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Unformatted text preview: The Beat Heard by a Bat Description: Find the velocity of a bat that ﬂies toward a wall while emitting a high-frequency sound, given the beat frequency heard by the animal. A bat ﬂies toward a wall, emitting a steady sound of frequency 2.00 kHz. This bat hears its own sound plus the sound reﬂected by the wall. How fast should the bat ﬂy to hear a beat frequency of 10.0 Hz? Take the speed of sound to be 344 m/s. Express your answer numerically in meters per second to two signiﬁcant ﬁgures.
Because the bat is moving as he emits a frequency, the frequency will be shifted by the Doppler effect. The frequency the bat hears will be fbeat = | f1 − f2 | 10 = | 2000 − f2 | → f2 = 1950, 2010 Doppler eﬀect: f = fo v ± vo v vs
where f = observed frequency f = emitted frequency v = speed of sound vo = speed of observer vs = speed of observer How to chose signs: upper limits (+ on numerator, - in denominator) if source (observer) is moving towards the observer (source). Lower limits (- in numerator, + in denominator) if source (observer) is moving away from the observer (source). The bat is both observer and the source. So, let’s label vs = vo = vbat . Also, chose the upper limits in the doppler equation, since the reﬂected sound of the bat moves towards it. Then solving for vbat in the doppler equation: v + vbat v − vbat f (v − vbat ) = fo (v + vbat ) f = fo f v − f vbat = fo v + fo vbat fo vbat + f vbat = f v − fo v vbat (fo + f ) = v (f − fo ) v (f − fo ) → vbat = fo + f The observed frequency could be f = 1950 Hz or 2010 Hz to have a beat frequency of 10 Hz. However, physically, it has to be 2010 Hz, otherwise we would have a negative speed for the bat which is physically impossible. The emitted frequency fo = 2000 Hz, and the speed of sound vs = 344 m/s. Plugging in these values, we get the speed of the bat as: vbat = = v (f − fo ) fo + f 344(2010 − 2000) = 0.86 m/s 2000 + 2010 ...
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This note was uploaded on 04/09/2010 for the course PHYSICS 8A taught by Professor Jacobsen during the Spring '07 term at Berkeley.
- Spring '07