To solve this problem we will apply the concepts related to the Doppler effect. The Doppler effect is a physical phenomenon where an apparent change in wave frequency is presented by a sound source with respect to its observer when that same source is in motion. We will start by defining our values and apply the concept of the Doppler effect to the first two points according to the respective considerations. Finally we will find the beat frequency as the difference between these two values
Our values are given as,
[tex]f = 1011Hz[/tex]
[tex]u = 14m/s[/tex]
[tex]v = 332m/s[/tex]
Part a ) The frequency heard by a stationary observer from a moving source is defined as,
[tex]f_1 = \frac{f_sv}{u+v}[/tex]
Here
[tex]f_1 =[/tex] Frequency heard by a stationary observer from a moving source
v = Speed of sound in given medium
u = Velocity of separation of the observer and source of the sound
[tex]f_1 = \frac{(1011)(332)}{14+332}[/tex]
[tex]f_1 = 970.09Hz[/tex]
The frequency heard by a stationary observer from a moving source is 970.09Hz
PART B) The frequency of the sound you heard reflected off the cliff is defined as,
[tex]f_2 = \frac{f_sv}{u+v}[/tex]
Here we will replace the value of the speed as negative because the direction seen from this perspective is the opposite, then
[tex]f_1 = \frac{(1011)(332)}{-14+332}[/tex]
[tex]f_1 = 1055.50Hz[/tex]
PART C) The beat frequency between the two sounds defined as,
[tex]f_b = f_2 -f_1[/tex]
[tex]f_b = 1055.50Hz - 970.09 Hz[/tex]
[tex]f_b = 84.61Hz[/tex]
Therefore the beat frequency between the two sounds is 84.61Hz
