Answer:
the frequency of the beats is 8.7687 kHz
Explanation:
Given the data in the question;
The frequency for stationary source and moving observer is;
f' = f( 1 +( v_observer/v_sound))
we know that, speed of sound in dry air = 343 m/s
so we substitute
f' = 41.2 kHz( 1 + (33.0 m/s / 343 m/s) ) = 41.2kHz( 1 + 0.0962) = 41.2kHz(1.0962)
f' = 45.1634 kHz
Now the frequency for stationary observer and moving source with frequency f' will be
f" = f'( 1 / (1 - ( v_observer/v_sound)))
45.1634 kHz( 343 / 343 - 33)
we substitute
f" = 45.1634 kHz( 1 / (1 - (33.0 m/s / 343 m/s)))
f" = 45.1634 kHz( 1 / (1 - 0.0962))
f" = 45.1634 kHz( 1 / 0.9038 )
f" = 45.1634 kHz( 1.1064 )
f" = 49.9687 kHz
Now the beat frequency will be;
f_beat = f' - f
we substitute
f_beat = 49.9687 kHz - 41.2 kHz
f_beat = 8.7687 kHz
Therefore, the frequency of the beats is 8.7687 kHz
