A closed organ pipe 150 cm long gives 7 beats per second with an open organ pipe of length 350 cm, both vibrating in fundamental mode. The velocity of sound is _____ m s$$^{-1}$$.

Closed organ pipe of length $$L_1 = 150$$ cm = 1.5 m. Fundamental frequency: $$f_1 = \frac{v}{4L_1} = \frac{v}{6}$$.

Open organ pipe of length $$L_2 = 350$$ cm = 3.5 m. Fundamental frequency: $$f_2 = \frac{v}{2L_2} = \frac{v}{7}$$.

Number of beats = $$|f_1 - f_2| = 7$$.

$$\left|\frac{v}{6} - \frac{v}{7}\right| = 7$$

$$\frac{v}{42} = 7$$

$$v = 294$$ m/s

The answer is $$\boxed{294}$$ m/s.