Question

The wavelength of two sound waves are 49 cm and 50 cm respectively. If the room temperature is 30${}^o$C then the number of beats produced by them is approximately :

(velocity of sound in air at 0${}^o$C = 332 m/s.)

• A. 6
• B. 10
• C. 14
• D. 18

Answer 1

The correct option is C 14

Velocity of sound in air $v\propto \sqrt{T}$

$\therefore$ $\frac{v}{v_o}=\sqrt{\frac{T}{T_o}}$

Given : $T_o=0^{o}C=273K$ $T={30}^o=30+273=303$ K $v_o=332$ m/s

$\therefore$ $\frac{v}{332}=\sqrt{\frac{303}{273}}$ $⟹v=350$ m/s

Number of beats $b={\nu }_1-{\nu }_2=\frac{v}{{\lambda }_1}-\frac{v}{{\lambda }_2}$

$\therefore$ $b=\frac{350}{0.49}-\frac{350}{0.50}=14$