Question

Sound waves travel at $350m{s}^{-1}$ through warm air and at $3500m{s}^{-1}$ through brass. The wavelength of a $700Hz$ acoustic wave as it enters brass from warm air:

• A. decrease by a factor $10$
• B. increase by a factor $20$
• C. increase by a factor $10$
• D. decrease by a factor $20$

Answer 1

Answer: (C)

increase by a factor $10$

For wave propagation, we have the formula for velocity as :

$v=n\times \lambda$

This for first medium,

$v_1=n\times {\lambda }_1$

and for second medium,

$v_1=n\times {\lambda }_1$

Ratio will be,

$\frac{v_1}{v_2}=\frac{{\lambda }_1}{{\lambda }_2}$

${\lambda }_2={\lambda }_1\times \frac{v_2}{v_1}$

Substituting the values,

${\lambda }_2={\lambda }_1\times \frac{3500}{350}$

${\lambda }_2=10\times {\lambda }_1$

Thus, increases by factor 10 times.

The correct option is C.