# 1) A car has two horns, one emitting a frequency of 199 Hz and the other emitting a frequency of...

## Question:

1) A car has two horns, one emitting a frequency of 199 Hz and the other emitting a frequency of 203 Hz. What beat frequency do they produce?

2) The middle-C hammer of a piano hits two strings, producing beats of 1.50 Hz. One of the strings is tuned to 260.00 Hz. What frequencies could the other string have?

## Beat

The periodic variation of loud and soft sound produced by interference of two sounds from two sources which produce sound with slightly different frequencies is called beat. The beat is produced by the interference of the sound waves in time and the beat frequency is given by the absolute difference between the frequencies of the two sound waves.

Problem (1)

• The frequency of the horn of first car is, {eq}f_1 = 199 \ Hz {/eq}
• The frequency of the horn of second car is, {eq}f_2 = 203 \ Hz {/eq}

The beat frequency produced by these two horns is given by:

{eq}\begin{align*} f_b &= f_2 f_1 \\ f_b &= 203 - 199 \\ \color{blue}{ f_b } &= \color{blue}{ \boxed{ 4 \ Hz } } \end{align*} {/eq}

Problem (2)

• The beat frequency of the two strings of the piano is, {eq}f_b = 1.5 \ Hz {/eq}

The frequency of the first string is, {eq}f_1 = 260 \ Hz {/eq}

The frequency of the other string is given by:

{eq}\begin{align*} f_2 &= f_1 \pm f_b \\ f_2 &= 260 \pm 1.5 \\ \color{blue}{ f_2 } &= \color{blue}{ \boxed{ 258.5 \ Hz \ \text{or} \ 261.5 \ Hz } } \end{align*} {/eq} 