Question

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)

Answer 1

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