一條簡單的物理問題 - Ans.fyi 參考答案

一條簡單的物理問題

Tieria

2010-03-24 6:01 am

1. Two identical loudspeakers X and Y are connected in parallel to a signal generator. A microphone connected to a CRO detects a maximum when it is 0.2 m from X and 0.4 m from Y. It detects a minimum when it is 0.9 m from X and 0.4 m from Y. What is the possible wavelength of the sound wave?

The answer is 0.2 m.

2. The ratio of the masses of two bodies are a : b. When an equal amount of thermal energy is supplied to each of them, the ratio of their rises in temperature is b : a. What is the ratio of their specific heat capacities?

The answer is 1 : 1.

回答 (1)

天同

2010-03-25 12:03 am

✔ 最佳答案

1. At constructive interference, path difference = m.w
where w is the wavelength of the wave, and m is an integer

hence, (0.4 - 0.2) = m.w
i.e. 0.2 = m.w
hence, w can be 0.2 m (when m= 1), 0.1 m (when m = 2), or 0.0.067m (when m=3).... etc
But at destructive interference, path difference = (m-1/2).w
hence, (0.9 - 0.4) = (m-1/2).w
i.e. 0.5 = (m-1/2).w
or w = 0.5/(m-1/2)
hence, w can take the values of 1 m (when m=1), 0.333 m(m =2), 0.2 m (m = 3), or 0.143 m (m =4)....etc

You could see that the wavelength that satisfies both conditions as given in the question is 0.2 m
Therefore, the wavelength of the sound wave is 0.2 m

2. Let M(a) and M(b) be the masses of the two bodies,
C(a) and C(b) be the specific heat capacities, and
T(a) and T(b) be the rise of temperatures

Since the heat supplied to the two bodies are the same, we have
Heat supplied = M(a).C(a).T(a) = M(b).C(b).T(b)
C(a)/C(b) = [M(b)/M(a)].[T(b)/T(a)] = (b/a).(b/a) = 1
i.e. C(a)/C(b) = 1:1

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