.

The speed of sound in a gas can be calculated using the formula:

v = sqrt(γRT),

where v is the speed of sound, γ is the ratio of specific heat capacities, R is the gas constant, and T is the temperature in Kelvin.

Typically, the value of γ for dry air is around 1.4, and R is approximately 287 J/(kg·K).

To find the new speed of sound, we need to convert -80 degrees Celsius to Kelvin. The conversion from Celsius to Kelvin is done by adding 273.15 to the Celsius temperature.

So, -80°C + 273.15 = 193.15 K.

Now, we can calculate the new speed of sound:

v = sqrt(1.4 * 287 J/(kg·K) * 193.15 K) ≈ 331.3 m/s.

Using the same equation as before:

wavelength = velocity / frequency,

wavelength = 331.3 m/s / 440 Hz ≈ 0.75 m or 75 cm.

Therefore, considering the change in temperature at the South Pole, the length of the pipe for the A440 note for the outdoor pipe organ would be about 75 cm.