What is the correct frequency of the reflected ultrasound received by the bat?

In summary, the bat uses ultrasound at 40kHz to locate a stationary insect. However, when flying directly towards the insect at a speed of 4m/s, the bat receives the ultrasound reflections from the insect at a frequency of 41kHz, not 40.4kHz as initially calculated. This is because the formula used only accounts for the frequency in the frame of the insect, not in the frame of the bat.
  • #1
slaw155
41
0
A bat uses ultrasound at 40kHz to locate a stationary insect. If bat is flying directly towards the insect at speed of 4m/s at what frequency does the bat receive the ultrasound reflections from the insect? Speed of sound = 340m/s.

I went frequency = frequency of source x (velocity of wave+velocity of bat)/(velocity of wave)
So 40 = f x (340+4)/(340).
This however gives me the wrong answer of 40.4kHz compared to the textbook answer of frequency = 41kHz. Using any doppler formula rearrangement doesn't lead me to 41kHz, so what have I done wrong?
 
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  • #2
What you have computed is the frequency with which the insect is receiving the ultrasound and thus of the reflected sound in the frame of the indect. The bat is still moving toward the insect when it receives the sound.
 

1. What is the Doppler effect frequency?

The Doppler effect frequency is the perceived change in frequency of a sound wave or light wave as the source of the wave moves closer to or farther away from the observer. It is also referred to as the Doppler shift.

2. How does the Doppler effect frequency occur?

The Doppler effect frequency occurs because as the source of the wave moves closer, the waves are compressed and the frequency appears higher to the observer. Conversely, as the source moves farther away, the waves are stretched and the frequency appears lower to the observer.

3. What factors affect the Doppler effect frequency?

The Doppler effect frequency is affected by the relative motion between the source and the observer, the speed of the source, and the speed of the wave propagation. It can also be influenced by the medium through which the wave is traveling.

4. What are some everyday examples of the Doppler effect frequency?

The Doppler effect frequency can be observed in everyday life, such as when a siren of an emergency vehicle passes by and the pitch of the siren changes as it gets closer and farther away. It also occurs when a train passes by and the sound of its horn appears to change as it approaches and moves away.

5. How is the Doppler effect frequency used in scientific research and technology?

The Doppler effect frequency is utilized in several fields of science and technology, such as astronomy, where it is used to determine the movement and velocity of celestial objects. It is also used in medical imaging, weather radar, and in the study of fluid dynamics.

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