A person places the speakers 4.0 m apart and connects a signal generator to both speakers that produces a single and consistent tone. (constant wavelength and frequency) He then walks to a point that is 2.0 m from one speaker and 2.3 m from the other. At that point he notices a quiet “spot”. If the speed of the sound in the room is known to be 350 m/s, calculate the possible frequencies being played by the speakers.
My Answer:
PD=2.3m-2m
PD=.3m
PD=(n-.5) λ, but λ=v/f
PD=(n-.5)(v/f)
.3=(n-.5)(350/f)
f=(n-.5)(350/.3)
f=(n-.5)(3500/3)
f=(3500n/3)-(3500/6)
f=(3500n/3)-(3500/6), where n is any real integer.
Is this right? Thanks for your help.
Yes, your calculations are correct. The formula PD = (n - 0.5)λ can be used to find the possible frequencies being played by the speakers given the distance between the quiet spot and the speakers, PD, and the speed of sound in the room, v. However, in order to find the frequencies, we need to substitute the wavelength in terms of frequency using the formula λ = v/f.
So, starting with PD = (n - 0.5)λ, we substitute λ = v/f:
PD = (n - 0.5)(v/f)
Rearranging the equation to solve for frequency (f):
f = (n - 0.5)(v/PD)
Substituting the given values PD = 0.3m and v = 350 m/s:
f = (n - 0.5)(350/0.3)
Simplifying further:
f = (3500n/3) - (3500/6)
Therefore, the possible frequencies being played by the speakers can be calculated using the equation f = (3500n/3) - (3500/6), where n is any real integer.