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Two harmonic waves traveling on a string in the same direction both have a frequency of 100 Hz, a wavelenqth of 2.0cm, and amplitude of 0.020 m. In addition, they overlap each other. What is the amplitude of the resultant wave if the original waves differ in phase by Syntax error from line 1 column 49 to line 1 column 73. Unexpected ‘mathsize’./6?
- a)3.5 cm
- b)4.2 cm
- c)3.7 cm
- d)3.9 cm
Correct answer is option 'D'. Can you explain this answer?
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Two harmonic waves traveling on a string in the same direction both ha...
Question:
Two harmonic waves traveling on a string in the same direction both have a frequency of 100 Hz, a wavelength of 2.0 cm, and amplitude of 0.020 m. In addition, they overlap each other. What is the amplitude of the resultant wave if the original waves differ in phase by 6π?
Solution:
Given parameters:
Frequency of each wave = 100 Hz
Wavelength of each wave = 2.0 cm
Amplitude of each wave = 0.020 m
Phase difference between the waves = 6π
To find: Amplitude of the resultant wave
We know that the displacement of a wave is given by the equation:
y = A sin(kx - ωt + φ)
where, A = amplitude of the wave, k = wave number, x = position, ω = angular frequency, t = time, and φ = phase constant.
For two waves with the same frequency and wavelength traveling in the same direction, the wave number and angular frequency are the same, and the displacement equation becomes:
y1 = A sin(kx - ωt + φ1)
y2 = A sin(kx - ωt + φ2)
where, φ1 and φ2 are the phase constants of the two waves.
The resultant wave is obtained by adding the two waves:
y = y1 + y2
= A sin(kx - ωt + φ1) + A sin(kx - ωt + φ2)
= 2A cos((φ1 - φ2)/2) sin(kx - ωt + (φ1 + φ2)/2)
where, cos((φ1 - φ2)/2) is the amplitude of the resultant wave.
Given that the phase difference between the waves is 6π, we have:
φ1 - φ2 = 6π
cos((φ1 - φ2)/2) = cos(3π) = -1
Substituting the given values, we get:
Amplitude of the resultant wave = 2(0.020) (-1) = -0.040 m
However, amplitude is always positive, so we take the absolute value:
Amplitude of the resultant wave = 0.040 m
Therefore, the amplitude of the resultant wave is 0.040 m.
Two harmonic waves traveling on a string in the same direction both have a frequency of 100 Hz, a wavelength of 2.0 cm, and amplitude of 0.020 m. In addition, they overlap each other. What is the amplitude of the resultant wave if the original waves differ in phase by 6π?
Solution:
Given parameters:
Frequency of each wave = 100 Hz
Wavelength of each wave = 2.0 cm
Amplitude of each wave = 0.020 m
Phase difference between the waves = 6π
To find: Amplitude of the resultant wave
We know that the displacement of a wave is given by the equation:
y = A sin(kx - ωt + φ)
where, A = amplitude of the wave, k = wave number, x = position, ω = angular frequency, t = time, and φ = phase constant.
For two waves with the same frequency and wavelength traveling in the same direction, the wave number and angular frequency are the same, and the displacement equation becomes:
y1 = A sin(kx - ωt + φ1)
y2 = A sin(kx - ωt + φ2)
where, φ1 and φ2 are the phase constants of the two waves.
The resultant wave is obtained by adding the two waves:
y = y1 + y2
= A sin(kx - ωt + φ1) + A sin(kx - ωt + φ2)
= 2A cos((φ1 - φ2)/2) sin(kx - ωt + (φ1 + φ2)/2)
where, cos((φ1 - φ2)/2) is the amplitude of the resultant wave.
Given that the phase difference between the waves is 6π, we have:
φ1 - φ2 = 6π
cos((φ1 - φ2)/2) = cos(3π) = -1
Substituting the given values, we get:
Amplitude of the resultant wave = 2(0.020) (-1) = -0.040 m
However, amplitude is always positive, so we take the absolute value:
Amplitude of the resultant wave = 0.040 m
Therefore, the amplitude of the resultant wave is 0.040 m.
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Two harmonic waves traveling on a string in the same direction both have a frequency of 100 Hz, a wavelenqth of 2.0cm, and amplitude of 0.020 m. In addition, they overlap each other. What is the amplitude of the resultant wave if the original waves differ in phase by Syntax error from line 1 column 49 to line 1 column 73. Unexpected ‘mathsize’./6?a)3.5 cmb)4.2 cmc)3.7 cmd)3.9 cmCorrect answer is option 'D'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Two harmonic waves traveling on a string in the same direction both have a frequency of 100 Hz, a wavelenqth of 2.0cm, and amplitude of 0.020 m. In addition, they overlap each other. What is the amplitude of the resultant wave if the original waves differ in phase by Syntax error from line 1 column 49 to line 1 column 73. Unexpected ‘mathsize’./6?a)3.5 cmb)4.2 cmc)3.7 cmd)3.9 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two harmonic waves traveling on a string in the same direction both have a frequency of 100 Hz, a wavelenqth of 2.0cm, and amplitude of 0.020 m. In addition, they overlap each other. What is the amplitude of the resultant wave if the original waves differ in phase by Syntax error from line 1 column 49 to line 1 column 73. Unexpected ‘mathsize’./6?a)3.5 cmb)4.2 cmc)3.7 cmd)3.9 cmCorrect answer is option 'D'. Can you explain this answer?.
Two harmonic waves traveling on a string in the same direction both have a frequency of 100 Hz, a wavelenqth of 2.0cm, and amplitude of 0.020 m. In addition, they overlap each other. What is the amplitude of the resultant wave if the original waves differ in phase by Syntax error from line 1 column 49 to line 1 column 73. Unexpected ‘mathsize’./6?a)3.5 cmb)4.2 cmc)3.7 cmd)3.9 cmCorrect answer is option 'D'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Two harmonic waves traveling on a string in the same direction both have a frequency of 100 Hz, a wavelenqth of 2.0cm, and amplitude of 0.020 m. In addition, they overlap each other. What is the amplitude of the resultant wave if the original waves differ in phase by Syntax error from line 1 column 49 to line 1 column 73. Unexpected ‘mathsize’./6?a)3.5 cmb)4.2 cmc)3.7 cmd)3.9 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two harmonic waves traveling on a string in the same direction both have a frequency of 100 Hz, a wavelenqth of 2.0cm, and amplitude of 0.020 m. In addition, they overlap each other. What is the amplitude of the resultant wave if the original waves differ in phase by Syntax error from line 1 column 49 to line 1 column 73. Unexpected ‘mathsize’./6?a)3.5 cmb)4.2 cmc)3.7 cmd)3.9 cmCorrect answer is option 'D'. Can you explain this answer?.
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