Answer:
351 m/s
Explanation:
Given information
Distance between speakers, d= 4 m
Distance between listener and speaker, l= 5 m
Distance moved by the speaker, r= 60 cm = 0.6 m
Frequency, f= 700 Hz
[tex]r_1=\sqrt {(d/2)^{2}+l^{2}}=\sqrt{(4/2)^{2}+5^{2}}=\sqrt{29}\approx 5.385 m[/tex]
[tex]r_2=\sqrt {(r+d/2)^{2}+l^{2}}=\sqrt {(0.6+4/2)^{2}+5^{2}}\approx 5.636 m[/tex]
The path difference between two sound waves reaching the listener is half the integral of wavelength for destructive interference to happen hence
[tex]r_2-r_1=\frac {\lambda}{2}[/tex]
[tex]5.636-5.385=\frac {\lambda}{2}[/tex]
[tex]\lambda= 0.502[/tex]
Speed of sound, [tex]v=f\lambda= 700 Hz \times 0.502 m= 351 m/s[/tex]
