Driven by the same amplifier system, two audio speakers are positioned some distance apart. A person is seated 6.0 m from one speaker and 6.4 m from the other. If the sound signal is continuously varied from 500 Hz to

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Quantrex Academy · Accepted Answer

Correct answer: D. 1200 Hz , 2000 Hz , 2800 Hz , 3600 Hz and 4400 Hz

The path difference between the sound waves reaching the listener is

\Delta x = 6.4 \text{ m} - 6.0 \text{ m} = 0.4 \text{ m}

.

For destructive interference, the path difference must be an odd multiple of half the wavelength:

\Delta x = (2n - 1) \dfrac{\lambda}{2}

where

n = 1, 2, 3, \dots

Using the relation

\lambda = \dfrac{v}{f}

, we get:

\Delta x = (2n - 1) \dfrac{v}{2f}

Substituting the given values

\Delta x = 0.4 \text{ m}

and

v = 320 \text{ m s}^{-1}

:

0.4 = (2n - 1) \dfrac{320}{2f}

f = \dfrac{160}{0.4} (2n - 1) = 400(2n - 1) \text{ Hz}

Substituting integer values for

n

:

For

n = 1

,

f = 400 \text{ Hz}

For

n = 2

,

f = 1200 \text{ Hz}

For

n = 3

,

f = 2000 \text{ Hz}

For

n = 4

,

f = 2800 \text{ Hz}

For

n = 5

,

f = 3600 \text{ Hz}

For

n = 6

,

f = 4400 \text{ Hz}

For

n = 7

,

f = 5200 \text{ Hz}

Since the frequency varies from

500 \text{ Hz}

to

5000 \text{ Hz}

, the frequencies producing destructive interference are

1200 \text{ Hz}

,

2000 \text{ Hz}

,

2800 \text{ Hz}

,

3600 \text{ Hz}

, and

4400 \text{ Hz}

.

Driven by the same amplifier system, two audio speakers are...

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