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The frequency of the first harmonic of a standing wave on a string is $f_1$ - AQA - A-Level Physics - Question 19 - 2022 - Paper 1
Question 19
The frequency of the first harmonic of a standing wave on a string is $f_1$. The tension in the string is $T$. The tension is increased to $4T$ without changing ... show full transcript
Worked Solution & Example Answer:The frequency of the first harmonic of a standing wave on a string is $f_1$ - AQA - A-Level Physics - Question 19 - 2022 - Paper 1
Step 1
Identify the relationship between tension and frequency
Answer
The frequency of a harmonic of a string is given by the formula:
ho^{1/2}}$$ where: - $f_n$ is the frequency of the nth harmonic, - $L$ is the length of the string, - $T$ is the tension, - and $ ho$ is the mass per unit length of the string. When the tension is increased to $4T$, we can express the new frequency as: $$f_n' = n rac{1}{2L} imes rac{(4T)^{1/2}}{ ho^{1/2}} = n rac{1}{2L} imes 2T^{1/2} rac{1}{ ho^{1/2}} = 2 f_n$$Step 2
Determine which harmonic corresponds to $2f$
Answer
Since the new tension doubles the frequency, we consider the first harmonic where: f_1 = rac{1}{2L} imes T^{1/2} Under the new tension, the first harmonic frequency becomes: Thus, the harmonic that has a frequency equal to after the tension change is the second harmonic.