Question

A sound source and a detector are moving away from each other with an equal speed of $20m/s$. The detector heard a sound of frequency $1800Hz$ from the source. What is the original frequency released by the source? Assume speed of sound $=$ $340m/s$

• A. $2200Hz$
• B. $1800Hz$
• C. $2025Hz$
• D. $1500Hz$

Answer 1

The correct option is C

$2025Hz$

Step 1 : Given data

Speed $=20m/s$

$$\begin{gathered} V_O=20m/s \\ {V}_S=20m/s \end{gathered}$$(Observer speed and source speed)

Frequency $f=1800Hz$

Speed of sound $C=340m/s$

Step 2: To find the frequency released by the source

$$\begin{gathered} f\text{'}=f\left(\frac{C-V_O}{C+V_S}\right) \\ 1800=f\left(\frac{340-20}{340+20}\right) \\ f=1800/0.88 \\ f=2025Hz \end{gathered}$$

Hence the exact frequency released by the source $f=2025Hz$

Therefore the correct answer is Option C