Question

In a given period of time, 12,000 peaks of wave A and 15,000 peaks of wave B passed through the same medium under the same conditions. The wavelength A is 2 m. What is the wavelength of wave B?

Answer 1

To find the wavelength of wave B, we first need to find the frequency of wave B using the number of peaks that passed through the medium in a given period of time.

Let's first find the frequency of wave A:
Number of peaks of wave A = 12,000
Wavelength of wave A = 2 m

Frequency of wave A = Number of peaks / Time
Frequency of wave A = 12,000 / Time

Now, let's find the frequency of wave B:
Number of peaks of wave B = 15,000
Frequency of wave B = Number of peaks / Time
Frequency of wave B = 15,000 / Time

Since the frequency of both waves A and B are the same (as they are passing through the same medium under the same conditions), we can set the two frequency equations equal to each other:

12,000 / Time = 15,000 / Time

Solving for Time:
12,000 = 15,000
Time = 15,000 / 12,000
Time = 1.25

Now that we have the time period, we can find the wavelength of wave B:
Wavelength of wave B = Speed of wave B / Frequency of wave B

Since the speed of both waves A and B is assumed to be the same, we can substitute the values we found earlier to find the wavelength of wave B:

Wavelength of wave B = Speed / Frequency of wave B
Wavelength of wave B = 2 / 1.25
Wavelength of wave B = 1.6 m

Therefore, the wavelength of wave B is 1.6 meters.