**Unformatted text preview: **Physics 7 C Quiz 2 First Name Last Name ID Section Two speakers playing sinusoidal tones with the same unknown frequency f are placed 8 meters apart, as shown in the ﬁgure below. When he stands midway between the two speakers, Ali ﬁnds that he hears almost no sound. a). 8m Speaker 1 Speaker 2 I—I
4m What is the ﬁxed phase constant difference Adm = ¢1 — $2 between the waves emitted by the two speakers? (Note:
there are multiple possible correct answers; please give only one.) Since Ali hears almost no sound, we know that the point midway between the two speakers must be a point of
destructive interference, and therefore that AfI) must equal an old multiple of 7r. Since Ali is midway between the two
speakers, Arr: = 0, and we can conclude the only source of phase difference is Aqﬁ, which must therefore also be an odd
multiple of 71'. Hence Aqﬁo = 7r is a possible correct answer. . Ali now walks three meters to the right (i.e., towards speaker 2). As he walks, he hears the sound of the two speakers ﬁrst get louder, than get quieter, and then get louder again, so that, after he has walked the three meters, he is at a
point of constructive interference. If the speed of sound in air is 340 m/s, what is the frequency of the sinusoidal tone
being played by the two speakers? We begin by noting that the Aqho contribution to Ad) is the same here as in part A (that is, A450 2 $1 — ¢2 = 7r).
However, at the point where Ali stops walking, Ax = :61 — 3:2 2 6 In, so we now have a contribution to A<I> from the
A1: term. (Notice that A1: = 6 In and not 3 In because every meter Ali moves towards speaker 2 takes him one meter
farther from speaker 1.) Since Ali heard the sound of the speaker grow louder, then quieter, then louder again as he
walked, this implies that the change in phase difference from the start to the end of his journey is 371' (i.e., one and a
half full cycles). Hence, if the total phase difference (in the convention <I>1 — (1)2) was 7r in part A, it is now —27r at
the point where Ali stops walking. (Notice that we subtract rather than add, the 37r, because the phase contribution
from the A3: term is negative for waves emanating off of sources). We can thus write down the following equation for
A<I> at the point where Ali stops walking 6
[email protected]=—27r=—27r( in)+7r=>3)\=12m=>)\=4m (5)
To ﬁnd the frequency, we now apply the equation 11 = A f for the case where A = 4 m and v = 340 m/s
1) 340 m/s Fun facts: 1) = Af, f = %, y(:1:,t) = Asin (21% :: 271'; +¢0) +y0, D—DO = 1010g10 (1—10), Io< A2, A3: = dsinﬂ = n)\ ...

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- Fall '08
- MAHMUD
- Physics, Wavelength, Ali, phase difference