Question

Sound waves of wavelength $\lambda$ traveling in a medium with a speed of $vm{s}^{-1}$ enter in another medium, where its speed is $2vm{s}^{-1}$. What will be the wavelength of sound waves in the second medium?

• A. $\lambda$
• B. $4\lambda$
• C. $2\lambda$
• D. $3\lambda$

Answer 1

The correct option is C

$2\lambda$

An explanation of the correct option C: $2\lambda$

Given data:

Let v be the speed and $\lambda$ be the wavelength of the sound waves:

$$\begin{gathered} v_1=vm/s \\ {v}_2=2vm/s \end{gathered}$$

$$\begin{gathered} {\lambda }_1=\lambda \\ {\lambda }_2=? \end{gathered}$$

Step 1: Relation between the speed and wavelength of the sound waves:

$v=f·\lambda$

Step 2: Calculation of wavelength of the sound wave in the second medium:

$$\begin{gathered} Now, \\ {v}_1=f{\lambda }_1...(eq1) \\ {v}_2=f{\lambda }_2...(eq2) \end{gathered}$$ (Frequency of the waves depends upon the source of the waves and hence remains the same)

Dividing eq 1 by eq 2.

$$\begin{gathered} \frac{v_1}{v_2}=\frac{{\lambda }_1}{{\lambda }_2} \\ Therefore, \\ \frac{v}{2v}=\frac{{\lambda }_{}}{{\lambda }_2}(Fromgivendata) \\ Hence, \\ {\lambda }_2=2{\lambda }_{} \end{gathered}$$

Thus, the wavelength of sound waves in the second medium is $2\lambda$.