Question

A bat flies at a constant speed of $0.04V$ toward a large tree trunk (where $V$ denotes the speed of sound), the bat emits an ultrasonic pulse. The pulse is reflected off the tree and returns to the bat, which can detect and analyse the returning signal. If the returning signal has a frequency of $61kHz$, Find out the frequency of the original ultrasonic pulse?

• A. $56kHz$
• B. $62kHz$
• C. $68kHz$
• D. $74kHz$
• E. $78kHz$

Answer 1

The correct option is A $56kHz$

Let the original frequency emitted be $f_0$.

Thus the frequency as observed by the tree trunk due to Doppler effect=$f_0\left(\frac{v-0}{v-0.04v}\right)=\frac{f_0}{0.96}=f_1$

Sound of same frequency is reflected by the trunk which is observed by the bat.

Frequency as observed by bat=$f_1\left(\frac{v+0.04v}{v-0}\right)=1.04f_1=\frac{1.04}{0.96}{f}_0=61kHz$

$⟹f_0=56kHz$