Question

In: Physics

Moe, Larry, and Curly stand in a line with a spacing of d = 1.50 m...

Moe, Larry, and Curly stand in a line with a spacing of d = 1.50 m . Larry is 3.00 m in front of a pair of stereo speakers 0.800 m apart, as shown in the figure(Figure 1) . The speakers produce a single-frequency tone, vibrating in phase with each other.

What are the two lowest frequencies that allow Larry to hear a loud tone while Moe and Curly hear very little?

Express your answers using two significant figures separated by a comma. (kHz)

The answer is close ot .48, 1.499 but I keep getting it wrong

Expert Solution

if given that

distance between the curly and larry or moe and larry is d = 1.60 m

distance between observers and screen L = 3.00 m

a = 0.800 m

path difference for Lary is zero, so always constructiveinterference.
path difference for the other 2 is

Δ =√[L² + (d +a)²] - √[L² + (d - a)²]

=√[(3.0 m)^2 + (1.60m + 0.40 m)^2 -√[L²+ ( 1.60 - 0.40 m)²

= 0.3755 m

for distructive interfernce λ/2 or 3λ/2 are condition

path difference for small value Δ = λ/2

0.3755 m = λ/2

λ = 0.7511m

frequency f = v/λ

= 343 m/s/ 0.7511 m

= 456.66 Hz

for next value Δ = 3λ/2

0.3755 m = 3λ/2

λ = 0.250 m

frequency f = v/λ

= 343 m/s/0.250 m

= 1.372 kHz

genius_generous answered 2 years ago

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