Doppler effect for reflected sound waves from approaching truck

[GingerBread27]

A stationary motion detector sends sound waves of 0.700 MHz toward a truck approaching at a speed of 38.0 m/s. The speed of sound in the air is 343 m/s. What is the frequency of the waves reflected back to the detector?

I tried doing F=f((v+vo)/(v)), which becomes F=.7MHz((343+38)/(343)), and this gives the wrong answer. Then I realized that something should be doubled becomes the waves are reflected twice, from the detector to truck and then from the truck to the detector, so I just double the answer I got previously and this is wrong. What am i doing wrong?

 

[Andrew Mason]

A stationary motion detector sends sound waves of 0.700 MHz toward a truck approaching at a speed of 38.0 m/s. The speed of sound in the air is 343 m/s. What is the frequency of the waves reflected back to the detector?

Since the objects are approaching, you have to use: $$f_{apparent} = f_{source} \frac{v_{sound}}{v_{sound} - v_{source}}$$

You then have to apply it again using the $f_{apparent}$ as the source frequency. The difference is not exactly doubled in doing this.

AM

 

[wais]

It seems like you are on the right track with your calculations, but there may be a few things that are causing the discrepancy in your answer. First, make sure that you are converting all units to the same system (e.g. meters and seconds) before plugging them into the equation. Also, when calculating the frequency of the waves reflected back, you need to take into account the relative motion of the truck and the detector. This means that the frequency of the waves will be affected by the relative speed of the truck and the speed of sound.

To calculate the frequency of the waves reflected back to the detector, you can use the formula F = f((v + vo) / v), where f is the original frequency of the waves (0.700 MHz), v is the speed of sound in air (343 m/s), and vo is the speed of the truck (38 m/s). Using this formula, the frequency of the reflected waves would be approximately 0.821 MHz.

It is important to note that this calculation assumes that the truck is moving directly towards the detector, and that there are no other factors such as wind or other sources of sound interference. Also, keep in mind that this calculation only gives the frequency of the waves reflected back to the detector, and does not take into account any other factors such as the amplitude or intensity of the reflected waves.

In summary, make sure to double check your units and consider the relative motion of the truck and the detector when calculating the frequency of the reflected sound waves. If you are still getting a different answer, it may be helpful to double check your calculations or consult with a teacher or tutor for further assistance.