Solution Found!
Answer: Two identical taut strings under the same tension
Chapter 16, Problem 57P(choose chapter or problem)
Problem 57P
Two identical taut strings under the same tension F produce a note of the same fundamental frequency f0. The tension in one of them is now increased by a very small amount ΔF. (a) If they are played together in their fundamental, show that the frequency of the beat produced is fbeat = f0 (ΔF/2F). (b) Two identical violin Strings, when in tune and stretched with the same tension, have a fundamental frequency of 440.0 Hz. one of the strings is retuned by increasing its tension. When this is done, 1.5 beats per second are heard when both strings are plucked simultaneously at their centers. By what percentage was the string tension changed?
Questions & Answers
QUESTION:
Problem 57P
Two identical taut strings under the same tension F produce a note of the same fundamental frequency f0. The tension in one of them is now increased by a very small amount ΔF. (a) If they are played together in their fundamental, show that the frequency of the beat produced is fbeat = f0 (ΔF/2F). (b) Two identical violin Strings, when in tune and stretched with the same tension, have a fundamental frequency of 440.0 Hz. one of the strings is retuned by increasing its tension. When this is done, 1.5 beats per second are heard when both strings are plucked simultaneously at their centers. By what percentage was the string tension changed?
ANSWER:Solution 57P
Step 1
The frequency of a string, f ∝
Where, F - tension on the string
The equation for the fundamental frequency, f0 ∝
Consider the tension has slightly increased. Then, the new frequency, f ’∝
Dividing both these equations.
f0 /f ’ = /