Answer:
wavelength = 4 m
Explanation:
For distance 6 and 8m and speed of sound in air = c.
The travel time form the various distances 6 and 8 are 6/c and 8/c respectively.
cos(wt1) + cos(wt2) = 0
for a shift in phase t1 = t - 6/c,
t2 = t - 8/c
substituting t1 and t2
cos(π - w(t - 8/c)) = cos(w(t - 6/c))
solving using trigonometry identities in radians.
we have,
π - 2πn = w(t - 8/c) - w(t - 6/c)
putting w = 2πf
π - 2πn = 2πf(t - 8/c) - 2πf(t - 6/c)
dividing both sides by π
1 - 2n = 2ft - 16(f/c) - 2ft + 12(f/c)
simplifying we have,
1 - 2n = -4(f/c)
solving for f we have,
f = c/4(2n - 1)
putting n=1 and c = 343m/s
f = (343/4)*(2(1) - 1)
f = 85.75 Hertz
wave lenght = c/f , where c= speed of sound in air , f= frequency
wave lenght = 343/85.75 = 4m
