A bat is flying toward a cave wall. If it hears reflected sound of frequency $60.9 \mathrm{kHz}$, what is its flying speed, assuming it emits sound at $52.0 \mathrm{kHz}$ ? The speed of sound is $341.5 \mathrm{~m} / \mathrm{s}$.
A) $28.1 \mathrm{~m} / \mathrm{s}$
B) $26.9 \mathrm{~m} / \mathrm{s}$
C) $25.9 \mathrm{~m} / \mathrm{s}$
D) $49.9 \mathrm{~m} / \mathrm{s}$
E) $58.4 \mathrm{~m} / \mathrm{s}$

Question

Quizplus · Accepted Answer

The frequency shift observed by the bat is due to the Doppler effect. The formula to calculate the speed of the source (bat) when the source is moving towards the observer (the wall, in this case, acts as the observer when the sound reflects back to the bat) is given by $v_s = \frac{v(f - f_0)}{f_0}$, where $v_s$ is the speed of the source, $v$ is the speed of sound, $f$ is the observed frequency, and $f_0$ is the emitted frequency. Plugging in the given values: $v_s = \frac{341.5 \times (60.9 - 52.0)}{52.0}$, which calculates to approximately $26.9 \mathrm{~m/s}$.

A Bat Is Flying Toward a Cave Wall 60.9kHz60.9 \mathrm{kHz}60.9kHz , What Is Its Flying Speed, Assuming It Emits Sound

A Bat Is Flying Toward a Cave Wall $60.9 \mathrm{kHz}$ , What Is Its Flying Speed, Assuming It Emits Sound