Question

Which of the following best describes the wave when it passes into the surrounding air if a sound wave travels through a metal rod with wavelength $\lambda$ and frequency f.

• A. Wavelength - Less than $\lambda$; Frequency - Equal to $f$
• B. Wavelength - Less than $\lambda$; Frequency - Less than $f$
• C. Wavelength - Greater than $\lambda$; Frequency - Equal to $f$
• D. Wavelength - Greater than $\lambda$; Frequency - Less than $f$
• E. Wavelength - Greater than $\lambda$; Frequency - Greater than $f$

Answer 1

The correct option is A Wavelength - Less than $\lambda$; Frequency - Equal to $f$

The frequency of wave does not change when it passes from one medium to another because frequency is characterized by source so frequency will remain same , equal to $f$ .

Velocity of sound is greater in solids (here in metal) than gases(air) due to high elasticity of solids .

Therefore by $v=f\lambda$

or $v\propto \lambda$ as $f=constant$ for both media

wavelength in air will be less than wavelength in metal ($\lambda$) as velocity in air is lesser than metal rod.