# Dopplers Effect Problem

## 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

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.