Device that detect waves in a frequency range and beats

In summary, the problem involves using a device to measure the minimum beat frequency produced by a whistle while riding a bike away from a wall. The device can only measure frequencies in the range of 0.8 kHz to 20 kHz. The question asks for the velocity needed to produce this minimum beat frequency. There is confusion about whether the device measures the frequency of the wave or the beat frequency. It is assumed that the device measures the beat frequency and the question should be solved based on that assumption.
  • #1
Soren4
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Homework Statement


You have a device that can measure sound waves only if the frequency of the wave is in the range ##0.8 kHz- 20 kHz##. You have a whistle that produces sound waves at ##21.5kHz##. You ride a bike moving away from a wall, at the same time you blow the whistle and hold the device in your hand. What is the velocity you must have in order to make the device measure the minimum beat frequency that it can detect?

Homework Equations


Doppler effect and beats

The Attempt at a Solution


I premit I don't have any problem with the Doppler effect, the only problem here is to understand what to look for if I'm asked the "minimum beat frequency" that can be detected by the instrument. If ##f_1## is the frequency of the whistle and ##f_2## is the frequency modified by the reflection on the wall at a certain velocity, which condition between the following two is correct?
  • ##|f_2-f_1| > 0.8 kHz##
  • ##\frac{f_2+f_1}{2} <20kHz##
##|f_2-f_1| ## is the beat frequency, while ##\frac{f_2+f_1}{2}##, as explaied at https://en.wikipedia.org/wiki/Beat_(acoustics) , is the frequency of the wave resulting from the interference of the two.

Now, in my view, what really counts is ##\frac{f_2+f_1}{2}##, because that's the "real" frequency of the resulting wave, and I know that the device has a limitation on the frequency of the wave, but I'm not convinced about it. Which of the two would be correct, and (possibly) why?

Thanks a lot in advice
 
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  • #2
Soren4 said:
which condition between the following two is correct?
  • ##|f_2-f_1| > 0.8 kHz##
  • ##\frac{f_2+f_1}{2} <20kHz##
  • Good question. The problem states at first that the device measures the frequency of the wave, but later it states that the device will measure the beat frequency. My guess is that you are to assume the device detects the beat frequency since that is what it says at the end of the problem statement. Try working it out for both conditions and see if one of the conditions leads to an unrealistic speed for a bike.
 
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Related to Device that detect waves in a frequency range and beats

1. What is a device that detects waves in a frequency range and beats?

A device that detects waves in a frequency range and beats is a type of electronic instrument that measures the frequency and amplitude of waves in a specific range. It is commonly used in fields such as physics, engineering, and telecommunications to analyze and manipulate signals.

2. How does a device that detects waves in a frequency range and beats work?

This device works by receiving an input signal and then separating it into different frequency components. It then compares these components to a reference frequency to detect any beats or differences in frequency. The output of the device is typically a waveform that represents the frequency and amplitude of the input signal.

3. What are the applications of a device that detects waves in a frequency range and beats?

There are many applications for this type of device, including audio and radio equipment, radar systems, and medical imaging. It can also be used in scientific research to study natural phenomena such as seismic waves and electromagnetic radiation.

4. How accurate is a device that detects waves in a frequency range and beats?

The accuracy of this device depends on the specific model and its components. However, most modern devices have a high level of accuracy and can measure frequencies within a very small range. The accuracy can also be improved by calibrating the device regularly.

5. Are there any limitations to using a device that detects waves in a frequency range and beats?

Like any electronic device, there are limitations to consider when using a device that detects waves in a frequency range and beats. These can include factors such as signal interference, environmental conditions, and the sensitivity of the device. It is important to understand these limitations in order to accurately interpret the data provided by the device.

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