Concept explainers
Two waves travel on the same string. Is it possible for them to have (a) different frequencies; (b) different wavelengths; (c) different speeds; (d) different amplitudes; (c) the same frequency but different wavelengths? Explain your reasoning.
(a)
Two waves travelling on the same string can have different frequencies or not.
Explanation of Solution
The frequency of the wave is the number of ups and down variation of wave from its mean position.
When two waves are travelling on the same string the waves get superimposed. The frequency of the waves depends upon the property of wave that can differ from one wave to another. So it is possible that two waves travelling on the same string can have different frequencies
Conclusion: Therefore, yes it is possible for two waves to have different frequencies of two waves that are travelling on the same string.
(b)
Two waves travelling on the same string can have different wavelengths or not.
Explanation of Solution
The wavelength is the measuring parameter of any radiation and light.
When two waves are travelling on the same string their wavelengths gets superimposed. The frequency of any wave describes the wavelength of the waves. At every unique frequency the wavelength of the spring is also unique. So any mechanical wave that is travelling on same string can have different wavelength.
Conclusion: Therefore, yes it is possible for two waves to have different wavelength of two waves that are travelling on the same string.
(c)
Two waves travelling on the same string can have different speed or not.
Explanation of Solution
The speed of any wave is the rate of travelling of wave from one medium to another.
When two waves are travelling on the same string the medium of propagation is same. For mechanical waves the product of frequency and wavelength is speed of the wave. That always has the same value for the same medium depending upon the mechanical property of the wave.
Conclusion: Therefore, no it is possible for two waves to have different speed of two waves that are travelling on the same string.
(d)
Two waves travelling on the same string can have different amplitudes or not.
Explanation of Solution
The amplitude of a wave is the maximum variation of the wave from its original position.
When two waves are travelling on the same string according to different mechanical properties of the string the amplitude of the waves also varies. That means two waves can have different displacements even though they are propagating in same string.
Conclusion: Therefore, yes it is possible for two waves to have different amplitudes of two waves that are travelling on the same string.
(e)
Two waves travelling on the same string can have same frequency but different wavelengths or not.
Explanation of Solution
The frequency of the wave is the number of ups and down variation of wave from its mean position and the wavelength is the measuring parameter of any radiation and light.
For any mechanical wave speed is the product of its frequency and wavelength. Since in the same propagating medium the speed cannot be changed so the product of frequency and wavelength will also be same. But for same frequency and different wavelength the product of two waves will not be same.
Conclusion: Therefore, no it is possible for two waves to have same frequency but different wavelengths that are travelling on the same string.
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