Two sources of sound S1 and S2 produce sound waves of the same frequency 660 Hz. A listener is moving from source S1 towards S2 with a constant speed u m/s, and he hears 10 beats/s. The velocity of sound is 330 m/s. Then, u equals:

Let f be the frequency of the sound waves emitted by both sources S1 and S2. f = 660 Hz.
Let v be the velocity of sound. v = 330 m/s.
Let u be the velocity of the listener moving from S1 towards S2.
The listener hears 10 beats per second. This means the difference in frequencies perceived by the listener from the two sources is 10 Hz.
The frequency perceived by the listener from source S1 (f1) is given by the Doppler effect formula:
f1 = f * (v - u) / (v)
The frequency perceived by the listener from source S2 (f2) is given by the Doppler effect formula:
f2 = f * (v + u) / (v)
The beat frequency is the absolute difference between f1 and f2:
|f1 - f2| = 10 Hz
Substituting the expressions for f1 and f2:
|f * (v - u) / v - f * (v + u) / v| = 10
|f(v - u - v - u) / v| = 10
|-2fu / v| = 10
Since frequency and velocity are positive, we can remove the absolute value and solve for u:
2fu / v = 10
u = 10v / (2f)
u = 5v / f
Substituting the given values:
u = 5 * 330 m/s / 660 Hz
u = 1650 m/s / 660 Hz
u = 2.5 m/s
Therefore, the velocity of the listener (u) is 2.5 m/s.