A person stands 6.00 m from a speaker, and 8.00 m from an identical speaker. What is the wavelength of the first (n=1) interference maximum (destructive)

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