# Two sound waves have frequencies of 340 Hz and 370 Hz. Determine the beat frequency produced by...

## Question:

Two sound waves have frequencies of 340 Hz and 370 Hz. Determine the beat frequency produced by these waves combining together. Will these beats be detected by humans? Explain.

## Beat

When two waves of same type having a very small frequency difference superimpose with each other they form beat. Where the beat frequency is equal to the difference in the frequency of the superimposing waves.

Data Given

• Frequency of the wave one {eq}\nu_1 = 340 \ Hz {/eq}
• Frequency of the wave two {eq}\nu_2 = 370 \ Hz {/eq}

We knaw that beat frequency is given by

{eq}\begin{align} \Delta \nu = \nu_2 - \nu_1 \end{align} {/eq}

{eq}\begin{align} \Delta \nu = 370 \ Hz - 340 \ Hz = 30 \ Hz \end{align} {/eq}

We know that humen ear are senstive to frequency range {eq}20 \ Hz \ to \ 20 \ kHz {/eq}

As the beat frequency {eq}\begin{align} \Delta \nu = 30 \ Hz \end{align} {/eq} is in the human audible range so beats will be detected by humans. 