Question

An ultrasonic source emits sound of frequency 220 kHz in air. If this sound meets a water surface, what is the wavelength of the transmitted sound? (At the atmospheric temperature, speed of sound in air $=352m{s}^{-1}andinwater=1.496m{s}^{-1}$)

• A. $5.8\times {10}^{-3}m$
• B. $6.8\times {10}^{-3}m$
• C. $7.8\times {10}^{-3}m$
• D. $8.8\times {10}^{-3}m$

Answer 1

The correct option is B $6.8\times {10}^{-3}m$

Here, $v=220kHz=220\times {10}^3$
$=2.2\times {10}^{5}Hz$;
Speed of sound in air, $v_a=352m{s}^{-1}$
Speed of sound in water, $v_w=1.496m{s}^{-1}$
The transmitted sound : The transmitted ultrasonic sound travels in water. If ${\lambda }_w$ is wavelength of ultrasonic sound in water, then
${\lambda }_w=\frac{v_w}{v}=\frac{1,496}{2.2\times {10}^5}=6.8\times {10}^{-3}m$