Question
Hey any help would be great
The figure to the right shows a tube in which a speaker creates a sound wave. The sound wave splits, one wave traveling through the bottom portion and on wave traveling through the top rectangular portion, for which L can be adjusted. The microphone detects maximum in intensity (the sound is "loudest") when L is 24 cm, 32 cm, and 40 cm, and no locations in between. What is the frequency of the sound wave emitted from the speaker? (Hint: This is a problem in sound interference. Think about what the path length difference between the waves must be in order to product maxima in intensity, and how this path length difference is created in this problem.) The figure to the right shows the intensity pattern produced on a screen by two narrow slits (the width is smaller than the wavelength of light) separated by a distance of 0.50 mm. The wavelength of light is 633 nm. Draw on the blank graph what you would expect the intensity pattern to look like if the right slit is covered up. Explain why this new pattern looks the way it does. If the spacing between the m = 0 and m = 1 maximum is 7.5 mm, what is the distance between the screen and the slits? What is the path length difference for the two waves created by the slits at the location of the m = 4 bright fringe? What is the phase difference between the waves when they reach the location of the m = 4 bright fringe?
Explanation / Answer
1.The L values are L1 = 24 cm,L2 = 32 cm and L3 = 40 cm(1 cm = 1 * 10^-2 m)
The frequency of the sound wave is
f = (v/L)
where v = 340 m/s
2.The slits are separated by d = 0.50 mm = 0.50 * 10^-3 m
The wavelength of light is lamda = 633 nm = 633 * 10^-9 m
when the right slit is covered up,the intensity pattern is like a cosine wave with one half below the negative x-axis.
3.Let D be the distance between the screen and the slits
we know that
B = (lamda * D/d)
where B = 7.5 mm = 7.5 * 10^-3 m
or D = (B * d/lamda)
4.The path length difference between the waves is (lamda/4)
5.The phase difference between the waves is pi radians.