Standing waves are produced by the interference of two traveling sinusoidal waves, each of frequency 100 Hz.The distance from the 2nd node to the 5th node is 60 cm.The wavelength of each of the two original waves is:
A)50 cm
B)40 cm
C)30 cm
D)20 cm
E)15 cm

Question

Quizplus · Accepted Answer

In a standing wave, the distance between any two adjacent nodes or antinodes is equal to λ/2. 
So the distance between the 2nd and 5th nodes is equal to 3λ/2. 
We know that the frequency (f) of the wave is 100 Hz. 
The speed (v) of the wave can be calculated as:
v = f λ
We have two waves with the same frequency, so their wavelengths (λ1 and λ2) are equal. 
Therefore, the distance between the 2nd and 5th nodes can be expressed as:
3λ1/2 = 3λ2/2 = 3λ/2
Simplifying this expression, we get:
λ = (2/3) * (2nd node to 5th node distance) = (2/3) * 60 cm = 40 cm
So the wavelength of each of the two original waves is 40 cm. 
Therefore, the best choice is B) 40 cm.

Standing Waves Are Produced by the Interference of Two Traveling