Question

A standing wave is produced by a wave y1 = (2.50 cm)cos(4.40 cm−1)x − (2.33 s−1)t  ...

A standing wave is produced by a wave

y1 = (2.50 cm)cos(4.40 cm−1)x − (2.33 s−1)t  

moving to the right, and a wave

y2 = (2.50 cm)cos(4.40 cm−1)x + (2.33 s−1)t  

moving to the left. What is the smallest value on the positive x axis for which the maximum transverse displacement of the standing wave is equal to 2.50 cm
?

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Homework Answers

Answer #1

The maximum transverse displacement of the standing wave occurs at antinode position. At the two endpoint the nodes are formed. Hence, the smallest distance on the positive x- axes for which the the maximum transverse displacement of the standing wave is equal to 2.50 cm, will be equal to one quarter of wavelength of standing wave.

If you compare the equation of standing wave to the given equation in this problem, you can obtain the value of wavelength.

where, is the wavelength and T is the time period and A is the amplitude. Comparing the given equation, you can write

Therefore, the answer will be

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