Question

Church 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 lowest frequency produced by an organ is 30.4 Hz, and the highest frequency is 1.48 kHz, then what is the shortest possible wavelength of sound the organ can produce? Assume that the speed of sound is 331 m/s.

Answer 1

Answer: The shortest possible wavelength of sound the organ can produce is 0.224 m

Explanation:

To calculate the wavelength of light, we use the equation:

$\lambda=\frac{c}{\nu}$

where,

$\lambda$ = wavelength of the light

c = speed of light = $331m/s$

As wavelength and frequency follows inverse relation, shortest wavelength is produced by highest frequency.

$\nu$ = highest frequency of light = $1.48kHz=1.48\times 10^3Hz=1.48\times 10^3s^{-1}$       $1Hz=1s^{-1}$

$\lambda=\frac{331m/s}{1.48\times 10^3s^{-1}}=0.224m$

Thus the shortest possible wavelength of sound the organ can produce is 0.224 m