Question

Speed of a longitudinal wave in air is $300\text{m/s}$ and in steel is $3000\text{m/s}$. If wavelength in air is $0.5\text{m}$ , then its wavelength in steel is

• A. $5\text{m}$
• B. $10\text{m}$
• C. $15\text{m}$
• D. $20\text{m}$

Answer 1

The correct option is A $5\text{m}$

We know that ,
Speed of a wave is given by $v=\lambda f$
where $\lambda$ is wavelength and $f$ is frequency
As frequency depends upon vibrating source, it remains unchanged.
$\therefore v\propto \lambda$
$\Rightarrow \frac{v_1}{v_2}=\frac{{\lambda }_1}{{\lambda }_2}$
From the data given in the question ,
${\lambda }_2=\frac{{\lambda }_1{v}_2}{v_1}\Rightarrow {\lambda }_2=\frac{0.5\times 3000}{300}=5\text{m}$
Thus, option (a) is the correct answer.