Question

A sound wave travels with a velocity of 300 m s–1 through a gas. 9 beats are produced in 3 s when two waves pass through hit simultaneously. If one of the waves has 2 m wavelength, the wavelength of the other wave is

• A. 1.98 m
• B. 2.04 m
• C. 2.06 m
• D. 1.99 m

Answer 1

Answer: (B)

2.04 m

Answer 2

No, of beats per seconds = $\frac{9}{3} = 3s^{- 1}$

No, of beats per seconds $= \upsilon_{1} - \upsilon_{2}$

$3 = \frac{v}{\lambda_{1}} - \frac{v}{\lambda_{2}} = v\left\lbrack \frac{1}{\lambda_{1}} - \frac{1}{\lambda_{2}} \right\rbrack$

$\frac{3}{300} = \frac{1}{2} - \frac{1}{\lambda_{2}}$

$\frac{1}{\lambda_{2}} = \frac{1}{2} - \frac{1}{100} = \frac{50 - 1}{100} = \frac{49}{100}$

$\lambda_{2} = \frac{100}{49} = 2.04m$