Two identical sources S1 and S2 are moving towards an observer P. The two sound sources S1 and S2 produce notes of frequency 500hz. If the speed of S1 and S2 are 20ms-1 and 23ms-1 respectively, calculate the beat frequency heard by P. (Speed of sound = 340ms-1)
I don't understand the questions well. Beat frequency formula is f1-f2. But if both produce the same frequency of 500hz, then won't I get 0? And how does velocity come into this question?
Fo = (340+Vo)/(340-Vs1)*Fs1.
Fo = (340+0)/(340-20) * 500 = 531.25 Hz.
= The freq. heard by the observer.
Fo = (340+0)/(340-23) * 500 = 536.28 Hz.
Fb = 536.28 - 531.25 = 5.028 Hz = Beat
freq.
Note: The Freq. of S1 and S2 are equal,
but their velocities are different. Therefore, the frequencies heard by the
observer are not equal. So the beat freq. is not zero.
f
In this scenario, the beat frequency refers to the frequency at which the amplitude of the sound waves heard by the observer fluctuates. It occurs when two sound waves of slightly different frequencies interfere with each other. The formula for calculating beat frequency is given by:
Beat Frequency (fbeat) = |f1 - f2|
Where f1 and f2 are the frequencies of the two sound sources.
Now, in this question, both sources S1 and S2 produce sounds of the same frequency, 500 Hz. However, the velocities of the sources relative to the observer P are given. The velocity of S1 is 20 m/s, and the velocity of S2 is 23 m/s.
To calculate the beat frequency, we need to consider the Doppler effect, which affects the perceived frequency of a sound wave due to the relative motion between the source and the observer.
The Doppler effect formula for sound waves can be expressed as:
f' = ((v + vo)/(v + vs)) × f
Where f' is the observed frequency, f is the actual frequency emitted by the source, v is the velocity of sound, vo is the velocity of the observer, and vs is the velocity of the source.
In this case, since the frequencies emitted by both sources are the same, we can calculate the beat frequency by applying the Doppler effect formula to each source separately and then subtracting the frequencies:
fbeat = |f'1 - f'2|
First, let's calculate the observed frequency from source S1:
f'1 = ((v + vo)/(v + vs1)) × f
Plugging in the values:
f'1 = ((340 + 0)/(340 + 20)) × 500
f'1 = 320 * 500 / 360
f'1 ≈ 444.44 Hz
Next, let's calculate the observed frequency from source S2:
f'2 = ((v + vo)/(v + vs2)) × f
Plugging in the values:
f'2 = ((340 + 0)/(340 + 23)) × 500
f'2 = 340 * 500 / 363
f'2 ≈ 469.25 Hz
Now, calculating the beat frequency:
fbeat = |f'1 - f'2|
fbeat = |444.44 - 469.25|
fbeat ≈ 24.81 Hz
Therefore, the beat frequency heard by the observer P is approximately 24.81 Hz.