1) Two speakers separated by a distance of 4.45 m emit sound. The speakers have

ID: 1389771 • Letter: 1

Question

1) Two speakers separated by a distance of 4.45

m emit sound. The speakers have opposite phase. A person listens from a location 2.95m directly in front of one of the speakers

What is the lowest frequency that gives destructive interference in this case?

2) Identical cellos are being tested. One is producing a fundamental frequency of 137.9

Hz on a string that is 1.00m long and has a mass of 109 g. On the second cello the same string is fingered to reduce the length that can vibrate.

If the beat frequency produced by these two strings is 4.03

Hzwhat is the vibrating length of the second string?

As they initiall have opposite phase, then for destructive interference,

The path difference is

PD = sqrt(2.95^2 + 4.45^2) - 4.45 m = 0.889 m

0.889 m = n *wavelength

where n is an integer.

If n = 1,

wavelength = 0.889 m

which makes

f = v / wavelength = 386 Hz [ANSWER]

I used 343 m/s for speed of sound.

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