Question

The frequency of a sound wave is $200Hz$ and its wavelength is $150cm$. What is the distance travelled by the sound wave in the time taken to produce 150 waves?
A.$110m$.
B. $225m$.
C. $112.5m$.
D. $336.5m$.

Answer 1

Hint: The problem can be solved by using the relation $c = \lambda \upsilon $, here $c$ is the speed of the wave $\lambda $ is the wavelength and $\upsilon $ is the frequency. A frequency is the number of oscillations in one second.

Complete step by step answer:
Step 1.
It is given that the frequency of the sound is $v = 200Hz$ and the wavelength is $\lambda = 150cm$.

Step 2.
Use the formula $c = \lambda \upsilon $ to calculate speed of the wave, where$c$ is the speed of the wave $\lambda $ is the wavelength and $\upsilon $ is the frequency.
$\Rightarrow c = \lambda \upsilon $
Put values $\lambda = 150cm$ and $v = 200Hz$ in above equation.
$\Rightarrow c = \lambda \upsilon $
$\Rightarrow c = 150 \times 200$
$\Rightarrow c = 30,000\dfrac{{cm}}{s}$
So, the speed of the wave is$c = 30,000\dfrac{{cm}}{s}$.
Since,
$1m = 100cm$,
Therefore,
$\Rightarrow c = 30,000 \times \dfrac{1}{{100}} \times \dfrac{{cm}}{s}$
$\Rightarrow c = 300\dfrac{{cm}}{s}$
Step 3.
The frequency of a wave tells us that the number of waves produced in one second. So let us calculate the time taken for producing $150$ waves.
Step 4.
As it is given that the frequency of the wave is $v = 200Hz$, which means that the number of waves produced in 1 second. The time taken by wave to produce $150$ waves is,
$\Rightarrow t = \dfrac{{150}}{{200}}$
$\Rightarrow t = 0.75\operatorname{s} $
So, the time taken to produce $150$ waves is $t = 0.75\sec $.
Step 5.
We know that,
$\Rightarrow {\text{Speed}} = \dfrac{{{\text{Distance}}}}{{{\text{Time}}}}$
Here we need to calculate the distance travelled by wave, so apply
$\Rightarrow {\text{Distance}} = \left( {{\text{Speed}}} \right) \times \left( {{\text{Time}}} \right)$
Put \[{\text{Speed}} = 300\dfrac{m}{s}\] and ${\text{Time}} = 0.75{\text{s}}$ in above equation.
$\Rightarrow {\text{Distance}} = \left( {{\text{Speed}}} \right) \times \left( {{\text{Time}}} \right)$
$\Rightarrow {\text{Distance}} = 300 \times 0.75$
$\Rightarrow {\text{Distance}} = 225m$
So, the distance travelled by the sound wave in the time taken to produce $150$ waves is$d = 225m$.
The correct answer for this problem is option B.

Note: The formula $c = \lambda \upsilon $ tells us about the relation between speed of wave and wavelength and frequency. Students should remember the frequency of a wave tells us about the number of waves produced in one second.