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Analyze the following questions and answer:
a) How is the speed of the wave affected if the mass decreases? Choose one to answer: increasing the mass has no effect on the speed of the wave, it increases, decreasing the mass is the only thing that affects the speed of the wave, it decreases
b) How does the wavelength vary with the linear mass density of the string? Choose one to answer: There is no variation, it varies directly proportional to the second power of the linear density, it varies inversely proportional to the square root of the linear density, it increases in the same proportion, it varies directly proportional to the square root of the linear density
c) How does the speed of the wave vary with the applied voltage (strain)? Choose one to answer: there is no variation, it increases in the same proportion, it varies inversely proportional to the square root of the voltage (strain), it varies directly proportional to the second power of the voltage (strain), it varies directly proportional to the square root of the voltage (strain)
Let's analyze each of the questions and provide a detailed explanation for each one, including a conclusion based on the principles of wave mechanics.
a) How is the speed of the wave affected if the mass decreases?
- Choose one to answer: increasing the mass has no effect on the speed of the wave, it increases, decreasing the mass is the only thing that affects the speed of the wave, it decreases.
Explanation: The speed of a wave on a string is determined by the tension in the string (T) and the linear mass density (μ) of the string material. The wave speed (v) is given by the equation:
v = √(T/μ)
Where:
- v = wave speed
- T = tension in the string
- μ = linear mass density of the string
From the equation, we can see that the wave speed is inversely proportional to the square root of the linear mass density (μ). Therefore, as the mass decreases, the linear mass density (μ) also decreases, and as a result, the speed of the wave increases. So, the correct answer is "it increases."
Conclusion: Decreasing the mass of the string affects the linear mass density (μ), and according to the wave speed equation, a decrease in mass results in an increase in wave speed.
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