Question

The displacement-time graph of a sound wave is given below. If the speed of the sound wave is $300m{s}^{–1}$ in a given medium, then the wavelength of the sound wave is

• A. $\frac{1}{2}m$
• B. $2m$
• C. $3m$
• D. $\frac{2}{3}m$

Answer 1

The correct option is B $2m$

Let the time period of the wave be T.

According to the definition of time period, time taken for one complete oscillation is called time period.

$\Rightarrow AB=Ts$


From the graph:
$AC=\frac{T}{2}andCD=\frac{T}{4}\Rightarrow AC+CD=\frac{T}{4}+\frac{T}{2}=(10-5)ms=5\times {10}^{-3}s(\because 1ms={10}^{-3}s)\Rightarrow \frac{T+2T}{4}=5\times {10}^{-3}s\Rightarrow 3T=4\times 5\times {10}^{-3}=20\times {10}^{-3}s\Rightarrow T=\frac{20}{3}\times {10}^{-3}s$

Speed of sound, $v=300m/s$

Now, $v=\frac{\text{Wave length}}{\text{Time period}}=\frac{\lambda }{T}\Rightarrow \lambda =vT=300\times \frac{20}{3}\times {10}^{-3}\Rightarrow \lambda =2m$

Hence, the correct answer is option (b).