Question

Sound waves of wavelength $\lambda $ travelling in a medium with a speed of $\nu m{s^{ - 1}}$ enter into another medium where its speed is $2\nu m{s^{ - 1}}$. Wavelength of the sound waves in the second medium is
A. $\lambda $
B. $\dfrac{\lambda }{2}$
C. 2$\lambda $
D. 4$\lambda $

Answer 1

Hint:Vibrations from a source that travel through a medium and can be heard once they reach a human’s or animal’s ear is known as sound. While traveling from one medium to a different medium, the speed of sound and its wavelength changes while its frequency remains constant in all the mediums. Sound travels by vibration of the medium particles so its speed depends on the density of the medium.

Complete step by step answer:
Sound wave is a result of back and forth vibration of the particles of the medium through which the sound passes. Wavelength is defined as the distance between two successive crests or troughs of a wave. It is represented by $\lambda $. Wave frequency is the number of waves per unit time. It is represented by $\upsilon $. We know,
$
speed = \dfrac{{distance}}{{time}} \\
speed = distance $\times$ frequency
So, Speed of sound = wavelength $\times$ frequency
The wavelength of sound in the first medium,
$
v = \lambda \times \upsilon \\
\Rightarrow \lambda = \dfrac{v}{\upsilon } \\ $
The speed of sound in second medium is $2\nu $ and let the frequency in the second medium be $\upsilon '$ , So the wavelength of sound in the second medium,
${\lambda ^1} = \dfrac{{2v}}{{{\upsilon ^1}}}$
When a wave travels from one medium to another their speed and wavelength changes proportionately but the frequency of the wave remains constant.
$\therefore {\upsilon ^1} = \upsilon $
So ${\lambda ^1} = \dfrac{{2v}}{\upsilon } = 2\lambda $

Hence option C is the correct answer.

Additional information:
Sound waves travel fast in a denser medium as vibrations are passed more easily, speed of sound is highest in solids and lowest in gases. During propagation, waves can also be reflected or refracted by the medium.

Note:Sound waves are produced by the vibration of the source, these vibrations then continue to move through the medium and away from the source at the speed of sound, thus forming the sound wave. The particles of the medium don’t travel with the sound wave, they just vibrate and pass on the vibrations to the particles around them. So the speed of the sound wave depends on the closeness of the particles in the medium.