Question

Two organ pipes sounded together to give 5 beats per second. If their length is in the ratio of 50:51, then the frequency of shorter and longer pipes are respectively

• A. 250,245
• B. 245,250
• C. 250,255
• D. 255,250

Answer 1

The correct option is D 255,250

Let $n_A$ and $n_B$ be the frequency of the organ pipes $A$ and $B$ respectively.

We have $n_A=\frac{V}{A{l}_A}$ and $n_B=\frac{V}{A{l}_B}$

$V=$ Velocity of sound in air

$l_A=$ Length of the air column resonating with pipe $A$

$l_B=$ Length of the air column resonating with pipe $B$

$\frac{n_A}{n_B}=\frac{l_A}{l_B}=\frac{51}{50}$ (given) (equation $1$)

Since both pipes together produce $5$ beats per second,

$n_A-n_B=5$ (equation $2$)

By solving equation $1$ and $2$ we get

$n_A=255H_z$ and $n_B=250H_z$