00:01
For this problem on the topic of waves and sound, we are told that the siren on an ambulance is emitting a sound wave with a frequency of 2 ,450 hertz.
00:11
We are also given the speed of sound on the day to be 343 meters per second.
00:16
Now we have three scenarios in which we want to calculate the wavelength of the sound and the frequency that is heard by the observer.
00:24
Firstly, if the ambulance is stationary and the observer is also stationary, secondly, if the ambulance is also stationary, ambulance is moving towards the observer at 26 .8 meters per second.
00:36
And lastly, if the ambulance is moving towards the observer at a speed of 26 .8 meters per second, and the observer is moving towards the ambulance as well, with the speed of 14 meters per second.
00:49
Now, the frequency of the sound is the same emitted by the siren in the first case, since there's no relative motion between the observer and the ambulance.
01:00
So the observed frequency, is equal to the source frequency, which is given as 2 ,450 hertz.
01:11
Now using this frequency, we can calculate the wavelength.
01:14
From the wave equation, the wavelength is simply the speed of sound divided by this frequency.
01:22
And so that's 343 meters per second divided by this frequency 2 ,450 hertz, which gives us the wavelength of 0 .14 meters.
01:42
The wavelength is also not shifted.
01:46
Now in part b, we will have a doppler effect occurring since the ambulance is moving towards the observer at 26 .8 meters per second.
01:55
So if we were to calculate a wavelength, we know the doppler -shifted wavelength lambda prime from the text we know is given to be the source wavelength lambda minus vs times t, where t is the period of the sound and vs at the speed of the source, which is the speed of the ambulance.
02:22
And this is lambda minus vs over the frequency of the source fs, since the period is one over the frequency...