Answer:
[tex]750\; {\rm m\cdot s^{-1}}[/tex].
Explanation:
The distance between two adjacent nodes of a standing wave is equal to one-half (that is, [tex](1/2)[/tex]) the wavelength of this wave.
Let [tex]\lambda[/tex] denote the wavelength of the standing wave in this question. The distance between two nodes of this wave is [tex]0.25\; {\rm m}[/tex], meaning that [tex](1/2)\, \lambda = 0.25\; {\rm m}[/tex]. Thus, [tex]\lambda = 2 \times 0.25\; {\rm m} = 0.50\; {\rm m}[/tex].
Given that [tex]f = 1500\; {\rm Hz}[/tex] is the frequency of the waves that formed this standing wave, the speed of these waves would be:
[tex]\begin{aligned}v &= \lambda\, f \\ &= 0.50\; {\rm m} \times 1500\; {\rm Hz} \\ &= 0.50\; {\rm m} \times 1500\; {\rm s^{-1}} \\ &= 750\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
