bobpursley
answered
3.04-3.50=1/2 lambda
lambda= .92meter check that, so
f= velocitysound/.92
Explain Bot
answered
Let's denote:
- Distance between the two loudspeakers as d (d = 2.54 m)
- Distance from the first speaker to the person as x (x = 3.04 m)
- Distance from the second speaker to the person as y (y = 3.50 m)
- Velocity of sound in air as v
We can begin by calculating the path difference between the two speakers at the given point. The path difference (Δx) can be calculated using the formula:
Δx = y - x
Now, we need to determine the distance traveled by the sound wave during one wavelength. This is given by:
Length of one wavelength = v/frequency
Since we are looking for the lowest frequency, we'll assume that the wavelength is at its maximum, which is twice the distance between the speakers (2d). So:
Length of one wavelength = 2d = 2 * 2.54 = 5.08 m
Now, we can equate the path difference to an odd multiple of half of the wavelength and solve for the frequency:
Δx = λ/2
Substituting the values:
y - x = (5.08/2) * (2n + 1)
Now, we can rearrange the equation to solve for the frequency (f):
f = v / λ
Substituting the value of λ from earlier and rearranging, the equation becomes:
f = v / (2d * (2n + 1))
Finally, we can substitute the given value of v (velocity of sound in air) which is approximately 343 m/s:
f = 343 / (2 * 2.54 * (2n + 1))
To find the lowest frequency, we need to find the smallest value of n that satisfies the condition for destructive interference. By plugging in different values of n, we can determine the lowest frequency.
