# Dopplers Effect Problem

• ron_jay
In summary, the conversation is discussing the calculation of wavelength and frequency of a sound wave emitted by a car moving towards a cliff, as well as the beat frequency heard by a person in the car. The second question involves the reflection of a sound signal off a moving car and the calculation of its speed. There seems to be a discrepancy in the answer for part d, with the book giving a different answer than the calculation suggests. The method used to solve the problem seems correct, so there may be an error in the calculations or the answer in the book.

## Homework Statement

1. A car moves with a speed of 54km/h towards a cliff.The horn of the car emits a frequency of 400Hz at a speed of 335m/s
(a)Find the wavelength of the sound emitted by the horn in front of the car
(b)Find the wavelength of the wave reflected from the cliff
(c)What frequency does a person sitting in the car hear for the reflected sound wave?
(d)How many beats does he hear in 10 secs between the sound coming directly from the horn and that coming after reflection?

2. An operator sitting in his base camp sends a sound signal of frequency 400Hz. The signal is reflected back from a car moving towards him . The frequency of the reflected sound is found to be 410 Hz. Find the speed of the car when the speed of sound in air is 324m/s.

## Homework Equations

Doppler's Effect equations.

## The Attempt at a Solution

I had no problem in finding out the a,b,c but have a problem in finding out part d.The answer says that there would be no beat frequency heard...how could that be when it is receiving two distinct frequencies (source, reflection)

In the second question, the answer is 12m/s, but i got it as 3m/s...how is that?

What I would do is find the beat frequency, then use that frequency to find out the number of cycles in that particular time interval.

Beat frequency=|F1-F2|

f=number of cycles/time interval

ron_jay said:
In the second question, the answer is 12m/s, but i got it as 3m/s...how is that?

Sorry for not having the answer but if you get the wrong answer it would be quiet useful to write down your calculations so people trying to help you can see what you did wrong. :)

Frequency of reflected wave:

$$\nu'=\nu (\frac{v+v_{L}}{v})$$

Now, the source and listener interchange as the sound wave is reflected:(as received back by operator)

$$\nu''=\nu'(\frac{v}{v-v_{L}})$$

$$\nu''=410 Hz$$

$$\nu=400 Hz$$

Plugging in the values we get 3m/s solving for v_l

*Is there something wrong with the concept?
OR
*Is there something wrong with the calculation?

You can always check your calculation by subsituting V_L = 3 m/s into it.
if you do that you'll notice your answer is too small, but the answer in the book is much too large. Maybe you've been rounding your intermediate results too much? I don't know why the book gets it wrong. Your method is OK.

## 1. What is the Doppler Effect?

The Doppler Effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. It is commonly observed in sound waves, such as the change in pitch of a siren as an ambulance passes by.

## 2. How does the Doppler Effect work?

The Doppler Effect occurs because the motion of the observer or the source causes the wave to be compressed or stretched. If the observer is moving towards the source, the frequency of the wave will appear higher, and if the observer is moving away from the source, the frequency will appear lower.

## 3. What are some real-life applications of the Doppler Effect?

The Doppler Effect has many practical applications, including its use in weather forecasting to track the movement of storms, in medical ultrasound technology, and in radar systems used for navigation and tracking objects.

## 4. How is the Doppler Effect related to redshift and blueshift?

Redshift and blueshift are both caused by the Doppler Effect. When an object is moving away from an observer, its light is redshifted, meaning the wavelength appears longer. Conversely, when an object is moving towards an observer, its light is blueshifted, meaning the wavelength appears shorter.

## 5. Can the Doppler Effect be observed in all types of waves?

Yes, the Doppler Effect can be observed in all types of waves, including sound waves, light waves, and other electromagnetic waves. However, the amount of shift in frequency or wavelength may vary depending on the speed of the observer or the source.

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