Standing Waves: 2m, 1m, 4m, 1.5m, 67cm - Which Doesn't Fit?

In summary, Standing waves are a type of wave that occurs when two waves with the same frequency and amplitude travel in opposite directions and interfere with each other. They are formed when a wave reflects off a fixed boundary and combines with the original wave to create a pattern of constructive and destructive interference. The numbers in the given question represent the wavelengths of the standing waves, with each value representing the distance between two consecutive nodes or antinodes. However, the value of 67cm does not fit the pattern as it is not a multiple of the other values. Standing waves have many applications in science and engineering, including in musical instruments and understanding electromagnetic radiation.
  • #1
jan2905
41
0
If two of the wavelengths of standing waves on a 12m rope secured at both ends are 2m and 1m, which of the following COULD NOT be a standing wave wavelength on the same rope with the same tension?

4m, 2.5m, 1.5m, or 67cm.


2L/n=lamda



I said 2.5m because this does not give an natural number solution to the formula. Is this correct?
 
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  • #2
Correct. It would not be a fundamental evenly divisible into the length.
 
  • #3


Yes, that is correct. According to the formula for standing wave wavelength, the value of the wavelength should be a natural number, which means it should be a whole number greater than 0. 2.5m is not a natural number, so it cannot be a standing wave wavelength on the same rope with the same tension.
 

Related to Standing Waves: 2m, 1m, 4m, 1.5m, 67cm - Which Doesn't Fit?

1. What are standing waves?

Standing waves are a type of wave that occurs when two waves with the same frequency and amplitude travel in opposite directions and interfere with each other, causing a pattern of nodes and antinodes.

2. How are standing waves formed?

Standing waves are formed when a wave reflects off a fixed boundary, such as a wall or a string tied at one end, and combines with the original wave to create a pattern of constructive and destructive interference.

3. What do the numbers in the given question represent?

The numbers 2m, 1m, 4m, 1.5m, and 67cm represent the wavelengths of the standing waves. Each value represents the distance between two consecutive nodes or antinodes in the wave pattern.

4. Why doesn't one of the given values fit the pattern?

The wavelength of 67cm does not fit because it is not a multiple of the other values. In standing waves, the wavelengths must be multiples of each other to create a consistent pattern of nodes and antinodes.

5. What is the significance of standing waves?

Standing waves have many applications in science and engineering. They are used in musical instruments, such as stringed instruments and wind instruments, to produce specific frequencies and harmonics. They are also important in understanding electromagnetic radiation, such as radio waves and microwaves, and can be used to study the properties of materials.

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