Question

Pipe organs have a set of pipes with different lengths. With those different pipes, organs can produce sounds over a wide range of frequencies. If the frequency range is from 31.3 Hz to 1.58kHz, then what is the shortest wavelength of sound the organ can produce? vsound = 343m/s

Answer 1

The shortest wavelength of sound a pipe organ can produce at the given frequency of 1.58 kHz is 0.21709 meters, calculated by dividing the speed of sound (343 m/s) by the highest frequency.

Step-by-step explanation:

The student asked about the shortest wavelength of sound a pipe organ can produce, given a frequency range from 31.3 Hz to 1.58 kHz and a speed of sound of 343 m/s. To find the shortest wavelength, we will use the highest frequency, which is 1.58 kHz or 1580 Hz, since wavelength and frequency are inversely related. The relationship between the speed of sound (Uw), its frequency (f), and wavelength (λ) is given by the equation Uw = fλ. Therefore, the shortest wavelength (λ) can be calculated using the formula: λ = Uw / f.

Substituting the given values, we get:

λ = 343 m/s / 1580 Hz = 0.21709 meters

This is the shortest wavelength of sound that the pipe organ can produce given the conditions.