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standing wave

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(See attached files for full problem descriptions)
1.
a. What are the three longest wavelengths for standing waves on a 240 cm long string that is fixed at both ends?
b. If the frequency of the second longest wavelength is 50 Hz, what is the frequency of the third longest wavelength?

2. A sheet of glass is coated with 500 nm thick layer of oil (n = 1.42).
a. for what visible wavelengths of light do the reflected waves interfere constructively?
b. for what visible wavelengths of light do the reflected waves interfere destructively?
c. what is the color of the reflected light and transmitted light?

3. You are standing 2.5 m directly in front of one the two loud speakers shown in Figure. They are 3.0 m apart and both are playing a 686 Hz tone in phase. As you begin to walk from away from the speaker, at what distances from the speaker do you hear a minimum sound intensity. The room temperature is 20 C.

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Dear Student,
Please see the solution to your problem in the attached word file
'Solution_Sound_Waves_&_Interference_Problems.doc'. a 10 ...

Solution Summary

It shows how to find the three longest wavelengths for standing waves on a string. It also helps to understand the interference of the waves by working out two examples.

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Standing wave as sum of wave traveling to left and right

See attached file for full problem description.

9.2 Show that the standing wave f(z,t) = Asin(kz)cos(kvt) satisfies the wave equation, and express it as the sum of a wave travelling to the left and a wave traveling to the right as shown in the following equation:
F(z,t) = g(z -vt) + h(z + vt)

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