Question

a female vocalist with a soprano voice can sing as high as 1000 hz. given that the speed of sound is 345 m/s what is the wavelength if the sound waves

Answer 1

0.345 m.

Explanation

The wavelength is the distance that the wave travels in each cycle. The wave travels 345 meters in each second. Let the wavelength of this wave be $\lambda$. That's the distance the wave travels in one cycle.

The frequency of the sound wave is 1 000 Hz, meaning that there are 1 000 cycles in each second. The wave travels a distance of 1 000 wavelengths in one second. That would be a distance of $1,000\;\lambda$.

From the speed of the wave, the wave travels 345 meters in one second. In other words,

$1,000\;\lambda = 345$.

$\lambda = \dfrac{345}{1,000} = 0.345\;\text{m}$.

To generalize:

$\lambda = \dfrac{v}{f}$,

where

• $\lambda$ wavelength of the wave,
• $v$ the speed of the wave, and
• $f$ the frequency of the wave.