In a given period of time, 12,000 peaks of wave A and 15,000 peaks of wave B pass through the same medium under the same conditions. The wavelength of wave A is 2 m. What is the wavelength of wave B?
To find the wavelength of wave B, we first need to find the frequency of wave B using the information given.
Let's start by calculating the frequency of wave A using the formula:
\( \text{Frequency} = \dfrac{\text{Number of peaks}}{\text{Time}} \)
For wave A:
Number of peaks = 12000
Time = 1 period
Frequency of wave A = \( \dfrac{12000}{1} = 12000 \) peaks per period
Now, since both waves pass through the same medium under the same conditions, we can assume that the frequency of wave B is the same as wave A. Therefore, the frequency of wave B is also 12000 peaks per period.
Now, we can calculate the wavelength of wave B using the formula:
\( \text{Wavelength} = \dfrac{\text{Wave speed}}{\text{Frequency}} \)
Given that the wave speed is the same for both waves, we can find the wavelength of wave B:
For wave A:
Wavelength = 2 m
For wave B:
Wavelength = \( \dfrac{2}{12000} \) m
Wavelength of wave B = \( \dfrac{1}{6000} \) m = 0.0001667 meters or 0.167 mm