Question

please give me the solution of this question​

Answer 1

Answer:

Question :

Wavelength of 2 sound waves in air are 81/173 m and 81/170 m. When these waves meet at a point , they produce 10 beats per second. Calculate velocity of sound wave in air.

Given:

Wavelength of the 2 waves are as follows :

• 81/173 m
• 81/170 m

They meet to give beat frequency of 10 Hz

To find:

Velocity of wave

Calculation:

Let velocity be v ,

we know that frequency of any wave is given as follows;

$\boxed{freq. = \dfrac{velocity}{wavelength}}$

$\therefore \: beats = f1 - f2$

$= > 10 = (\dfrac{v}{ \frac{81}{173} } ) - (\dfrac{v}{ \frac{81}{170} } )$

$= > 10 = \dfrac{173v}{81} - \dfrac{170v}{81}$

$= > 10 = \dfrac{3v}{81}$

$= > 10 = \dfrac{v}{27}$

$= > v = 270 \: m {s}^{ - 1}$

So final answer :

$\boxed{ \red{velocity = 270 \: m {s}^{ - 1}}}$

Answer 2

$\mathfrak{ \huge{ \red{ \underline{ \underline{Answer:}}}}} \\ \\ \star \: \boxed{\bold{ \green{Given:}}}$

=> wavelengths of sound waves are 81/173m and 81/170m

=> they produce 10 beats per second

$\star \: \boxed{ \bold{ \green{To \: Find:}}}$

=> velocity of sound in air

$\star \: \boxed{\bold{ \green{Formula:}}}$

=> number of beats produce are given by

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \pink{n = f1 - f2}}$

=> relation between frequency, velocity and wavelength is given by

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \pink{f = \frac{V}{ \lambda}}}$

$\star \: \boxed{\bold{ \green{Calculation:}}}$

$\implies \: beat(n) = f1 - f2 \\ \\ \implies \: n = \frac{V}{ \lambda1} - \frac{V}{ \lambda2} \\ \\ \implies \: 10 = V \: ( \frac{173}{81} - \frac{170}{81} ) \\ \\ \implies \: V = 10 \times \frac{81}{3} = 270 \frac{m}{s} \\ \\ \\ \huge{ \blue{\star}} \: \boxed{ \boxed{ \pink{Velocity = 270 \frac{m}{s} }}} \: \huge{ \blue{ \star}}$